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This work reviews theoretical–experimental studies undertaken at COPPE/UFRJ on conjugated heat transfer problems associated with the transient thermal behavior of heated aeronautical Pitot tubes and wing sections with anti-icing systems. One of the main objectives is to demonstrate the importance of accounting for the conduction–convection conjugation in more complex models that attempt to predict the thermal behavior of the anti-icing system under adverse atmospheric conditions. The experimental analysis includes flight tests validation of a Pitot tube thermal behavior with the military aircraft A4 Skyhawk (Brazilian Navy) and wind tunnel runs (INMETRO and NIDF/COPPE/UFRJ, both in Brazil), including the measurement of spatial and temporal variations of surface temperatures along the probe through infrared thermography. The theoretical analysis first involves the proposition of an improved lumped-differential model for heat conduction along a Pitot probe, approximating the radial temperature gradients within the metallic and ceramic (electrical insulator) walls. The convective heat transfer problem in the external fluid is solved using the boundary layer equations for compressible flow, applying the Illingsworth variables transformation considering a locally similar flow. The nonlinear partial differential equations are solved using the Generalized Integral
Transform Technique in the Mathematica platform. In addition, a fully local differential conjugated problem model was proposed, including both the dynamic and thermal boundary layer equations for laminar, transitional, and turbulent flow, coupled to the heat conduction equation at the sensor or wing section walls. With the aid of a single-domain reformulation of the problem, which is rewritten as one set of equations for the whole spatial domain, through space variable physical properties and coefficients, the GITT is again invoked to provide hybrid numerical–analytical solutions to the velocity and temperature fields within both the fluid and solid regions. Then, a modified Messinger model is adopted to predict ice formation on either wing sections or Pitot tubes, which allows for critical comparisons between the simulation and the actual thermal response of the sensor or structure. Finally, an inverse heat transfer problem is formulated aimed at estimating the heat transfer coefficient at the leading edge of Pitot tubes, in order to detect ice accretion, and estimating the relative air speed in the lack of a reliable dynamic pressure reading. Due to the intrinsic dynamical behavior of the present inverse problem, it is solved within the Bayesian framework by using particle filter.

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... Within this field of research, because of the mentioned importance regarding correct velocity measurements, icing specifically in aeronautical pitot tubes has attracted attention in the recent years, as presented in Fig. 3. It can also be distinguished different lines of research that include ice detection [8,[15][16][17][18][19][20][21][22][23][24][25], numerical simulation [26][27][28][29][30][31][32], review or reports containing PT icing [3,6,[33][34][35] and experimentation [36,37]. Despite increasing attempts, the experimental research dedicated to experimentation of aeronautical PT icing is quite limited. ...

... As Pitot tubes are commercially traded in the aircraft industry, for public research institutions it can be rather difficult to obtain detailed information on composition and performance directly from the manufacturer. Therefore, the discovery of dangerously underperforming designs on the market is very rare and normally taken out "postmortem", as done by Ref. [28], who predicted the icing of the "Thales AA" model Pitot tubes installed on the unlucky AF 447 Airbus very precisely by means of numerical simulation. ...

... PIV is a technique to visualize flow patterns in fluids that is nonintrusive, which is its major advantage on Pitot tube characterization as it was done by Refs. [27,28]. The principle is based on the optical determination of the displacement of flow tracer particles in known time intervals. ...

The correct measurement of airspeed is a crucial task since a lot of algorithms for the autopilot are based on it and even human pilots depend completely on this reading to take corrective and non-corrective actions to control the aircraft. This work presents a detailed review concerning an important aspect of aeronautical safety, i.e., Pitot Tube (PT) icing. The topics covered include first the risks present in flight, relating meteorological conditions, and antecedents of air accidents related to the icing of the PT. Then, the principles of operation of the PT, its conventional design, how such design is currently regulated, as well as unique guidance for experimentation of PT. Also discussed are the principal modelling considerations for the numerical analysis of PTs including the proper selection of geometry, governing equations, turbulence models, and boundary conditions for the simulation of different flight circumstances. This guidance for both experimental and numerical analysis is enriched with a well-selected state the art research. Finally, a summary of the most recent advances and future trends is offered. The outcomes of this review exhibit several interesting ideas showing promising results, such as microwave heating of the pitot surroundings, phase change materials that delay ice formation, and even mechanical internal arrangement of bulkheads to prevent the ice to travel through the throat of the probe. The combined research efforts on novel safety measures and new designs for aeronautical PT represent a remarkable potential to improve flight security.

... The geometry of the tube was optimised with numerical simulations using CFD, then the flow co-efficients were obtained as a function of Re. Souza et al. (12) worked theoretically and experimentally on transient thermal behaviour of heated aeronautical PP and wing sections with anti-icing systems. A model is adopted to predict ice formation on wing sections and Pitot tubes, for both incompressible and compressible flow. ...

... There is very little information available on the composition and performance of commercial PPs. In addition, in order to validate a mathematical model, which predicts the thermal behaviour of a PP under regular operating conditions or its behaviour in case of a heating failure during flight (12)(13)(14) , the data gathered in this work will be required. A variety of experiments and tests were conducted in order to obtain such data. ...

... At high Re, flow heating by solid-fluid interactions are no longer negligible. Therefore, term 4 considers pressure work Q p and viscous dissipation heating Q vd : (12) where Q gen represents the volumetric joule heating of the EHE, which is located in the solid domain: The time-dependent power consumption Power(t) was experimentally obtained (Section 5) for the respective test condition. For the solid domains where heat transfer occurs by conduction only, just terms 1, 3 and 4 need to be solved. ...

Aeronautic Pitot probes (PPs) are extremely important for airspeed and altitude measurements in aviation. Failure of the instrument due to clogging caused by ice formation can lead to dangerous situations. In this work, a commercial aeronautic PP was characterised experimentally regarding its inner composition, material properties and its thermal performance in a climatic wind tunnel. Performance runs were taken out in order to analyse the thermal response of the PP under various operating conditions with a particular emphasis on the cooling process in the case of a heating element failure. Data for the thermal conductivity, diffusivity and specific heat for each material forming the PP were obtained. A numerical model to simulate the thermal behaviour of the PP was created using Comsol Multiphysics (CM). Experimental data were compared with their numerical counterparts for model validation purposes. After the model was validated, the operation of the PP in flight conditions was simulated. The failure of the conventional heating system was analysed to obtain the time until the PP reaches a tip temperature where ice formation can be expected. The tip temperature undercut the zero degrees Celsius mark 165 seconds after the heating element was switched off. The data collected in this work can be used to implement and validate mathematical models in order to predict the thermal performance of Pitot probes in flight conditions.

... While developing and applying such general purpose algorithm, the need for a number of computational improvements and additional theoretical developments became more evident and led to some recent advances on the GITT methodology [15][16][17][18][19][20][21][22][23][24][25][26], which are here consolidated. Among such recent advancements, one may point out the single domain reformulation strategy for complex geometries, the integral balance approach for convergence enhancement of problems with multiscale or abruptly varying coefficients, the proposition of convective eigenvalue problems for formulations with significant convective effects, and the direct use of nonlinear eigenvalue problems in the integral transformation process of nonlinear PDEs [15][16][17][18][19][20][21][22][23][24][25][26]. ...

... While developing and applying such general purpose algorithm, the need for a number of computational improvements and additional theoretical developments became more evident and led to some recent advances on the GITT methodology [15][16][17][18][19][20][21][22][23][24][25][26], which are here consolidated. Among such recent advancements, one may point out the single domain reformulation strategy for complex geometries, the integral balance approach for convergence enhancement of problems with multiscale or abruptly varying coefficients, the proposition of convective eigenvalue problems for formulations with significant convective effects, and the direct use of nonlinear eigenvalue problems in the integral transformation process of nonlinear PDEs [15][16][17][18][19][20][21][22][23][24][25][26]. All the methodological variants here discussed are aimed at the enrichment of the eigenfunction expansion basis, towards increasing the amount of information from the original formulation that is carried into the eigenvalue problem and then recovered at any spatial position by the corresponding eigenfunctions. ...

... The idea in the single domain formulation is to avoid either approach, and proceed to interpret problem (11) as one single convection-diffusion problem written for a heterogeneous media [29]. This alternative has been recently proposed, in the context of conjugated heat transfer problems [15][16][17][18][19][20][21], when fluid and solid regions were treated as a heterogeneous single medium, after defining space variable coefficients for the whole domain, that account for the abrupt variations of thermophysical properties and other coefficients, through the solid-fluid transitions. Figure 1 provides two possibilities for representation of the single domain, either by keeping the external borders of the original overall domain, after definition of the space variable coefficients, as shown in Fig. 1b, or, if desired, by considering a regular overall domain contour that envelopes the original one, as shown in Fig. 1c. ...

An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on this well-established hybrid numerical-analytical methodology for partial differential equations. Special emphasis is given to novel algorithm implementations, all directly connected to enhancing the eigenfunction expansion basis, such as a single domain reformulation strategy for handling complex geometries, an integral balance scheme in dealing with multiscale problems, the adoption of convective eigenvalue problems in formulations with significant convection effects, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Then, selected examples are presented that illustrate the improvement achieved in each class of extension, in terms of convergence acceleration and accuracy gain, which are related to conjugated heat transfer in complex or multiscale microchannel-substrate geometries, multidimensional Burgers equation model, and diffusive metal extraction through polymeric hollow fiber membranes. Numerical results are reported for each application and, where appropriate, critically compared against the traditional GITT scheme without convergence enhancement schemes and commercial or dedicated purely numerical approaches.

... In recent years, there has been an effort to consolidate this knowledge on the GITT into a general purpose open source algorithm, known as the UNIT (UNified Integral Transforms) algorithm [11][12][13][14]. Such a demand, together with fairly recent application challenges [15][16][17][18][19][20][21][22][23][24], have induced the proposition of novel computational schemes and theoretical extensions, that have not yet been presented in a systematic form, as here attempted. Among such recent advancements, one may point out the proposition of progressive filtering for multidimensional problems [13][14], the implementation of reordering schemes via multiple criteria [13][14], the single domain reformulation strategy for complex geometries [15][16][17][18][19], the solution of coupled nonlinear reactive flow systems [20], the integral balance approach for convergence enhancement of multiscale problems [21][22], the proposition of convective eigenvalue problems for highly convective formulations [23], and the direct use of nonlinear eigenvalue problems in the integral transformation process of nonlinear PDEs [24]. ...

... Such a demand, together with fairly recent application challenges [15][16][17][18][19][20][21][22][23][24], have induced the proposition of novel computational schemes and theoretical extensions, that have not yet been presented in a systematic form, as here attempted. Among such recent advancements, one may point out the proposition of progressive filtering for multidimensional problems [13][14], the implementation of reordering schemes via multiple criteria [13][14], the single domain reformulation strategy for complex geometries [15][16][17][18][19], the solution of coupled nonlinear reactive flow systems [20], the integral balance approach for convergence enhancement of multiscale problems [21][22], the proposition of convective eigenvalue problems for highly convective formulations [23], and the direct use of nonlinear eigenvalue problems in the integral transformation process of nonlinear PDEs [24]. Before incorporating such developments into a general purpose algorithm, it is of interest to compile and link these ideas, so as to permit a continuous unification effort, as here discussed. ...

... Problem (18) allows for the definition of the following integral transform pair: ...

This lecture offers an updated review on the Generalized Integral Transform Technique (GITT), with focus on handling complex geometries, coupled problems, and nonlinear convection-diffusion, so as to illustrate some new application paradigms. Special emphasis is given to demonstrating novel developments, such as a single domain reformulation strategy that simplifies the treatment of complex geometries, an integral balance scheme in handling multiscale problems, the adoption of convective eigenvalue problems in dealing with strongly convective formulations, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Representative application examples are then provided that employ recent extensions on the Generalized Integral Transform Technique (GITT), and a few numerical results are reported to illustrate the convergence characteristics of the proposed eigenfunction expansions.

... Recent developments in the GITT extended its applicability to complex configurations, once solvable essentially by purely numerical approaches. The so-called single domain formulation strategy allows for a more straightforward treatment of models involving heterogeneous media and complex geometries by the introduction of abruptly spatially varying physical properties and source terms [31][32][33][34][35][36][37]. Then, the associated eigenvalue problem carries the information on the space variable coefficients, which account for the transition at the various interfaces between different materials or geometric regions. ...

... (14a-g) in terms of elementary functions, the GITT itself is employed as a hybrid solution methodology. This strategy has already been successfully applied in previous works, including those that adopt the single domain formulation [31][32][33][34][35][36][37]. To proceed with the GITT formalism in the solution of Eqs. ...

An analysis of natural convection within a rectangular cavity partially filled with a heat-generating porous medium is carried out through the Generalized Integral Transform Technique (GITT), in which the laminar flow and energy equations are solved with automatic error control. A single domain reformulation strategy is adopted to rewrite the governing equations within the fluid and the porous medium as a single heterogeneous medium formulation, with spatially variable physical properties and source terms that account for the abrupt transition of the two regions. This fundamental study is motivated by the analysis of wet storage of spent nuclear fuel elements with passive cooling of the pool and physical conclusions are drawn from the hybrid numerical-analytical solution. Increases in the Rayleigh number with constant internal heat generation are found to lower the maximum temperature within the cavity. Moreover, decreasing the aspect ratio also has positive effects on the cooling of the cavity.

... The geometry of the tube was optimized with numerical simulations using CFD and then the flow coefficients are obtained as a function of Re. Souza et al. [12], worked theoretical and experimentally on transient thermal behavior of heated aeronautical PP and wing sections with anti-icing systems. A model is adopted to predict ice formation on wing sections and Pitot tubes, for both incompressible and compressible flow. ...

... From the above summary, it is notorious that most work development on pitot probes do not focus on aeronautical pitot probes. In addition, in order to develop mathematical models, which predict the thermal behavior of a PP under regular operating conditions or its behavior in case of a heating failure during flight ( [13], [12,14]), the data gathered in this work will be required. In addition, such models will need a proper validation. ...

In this work, the cool-down and ice accumulation on an aeronautic Pitot probe (PP) in case of a heating element failure was studied experimentally in a climatic wind tunnel (CWT). Through injector nozzles located in front of the test section, atomized water was introduced into the tunnel in order to simulate the presence of humidity found in different cloud types. Using high-resolution cameras, the subsequent ice accumulation along the PP was recorded. The experiment runs were taken out under three different conditions, controlling the air temperature, flow velocity and liquid water content (LWC) in the test section. The flow conditions in the CWT have dynamic similarity with those encountered at cruise speeds of common single-engined propeller aircraft. Analyzing the indicated pressure measured through the PP's pressure ports, it was possible to correlate the (cone-shaped) ice accumulation on the stagnation pressure port to the measurement error for one test condition. For the other two test conditions, it was observed that the ice cone's lateral section grew so fast, that it did not allow the blockage of the stagnation port, keeping it in contact with the atmosphere and thus performing correctly.

... In social production and life, certain parts of equipment and machinery are exposed to icy weather conditions. Moreover, ice accumulation is prone to occur as one of the major hidden dangers affecting the safety of aviation [1], navigation [2], rail transit [3], and power [4]. For example, accreted ice of the aircraft damages the maneuverability, safety, and stability of the aircraft and leads to the tragedy of aircraft destruction and human death in severe cases [5]. ...

Ice detection is an important issue in the field of icing prevention and de-icing. In this study, an experimental platform was built for ice detection using flash pulse infrared thermal wave detection, followed by a quantitative recognition approach for identifying the three-dimensional shape of ice. The new method was combined the edge recognition with thickness calculation of inverse heat transfer problem. And the edge of the ice was based on the Principal Component Analysis (PCA) and the Canny algorithm. Thus, by processing the ice edges and giving an initial thickness, the finite element model of the ice was established to numerically simulate the temperature distribution for ice thickness inversion based on the forward heat transfer problem. Meanwhile, the thickness of the ice was inversed by the Levenberg-Marquardt (LM) method based on the inverse heat transfer problem. The resulting edges and thickness of the ice were found to be in good agreement with the experimental results, demonstrating the feasibility of the proposed methods. This paves the way to explore an effective accurate and quantitative identification method for three-dimensional ice shape detection in infrared thermal wave detection.

... Combined research of aircraft icing and pitot tubes is not very frequent in the literature. The work developed by Souza et al. [15], worked theoretical and experimentally on transient thermal behavior of heated aeronautical PP and wing sections with anti-icing systems. A model is adopted to predict ice formation on wing sections and Pitot tubes, for both incompressible and compressible flow. ...

The aim of this work is the design of a pitot probe (PP) prototype in order to retard the cool down of the tip, in case of a heating element failure. The viability of operation in flight conditions is evaluated. The design consists of a redundant heating system incorporating phase change materials (PCM). Combining experimental observations of ice formation with the implementation of the conjugate heat transfer (CHT) model, with the addition of the heat release due to the phase change of the PCM, the numerical evaluation is developed. The modelling assumptions and numerical implementation of the phase change process are presented. Then, the selection an appropriate PCM is based on the low flammability and volume dilation and the quantitative effects of the material properties on the heat transfer. A commercial PCM solution based on salt hydrates was chosen as the most adequate for the design. The parametric design of the prototype, based on the design of experiment method and fractional factorial testing, is established. A multiple linear regression model was obtained in order to maximize the cooling retardation. The numerical simulations demonstrate that the prototype PP tip temperature remains 194 s longer above 0 °C than that of the conventional model analyzed.

... Recently, Knupp et al. [14] proposed a single-domain formulation strategy in combination with the Generalized Integral Transform Technique (GITT). This methodology allows for heterogeneous multi-region problems to be written as single-domain formulations by making use of spatially variable coefficients with abrupt transitions occurring at the interfaces and was successfully employed in the solution of different conjugated heat transfer problems [21][22][23][24][25]. This strategy was then improved in order to deal with conjugated conduction-convection heat transfer for incompressible laminar gas flow in microchannels, within the range of validity of the slip flow regime, in which velocity slip and temperature jump at the wall play a major role in heat transfer. ...

In this work, it is proposed the direct and inverse analyses of the forced convection of an incompressible gas flow within rectangular channels in the range of the slip flow regime by taking into account the wall conjugation and the axial conduction effects.
The Generalized Integral Transform Technique (GITT) combined with the single-domain reformulation strategy is employed in the direct problem solution of the three-dimensional steady forced convection formulation.
A non-classical eigenvalue problem that automatically accounts for the longitudinal diffusion operator is here proposed. The Bayesian framework implemented with the maximum a posteriori objective function is used in the formulation of the inverse problem, whose main objective is to estimate the temperature jump coefficient, the velocity slip coefficient, and the Biot number, using only external temperature measurements, as obtained, for instance, with an infrared measurement system. A comprehensive numerical investigation of possible experimental setups is performed in order to verify the influence of the Biot number, wall thickness, and Knudsen number on the precision of the unknown parameters estimation.

... In addition, the last section deals with lumpeddifferential formulations, when full or partial lumping of the partial differential heat conduction equation can lead to significant simplification of the problem to be mathematically solved. Special emphasis is given to an improved lumpeddifferential formulation methodology, known as the Coupled Integral Equations Approach (CIEA) (Mennig and Özişik 1985;Aparecido et al. 1989;Cotta et al. 1990;Scofano Neto and Cotta 1993;Traiano et al. 1997;Cheroto et al. 1997;Corrêa and Cotta 1998;Cotta 1998;Alves et al. 2000;Regis et al. 2000;Reis et al. 2000;Su 2001;Su and Cotta 2001;Cotta et al. 2003;Su 2004;Ruperti et al. 2004;Dantas et al. 2007;Pontedeiro et al. 2008;Su et al. 2009;Tan et al. 2009;Naveira et al. 2009;Naveira-Cotta et al. 2010;da Silva and Sphaier 2010;An and Su 2011;Knupp et al. 2012;Sphaier and Jurumenha 2012;An and Su 2013;De Souza et al. 2015;An and Su 2015;Moreira et al. 2015;de Souza et al. 2016). This approach is based on integral equations for the temperature and heat flux averaged over one or more space variables, combined with approximate Hermite formulas for integration, to offer improved accuracy, but at the same level of complexity, with respect to the classical lumped analysis procedure. ...

In this chapter, mathematical formulations of macroscopic heat conduction are derived from the First Law of Thermodynamics. Specific forms of the heat conduction equation in isotropic media are given in Cartesian, Cylindrical, and Spherical coordinates systems, as well as in a general orthogonal coordinate system. Heat conduction equations in anisotropic media and in heterogeneous media are then derived. Mathematical formulations of one-dimensional transient heat conduction with phase change and in multilayered composite media are presented. Finally, classical and improved lumped parameter formulations for transient heat conduction problems are analyzed more closely. The so-called Coupled Integral Equations Approach (CIEA) is reviewed as a problem reformulation and simplification tool in heat and mass diffusion. The averaged temperature and heat flux, in one or more space coordinates, are approximated by Hermite formulae for integrals, yielding analytic relations between boundary and average temperatures, to be used in place of the usual plain equality assumed in the classical lumped system analysis. The accuracy gains achieved through the improved lumped-differential formulations are then illustrated through a few typical examples. © Springer International Publishing AG, part of Springer Nature 2018. All rights reserved.

An experimental study was conducted to characterize the dynamic ice accretion process over the surface of a typical aeronautic Pitot probe model under different icing conditions. The experimental study was conducted in the Icing Research Tunnel available at Iowa State University. While a high-speed imaging system was used to record the dynamic ice accretion process, a three-dimensional (3D) scanning system was also used to measure the 3D shapes of the ice layers accreted on the test model. While opaque and grainy ice structures were found to accrete mainly along the wedge-shaped lip of the front port and over the front surface of the probe holder under a dry rime icing condition, much more complicated ice structures with transparent and glazy appearance were observed to cover almost entire surface of the Pitot probe under a wet glaze icing condition. While a flower-like ice structure was found to grow rapidly along the front port lip, multiple irregular-shaped ice structures accreted over the probe holder under a mixed icing condition. The characteristics of the icing process under different icing conditions were compared in terms of 3D shapes of the ice structures, the profiles of the accreted ice layers, the ice blockage to the front port, and the total ice mass on the Pitot probe model. The acquired ice accretion images were correlated with the 3D ice shape measurements to elucidate the underlying icing physics.

The present work analyzes a coupled nonlinear mathematical model for heat transfer in compressible laminar flow within a parallel plates channel. The governing partial differential equations are obtained considering the conservation of mass, momentum and energy, based on a two-dimensional steady laminar flow of an ideal gas with constant physical properties and taking into account viscous dissipation. Two kinds of boundary conditions at the wall were considered, namely, prescribed arbitrary temperature or heat flux longitudinal distributions. The mathematical model was solved using the hybrid numerical-analytical method known as the Generalized Integral Transform Technique (GITT). A convergence analysis of the proposed eigenfunction expansions for velocity and temperature fields was undertaken, indicating that fairly low truncation orders are required for the accurate representation of the potentials. The proposed hybrid solution was also critically compared with the Mathematica NDSolve finite difference-based routine and additional theoretical and experimental results in the literature, with good agreement in all cases considered.

Purpose
The purpose of this paper is to identify freezing in pitot tubes at real-time, by means of the estimated heat transfer coefficient (HTC) at the tip of the probe. The prompt identification of such freezing is paramount to activate and control mechanisms for ice removal, which in turn are essential for the safety of the aircraft and its passengers.
Design/methodology/approach
The proposed problem is solved by means of an inverse analysis, performed within the Bayesian approach of inverse problems, with temperature measurements assumed available along the pitot probe over time. A heat conduction model is used for describing the average temperature of the pitot tube, which is then rewritten in the form of a state estimation problem. The model is linear and time invariant, so that the inverse problem can be solved using the steady-state Kalman filter (SSKF), a computationally efficient algorithm.
Findings
The results show that the SSKF is fully capable of recovering the HTC information from the temperature measurements. Any variation of the HTC – either smooth or discontinuous – is promptly detected with high accuracy. Computational effort is significantly lower than the physical time, so that the proposed methodology is fully capable of estimating the HTC at real-time.
Originality/value
The methodology herein solves the proposed problem not only by estimating the HTC accurately but also doing so with a very small computational effort, so that real-time estimation and freezing control become possible. To the best of the authors’ knowledge, no likewise publications have been found so far.

The injection of CO2 into oil reservoirs is used by the oil and gas industry for enhanced oil recovery (EOR) and/or the reduction of environmental impact. The compression systems used for this task work with CO2 in supercritical conditions, and the equipment used is energy intensive. The application of an optimization procedure designed to find the optimum operating conditions leads to reduced energy consumption, lower exergy destruction, and reduced CO2 emissions. First, this work presents two thermodynamic models to estimate the amount of power necessary for a multi-stage CO2 compression system in floating production storage and offloading (FPSO) using accurate polytropic relationships and equations of state. Second, a thermodynamic analysis using the first and second laws of thermodynamics is conducted to identify possible improvements in energy consumption and the sources of the compression unit’s irreversibilities. In the final step, optimization procedures, using two methods with different approaches, are implemented to minimize the total power consumption. As the number of stages and the pressure drop between them influence the total power required by the compressors, these are considered as the input parameters used to obtain the inlet pressure at each stage. Three different compositions with variations in CO2 content, i.e., pure CO2, pure \({\mathrm{CH}}_{4}\), and 70% CO2 + 30% \({\mathrm{CH}}_{4}\), are also investigated as three different operating scenarios. The optimal configurations and pressure ratios result in a reduction in power consumption of up to 9.65%, mitigation of CO2 emissions by up to 1.95 t/h, and savings in exergy loss of up to 23.9%, when compared with conventional operating conditions.

Vessels that have navigation routes in areas with ambient temperatures that can drop below + 5 [°C], with a relative humidity of over 65%, will have implemented technical solutions for monitoring and combating ice accumulations in the intake routes of gas turbine power plants. Because gas turbines are not designed and built to allow the admission of foreign objects (in this case - ice), it is necessary to avoid the accumulation of ice through anti-icing systems and not to melt ice through defrost systems. Naval anti-icing systems may have as a source of energy flow compressed air, supersaturated steam, exhaust gases, electricity or a combination of those listed. The monitoring and optimization of the operation of the anti-icing system gives the gas turbine power plant an operation as close as possible to the normal regimes stipulated in the ship's construction or retrofit specification.

This work presents an application of an exact analytical approach to estimate the temperature field of solid-state electronics (SSE). A partial lumped approach in the chip’s height was performed, obtaining a two-dimensional mathematical model. The internal heat generation (HG) regions caused by Joule effect due to internal components were modeled as Gaussian functions, and the classical integral transform technique (CITT) was used to solve the problem. The developed formulation was applied in three illustrative HG layouts for chips. In addition, the finite difference method was also implemented for verification and comparison purposes. The CITT provided fast computing and accurate results with small truncation orders in problems with multiple non-uniform heated regions. Furthermore, the formulation presented in this work may be applied to any SSE internal HGs layout, being a useful tool for thermal assessment of SSEs.

It is very difficult to remove ice accreting on some miniature aircraft components with irregular surfaces such as flight sensors, increasing the risk of serious flight accidents. However, few existing anti-icing/de-icing systems can be fabricated on such complex surfaces. In this study, a novel sandwich structural electric heating coating (SEHC) is proposed to solve this problem. An intermediate heating layer was coated between the upper and lower electrode layers in SEHC for heating on complex surfaces. The heating layer was prepared by adding multi-wall carbon nanotubes (MWCNTs) into a polyurethane matrix. The SEHC with 2% MWCNTs weight fraction showed the best electric heating properties. The electric heating uniformity mechanism of SEHC was explained by establishing the resistance model and simulation analysis. Moreover, apart from the high efficiency of anti-icing/de-icing ability, SEHC exhibited excellent electric heating properties, including timely response, repeatability, and reliability towards coating damage. In addition, the synthetic strategy of combined SEHC with super-hydrophobic coating demonstrates more efficient anti-icing/de-icing property. Thus the SEHC concept provides a potential application of anti-icing/de-icing for the miniature complex components, due to its advances in fabricating convenience, damage resistance as well as anti-icing/de-icing functions.

Purpose
The purpose of this work is to revisit the integral transform solution of transient natural convection in differentially heated cavities considering a novel vector eigenfunction expansion for handling the Navier-Stokes equations on the primitive variables formulation.
Design/methodology/approach
The proposed expansion base automatically satisfies the continuity equation and, upon integral transformation, eliminates the pressure field and reduces the momentum conservation equations to a single set of ordinary differential equations for the transformed time-variable potentials. The resulting eigenvalue problem for the velocity field expansion is readily solved by the integral transform method itself, while a traditional Sturm–Liouville base is chosen for expanding the temperature field. The coupled transformed initial value problem is numerically solved with a well-established solver based on a backward differentiation scheme.
Findings
A thorough convergence analysis is undertaken, in terms of truncation orders of the expansions for the vector eigenfunction and for the velocity and temperature fields. Finally, numerical results for selected quantities are critically compared to available benchmarks in both steady and transient states, and the overall physical behavior of the transient solution is examined for further verification.
Originality/value
A novel vector eigenfunction expansion is proposed for the integral transform solution of the Navier–Stokes equations in transient regime. The new physically inspired eigenvalue problem with the associated integmaral transformation fully shares the advantages of the previously obtained integral transform solutions based on the streamfunction-only formulation of the Navier–Stokes equations, while offering a direct and formal extension to three-dimensional flows.

A novel strategy to improve the mass transport performance in membraneless redox flow batteries (MRFB) is proposed, based on a symmetrical sinusoidal wall corrugation of the solid electrodes. The continuity, Navier–Stokes, and mass transport equations are solved with a hybrid analytical-numerical method known as the Generalized Integral Transform Technique (GITT). The effects of the Reynolds number and the amplitude of the corrugation are analyzed. The corrugated MRFBs are shown to be more suitable for higher Reynolds number applications, still within the laminar flow regime, when crossover is a less limiting factor. For smaller Reynolds numbers, the crossover is shown to offset the gains in reactant conversion with the introduction of the corrugation. In addition, the benefits in terms of limiting current density with corrugated RFBs are mainly associated with the increase in reactive area with its use.

A generalized and systematic approach is presented to the analytic solution of seven different classes of linear heat and mass diffusion problems. After the basic general equations are set forth, they are solved foe a wide range of applications. In many cases, solutions are presented graphically. The first 4 chapters provide a unified solutions.The remaining chapters are devoted to many applications from science and engineering.

A mathematical model was developed to both describe an airfoil electrothermal anti-ice system operation and enable prediction of its main parameters. A reference case was chosen to define the mathematical model and support the results validation. The first law of thermodynamics is applied to airfoil solid surface and runback water flow. In addition, liquid water is subjected to mass and momentum conservation principles. The overall heat transfer coefficient, between gaseous flow and airfoil, is very sensitive to solid surface temperature gradients and runback water evaporation, requiring an adequate solution of the thermal boundary layer. Therefore, the mathematical model included dynamic and thermal boundary layer equations in integral form, which considers variable properties, pressure, and temperature gradients on the surface, coupled heat and mass transfer effects, and laminar to turbulent transition region modeling.

Energy conservation and sustainable development demands have been driving research efforts, within the scope of thermal engineering,
towards more energy efficient equipments and processes. In this context, the scale reduction in mechanical fabrication has
been permitting the miniaturization of thermal devices, such as in the case of micro-heat exchangers [1]. More recently, heat
exchangers employing micro-channels with characteristic dimensions below 500 μm have been calling the attention of researchers
and practitioners, towards applications that require high heat removal demands and/or space and weight limitations [2]. Recent
review works [2, 3] have pointed out discrepancies between experimental results and classical cor-relation predictions of
heat transfer coefficients in micro-channels. Such deviations have been stimulating theoretical research efforts towards a
better agreement between experiments and simulations, through the incorporation of different effects that are either typically
present in micro-scale heat transfer or are effects that are normally disregarded at the macro-scale and might have been erroneously
not accounted for in micro-channels. Our own research effort was first related to the fundamental analysis of forced convection
within micro-channels with and without slip flow, as required for the design of micro-heat exchangers in steady, periodic
and transient regimen [4, 5]. Also recently in Refs. [6–11], the analytical contributions were directed towards more general
problem formulations, including viscous dissipation, axial diffusion in the fluid and three-dimensional flow geometries. Then,
this fundamental research was extended to include the effects of axial fluid heat conduction and wall corrugation or roughness
on heat transfer enhancement [12]. The work of Maranzana et al. [13] further motivated the present analysis, dealing with
longitudinal wall heat conduction effects in symmetric micro-channels.

This paper analyses the recently suggested particle approach to filtering time series. We suggest that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution. Both problems are tackled in this paper. We believe we have largely solved the first problem and have reduced the order of magnitude of the second. In addition we introduce the idea of stratification into the particle filter which allows us to perform on-line Bayesian calculations about the parameters which index the models and maximum likelihood estimation. The new methods are illustrated by using a stochastic volatility model and a time series model of angles. Some key words: Filtering, Markov chain Monte Carlo, Particle filter, Simulation, SIR, State space. 1 1

Kernel density estimation techniques are used to smooth simulated samples from importance sampling function approximations to posterior distributions, resulting in revised approximations that are mixtures of standard parametric forms, usually multivariate normal or T‐distributions. Adaptive refinement of such mixture approximations involves repeating this process to home‐in successively on the posterior. In fairly low dimensional problems, this provides a general and automatic method of approximating posteriors by mixtures, so that marginal densities and other summaries may be easily computed. This is discussed and illustrated, with comment on variations and extensions suited to sequential Bayesian updating of Monte Carlo approximations, an area in which existing and alternative numerical methods are difficult to apply.

The purpose of this work is to propose a simple combined model for the thermal analysis of Pitot probes that includes conjugated heat transfer and a modified Messinger ice formation formulation, in order to describe ice accretion in electrically heated aeronautical Pitot tubes. The proposed lumped-differential model is solved by making use of the Method of Lines as implemented in the routine NDSolve, from the numerical-symbolic computational system Mathematica v.9.0. It is then illustrated the importance of considering the heat transfer within the probe structure, that accounts for heat conduction along the probe and the thermal capacitance of its internal elements, in adequately predicting the ice formation on the stagnation and tip regions. Solutions are provided for actual adverse atmospheric conditions, extracted from a recently proposed certification envelope for Pitot probes.

This work advances a hybrid integral transforms methodology for the solution of conjugated heat transfer problems involving the thermal interaction between a solid wall and an external flow. A single domain formulation strategy is employed, coupling the two regions (solid and fluid) by accounting for the transition of the materials through space variable thermophysical properties and source terms with abrupt variations at the interface. The resulting energy equation is solved using a hybrid numerical-analytical technique known as the Generalized Integral Transform Technique (GITT). Illustrative results of the converged eigenfunction expansions for the temperature field are presented, for the test case of a flat plate subjected to an internal uniform heat generation.

The present work advances a recently introduced approach based on combining the Generalized Integral Transform Technique (GITT) and a single domain reformulation strategy, aimed at providing hybrid numerical–analytical solutions to convection–diffusion problems in complex physical configurations and irregular geometries. The methodology has been previously considered in the analysis of conjugated conduction–convection heat transfer problems, simultaneously modeling the heat transfer phenomena at both the fluid streams and the channels walls, by making use of coefficients represented as space variable functions with abrupt transitions occurring at the fluid–wall interfaces. The present work is aimed at extending this methodology to deal with both fluid flow and conjugated heat transfer within arbitrarily shaped channels and complex multichannel configurations, so that the solution of a cumbersome system of coupled partial differential equations defined for each individual sub-domain of the problem is avoided, with the proposition of the single-domain formulation. The reformulated problem is integral transformed through the adoption of eigenvalue problems containing the space variable coefficients, which provide the basis of the eigenfunction expansions and are responsible for recovering the transitional behavior among the different regions in the original formulation. For demonstration purposes, an application is first considered consisting of a microchannel with an irregular cross-section shape, representing a typical channel micro-fabricated through laser ablation, in which heat and fluid flow are investigated, taking into account the conjugation with the polymeric substrate. Then, a complex configuration consisting of multiple irregularly shaped channels is more closely analyzed, in order to illustrate the flexibility and robustness of the advanced hybrid approach. In both cases, the convergence behavior of the proposed expansions is presented and critical comparisons against purely numerical approaches are provided.

An extension of a recently proposed single domain formulation of conjugated conduction-convection heat transfer problems is presented, taking into account the axial diffusion effects at both the walls and fluid regions, which are often of relevance in microchannels flows. The single domain formulation simultaneously models the heat transfer phenomena at both the fluid stream and the channel walls, by making use of coefficients represented as space variable functions, with abrupt transitions occurring at the fluid-wall interface. The generalized integral transform technique (GITT) is then employed in the hybrid numerical-analytical solution of the resulting convection-diffusion problem with variable coefficients. With axial diffusion included in the formulation, a nonclassical eigenvalue problem may be preferred in the solution procedure, which is itself handled with the GITT. To allow for critical comparisons against the results obtained by means of this alternative solution path, we have also proposed a more direct solution involving a pseudotransient term, but with the aid of a classical Sturm-Liouville eigenvalue problem. The fully converged results confirm the adequacy of this single domain approach in handling conjugated heat transfer problems in microchannels, when axial diffusion effects must be accounted for.

The theory and algorithm behind the open-source mixed symbolic-numerical computational code named UNIT (unified integral transforms) are described. The UNIT code provides a computational environment for finding solutions of linear and nonlinear partial differential systems via integral transforms. The algorithm is based on the well-established analytical-numerical methodology known as the generalized integral transform technique (GITT), together with the mixed symbolic-numerical computational environment provided by the Mathematica system (version 7.0 and up). This paper is aimed at presenting a partial transformation scheme option in the solution of transient convective-diffusive problems, which allows the user to choose a space variable not to be integral transformed. This approach is shown to be useful in situations when one chooses to perform the integral transformation on those coordinates with predominant diffusion effects only, whereas the direction with predominant convection effects is handled numerically, together with the time variable, in the resulting transformed system of one-dimensional partial differential equations. Test cases are selected based on the nonlinear three-dimensional Burgers' equation, with the establishment of reference results for specific numerical values of the governing parameters. Then the algorithm is illustrated in the solution of conjugated heat transfer in microchannels.

In this rigorous and thorough analysis three concepts of heat conduction are studied: improved lumped-differential formulations, the generalized integral transform technique, and symbolic computation.
Addressing problem formulation, solution methodology and computational implementation, the authors develop an improved lumped-differential formulation for heat conduction problems, present a unified hybrid numerical-analytical solution methodology for linear and nonlinear problem, and provide an introduction to mixed symbolic-numerical computation.
Special topic and applications illustrate the theory, including extended surfaces, drying, ablation, conjugated problems and anisotropic media. Sample computer programs, using mixed symbolic-numerical computation, are presented in notebook format, developed within the Mathematica system.

A theoretical–experimental study of the conjugated heat transfer problem associated with the transient thermal behavior of a heated aeronautical Pitot tube is undertaken, including flight tests of experimental validation with the military aircraft A4 Skyhawk probe. The aim is to demonstrate the importance of accounting for the conduction–convection conjugation in more complex models that attempt to predict the thermal behavior of the anti-icing system of such sensors under adverse atmospheric conditions. The theoretical analysis involves the proposition of an improved lumped-differential model for heat conduction along the probe, approximating the transversal temperature gradients within the metallic and ceramic walls. The convective heat transfer problem in the external fluid is solved using the boundary layer equations for compressible flow, applying the Illingsworth variables transformation considering a locally similar flow. The nonlinear partial differential equations are solved using the Generalized Integral Transform Technique in the Mathematica v7.0 platform. The experimental analysis involves the use of thermocouples fixed to the surface of the Pitot tube and temperature measurements acquired by a data logger installed in the frontal cone of the airplane. The transient thermal behavior has been promoted by the A4 pilot through intermittent disconnection and reconnection of the Pitot probe heating system, which allowed for critical comparisons between the model and the actual flight thermal response of the Pitot tube structure.

The transient behaviour of conjugated heat transfer in laminar microchannel flow is investigated, taking into account the axial diffusion effects, which are often of relevance in microchannels, and including pre-heating or pre-cooling of the region upstream of the heat exchange section. The solution methodology is based on the Generalized Integral Transform Technique (GITT), as applied to a single domain formulation proposed for modelling the heat transfer phenomena at both the fluid stream and the channel wall regions. By making use of coefficients represented as space dependent functions with abrupt transitions occurring at the fluid–wall interfaces, the mathematical model carries the information concerning the transition of the two domains, unifying the model into a single domain formulation with variable coefficients. The proposed approach is illustrated for microchannels with polymeric walls of different thicknesses. The accuracy of approximate internal wall temperature estimates deduced from measurements of the external wall temperatures, accounting only for the thermal resistance across the wall thickness, is also analyzed.

The objective of this paper is to introduce applications of Bayesian filters to state estimation problems in heat transfer. A brief description of state estimation problems within the Bayesian framework is presented. The Kalman filter, as well as the following algorithms of the particle filter: sampling importance resampling and auxiliary sampling importance resampling, are discussed and applied to practical problems in heat transfer.

The present work summarizes the theory and describes the algorithm related to the construction of an open source mixed symbolic-numerical computational code named UNIT — Un ified I ntegral T ransforms, that provides a development platform for finding solutions of linear and nonlinear partial differential equations via integral transforms. The reported research was performed by making use of the symbolic computational system Mathematica v.7.0 and the hybrid numerical-analytical methodology Generalized Integral Transform Technique — GITT. The aim here is to illustrate the robust and precision controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source code. Test cases are selected based on nonlinear multi-dimensional formulations of the Burgers equations, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects and computational behaviors of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code.

The present work deals with conjugated heat transfer in heat spreaders made of a nanocomposite substrate with longitudinally molded multiple straight micro-channels. An experimental analysis is undertaken to validate a recently proposed methodology for the solution of conjugated conduction–convection heat transfer problems, which are often of relevance in thermal micro-systems analysis, based on a single domain formulation and solution of the resulting problem through integral transforms. The single domain formulation simultaneously models the heat transfer phenomena at both the fluid streams and the channels walls by making use of coefficients represented as space variable functions with abrupt transitions occurring at the fluid–wall interfaces. The Generalized Integral Transform Technique (GITT) is then employed in the hybrid numerical–analytical solution of the resulting convection–diffusion problem with variable coefficients. The experimental investigation involves the determination of the surface temperature distribution over the heat spreader with the molded microchannels that exchange heat with the base plate by flowing hot water at a prescribed mass flow rate. The infrared thermography technique is employed to investigate the response of the heat spreader surface temperature to a hot inlet fluid flow, aiming at the analysis of micro-systems that provide a thermal response from either their normal operation or due to a promoted stimulus for characterization purposes.

Heat transfer in microchannels is analyzed, including the coupling between the regions upstream and downstream of the heat transfer section and taking into account the wall conjugation and axial diffusion effects which are often of relevance in microchannels. The methodology is based on a recently proposed single-domain formulation for modeling the heat transfer phenomena simultaneously at the fluid stream and the channel walls, and applying the generalized integral transform technique (GITT) to find a hybrid numerical–analytical solution to the unified partial differential energy equation. The proposed mathematical model involves coefficients represented as space-dependent functions, with abrupt transitions at the fluid–wall interfaces, which carry the information concerning the transition of the two domains, unifying the model into a single-domain formulation with variable coefficients. Convergence of the proposed eigenfunction expansions is thoroughly investigated and the physical analysis is focused on the effects of the coupling between the downstream and the upstream flow regions.

A class of nonlinear diffusion-type problems is handled through a hybrid method. This method incorporates the ideas in the generalized integral transform technique to reduce the original partial differential equation into a denumerable system of coupled ordinary differential equations. These equations can then be solved through standard numerical techniques, once the system is truncated to a finite order. Sufficient conditions for the convergence of the truncated finite system are then examined. An application is considered that deals with a transient radiative fin problem, which is quite suitable for illustrating the solution methodology and convergence behavior.

This paper reviews the background to and the current status of analyses developed to address the problem of icing on aircraft.
Methods for water droplet trajectory calculation, ice accretion prediction, aerodynamic performance degradation and an overvie of ice protection system modelling are presented. The paper addresses the issues involved in the development of icing analyse including problem formulation and assumptions, solution techniques, validation and the incorporation of empirical inputs wher a purely theoretical approach is not feasible. Results are presented to illustrate the capabilities of the analyses when applie to practical design problems. Recommendations are made for further research.

The present work summarizes the theory and describes the algorithm related to an open-source mixed symbolic-numerical computational code named unified integral transforms (UNIT) that provides a computational environment for finding hybrid numerical-analytical solutions of linear and nonlinear partial differential systems via integral transforms. The reported research was performed by employing the well-established methodology known as the generalized integral transform technique (GITT), together with the symbolic and numerical computation tools provided by the Mathematica system. The main purpose of this study is to illustrate the robust precision-controlled simulation of multidimensional nonlinear transient convection-diffusion problems, while providing a brief introduction of this open source implementation. Test cases are selected based on nonlinear multidimensional formulations of Burgers’ equation, with the establishment of reference results for specific numerical values of the governing parameters. Special aspects in the computational behavior of the algorithm are then discussed, demonstrating the implemented possibilities within the present version of the UNIT code, including the proposition of a progressive filtering strategy and a combined criteria reordering scheme, not previously discussed in related works, both aimed at convergence acceleration of the eigenfunction expansions.

The present paper presents solution methods of convective heat transfer problems which take into account heat propagation in the solid in contact with a moving fluid. The method is referred to as the solution of conjugated problems. In particular, the paper treats heat transfer in laminar fluid flow in circular and planar tubes with allowance for the dissipation of mechanical energy. In addition, there are considered both steady-and unsteady-state heat transfer problems for flow of a compressible fluid past a plate. In all cases heat transfer in the fluid is discussed in relation to that in a solid wall. On the basis of the analysis of the solution a new criterion is introduced which characterizes the effect of thermophysical properties of the wall on heat transfer. A few examples are considered for illustration purposes.

This text presents several generalized analytical methods of solution for a variety of classes of commonly incurred heat transfer problems. It covers problems that are time-dependent, linear heat-oriented, or involve mass diffusion.

A theoretical model for ice growth due to droplets of supercooled fluid impacting on a subzero substrate is presented. In cold conditions rime (dry) ice forms and the problem reduces to solving a simple mass balance. In milder conditions glaze (wet) ice forms. The problem is then governed by coupled mass and energy balances, which determine the ice height and water layer thickness. The model is valid for “thin” water layers, such that lubrication theory may be applied and the Peclet number is small; it is applicable to ice accretion on stationary and moving structures. A number of analytical solutions are presented. Two- and three-dimensional numerical schemes are also presented, to solve the water flow equation, these employ a flux-limiting scheme to accurately model the capillary ridge at the leading edge of the flow. The method is then extended to incorporate ice accretion. Numerical results are presented for ice growth and water flow driven by gravity, surface tension, and a constant air shear.

A one-dimensional mathematical model is developed describing ice growth due to supercooled fluid impacting on a solid substrate. When rime ice forms, the ice thickness is determined by a simple mass balance. The leading-order temperature profile through the ice is then obtained as a function of time, the ambient conditions, and the ice thickness. When glaze ice forms, the energy equation and mass balance are combined to provide a single first-order nonlinear differential equation for the ice thickness, which is solved numerically. Once the ice thickness is obtained, the water height and the temperatures in the layers may be calculated. The method for extending the one-dimensional model to two and three dimensions is described. Ice growth rates and freezing fractions predicted by the current method are compared with the Messinger model. The Messinger model is shown to be a limiting case of the present method.

Flight in all weather conditions has necessitated correctly detecting icing and taking reasonable measures against it. This work aims at the detection and identification of airframe icing based on statistical properties of aircraft dynamics and reconfigurable control protecting aircraft from hazardous icing conditions. A Kalman filter is used for the data collection for the detection of icing, which aerodynamically deteriorates flight performance. A neural network process is applied for the identification of icing model of the aircraft, which is represented by five parameters based on past experiments for iced wing airfoils. Icing is detected by a Kalman filtering innovation sequence approach. A neural network structure is embodied such that its inputs are the aircraft estimated measurements and its outputs are the parameters affected by ice, which corresponds to the aircraft inverse dynamic model. The necessary training and validation set for the neural network model of the iced aircraft are obtained from the simulations of nominal model, which are performed for various icing conditions. In order to decrease noise effects on the states and to increase training performance of the neural network, the estimated states by the Kalman filter are used. A suitable neural network model of aircraft inverse dynamics is obtained by using system identification methods and learning algorithms. This trained model is used as an application for the control of the aircraft that has lost its controllability due to icing. The method is applied to F16 military and A340 commercial aircraft models and the results seem to be good enough.

The simplest conjugated boundary value problems of heat transfer, in ; which heat conduction equations are solved in common for a body with heat ; sources and for a liquid flowing round the body, are studied. The method of the ; asymptotic solution of integral equations occurring in conjugated problems is ; presented. (auth);

This second edition of our book extends the modeling and calculation of boundary-layer flows to include compressible flows. The subjects cover laminar, transitional and turbulent boundary layers for two- and three-dimensional incompressible and compressible flows. The viscous-inviscid coupling between the boundary layer and the inviscid flow is also addressed. The book has a large number of homework problems.

Analytical solution is obtained for laminar forced convection inside
tubes including wall conduction effects in the axial direction, based on
a radially lumped wall temperature model, and accounting for external
convection. The ideas in the generalized integral transform technique
are extended to accommodate for the resulting more involved boundary
condition and accurate numerical results obtained for quantities of
practical interest such as bulk fluid temperature, lumped wall
temperature, and Nusselt number. The effects of external convection and
axial conduction along the wall on these heat transfer quantities are
then investigated through consideration of typical values for,
respectively, Biot number and a wall-to-fluid conjugation parameter.
Convergence characteristics of the present approach are also briefly
examined.

A unified approach for solving convection-diffusion problems using the Generalized Integral Transform Technique (GITT) was advanced and coined as the UNIT (UNified Integral Transforms) algorithm, as implied by the acronym. The unified manner through which problems are tackled in the UNIT framework allows users that are less familiar with the GITT to employ the technique for solving a variety of partial-differential problems. This paper consolidates this approach in solving general transient one-dimensional problems. Different integration alternatives for calculating coefficients arising from integral transformation are discussed. Besides presenting the proposed algorithm, aspects related to computational implementation are also explored. Finally, benchmark results of different types of problems are calculated with a UNIT-based implementation and compared with previously obtained results.

In the current article, the problem of in-flight ice accumulation on multi-element airfoils is studied numerically. The analysis
starts with flow field computation using the Hess-Smith panel method. The second step is the calculation of droplet trajectories
and droplet collection efficiencies. In the next step, convective heat transfer coefficient distributions around the airfoil
elements are calculated using the Integral Boundary-Layer Method. The formulation accounts for the surface roughness due to
ice accretion. The fourth step consists of establishing the thermodynamic balance and computing ice accretion rates using
the Extended Messinger Model. At low temperatures and low liquid water contents, rime ice occurs for which the ice shape is
determined by a simple mass balance. At warmer temperatures and high liquid water contents, glaze ice forms for which the
energy and mass conservation equations are combined to yield a single first order ordinary differential equation, solved numerically.
Predicted ice shapes are compared with experimental shapes reported in the literature and good agreement is observed both
for rime and glaze ice. Ice shapes and masses are also computed for realistic flight scenarios. The results indicate that
the smaller elements in multielement configurations accumulate comparable and often greater amount of ice compared to larger
elements. The results also indicate that the multi-layer approach yields more accurate results compared to the one-layer approach,
especially for glaze ice conditions.

From the analysis of a conjugate problem of convective heat transfer in a laminar incompressible flow around a flat plate of a finite thickness the design formulas are suggested for a local Nusselt number Nux(Nux/Nux0)−1 = CBx, (0 < Brx < 1.5), (Nux/Nux0)−1 = C0−(C/Brx), (1.5 < Brx <∞), where Nux0 is the Nusselt number with Brx = 0 (the Nusselt number defined by the ordinary heat transfer equations) and Brx is the localBrun number (a conjugation number).RésuméOn analyse un problème conjugué de transfert thermique convectif dans un écoulement laminaire incompressible autour d'une plaque plane d'épaisseur finie. Pour le nombre de Nusselt local Nux on propose les formules suivantes: (Nux/Nux0)−1 = CBx (0 < Brx < 1,5)(Nux/Nux0)−1 = C0−(C/Brx) (1,5 < Brx) où Nux0 est le nombre de Nusselt pour Brx = 0 (le nombre de Nusselt défini par les équations ordinaires) et Brx est le nombre de Brun local (un nombre lié à la conjugaison).ZusammenfassungAusgehend von der Analyse eines konjugierten Problems der konvektiven Wärmeübertragung bei laminarer inkompressibler Strömung beidseitig einer ebenen Platte endlicher Dicke sind zwei Gleichungen für die örtliche Nusselt-Zahl Nux vorgeschlagen worden. Dabei ist Nux0 die Nusselt-Zahl mit Brx = 0 (die Nusselt-Zahl ist durch die Wärmeübergangsgleichung definiert) und Brx ist die örtliche Brun-Zahl (eine Konjugations-Zahl).РефератHa ocнoвe пpиближeнныч peшeний coпpяжeннoй зaдaчи кoнвeктивнoгo тeплooбмeнa пpи лaминapнoм oбтeкaнии плocкoй плacтины кoнeчнoй тoлщины нecжимaeмoй жидкocтью пpeдлoжeны pacчeтныe фopмuлы для лoк льнoгo чиcлa Пuccкльтa Nux/Nux0−1 = CBrx(0 < Brx < 1,5)Nux/Nux0−1 = C0−C1/Brx (1,5 < Brx <∞), гдe Nux0 — знaчeниe чиcлa Hucceльтa пpи Brx = 0 (чиcлo Huccкльтa, oпpeдeляeмoe пo oбщeизвecтным фopмuлaм тeплooбмeны), Brx — лoкaльнoe чиcлo чиcлo Бpюнa (кpитepий coпpяжeннocти).

This work presents a hybrid numerical–analytical solution for transient laminar forced convection over flat plates of non-negligible thickness, subjected to arbitrary time variations of applied wall heat flux at the fluid–solid interface. This conjugated conduction–convection problem is first reformulated through the employment of the coupled integral equations approach (CIEA) to simplify the heat conduction problem on the plate by averaging the related energy equation in the transversal direction. As a result, an improved lumped partial differential formulation for the transversally averaged wall temperature is obtained, while a third kind boundary condition is achieved for the fluid from the heat balance at the solid–fluid interface. From the available steady velocity distributions, a hybrid numerical–analytical solution based on the generalized integral transform technique (GITT), under its partial transformation mode, is then proposed, combined with the method of lines implemented in the Mathematica 5.2 routine NDSolve. The interface heat flux partitions and heat transfer coefficients are readily determined from the wall temperature distributions, as well as the temperature values at any desired point within the fluid. A few test cases for different materials and wall thicknesses are defined to allow for a physical interpretation of the wall participation effect in contrast with the simplified model without conjugation.

An analysis is made of transient conjugated convective-conductive heat transfer in laminar flow of a Newtonian fluid between parallel-plates subjected to periodically varying inlet temperature. A “thin wall” model is adopted that neglects transversal temperature gradients in the solid, but takes into account heat conduction along the duct wall. The quasi-steady solution is analytically obtained through the generalized integral transform technique, providing accurate numerical results for the axial distributions of amplitudes and phase lags of wall temperature, wall heat flux, and bulk temperature. The behavior of such periodic responses is then critically discussed, in terms of a conjugation parameter, fluid-to-solid capacitance ratio, and Biot number.

Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

Bayesian methods provide a rigorous general framework for dynamic state estimation problems. We describe the nonlinear/non-Gaussian tracking problem and its optimal Bayesian solution. Since the optimal solution is intractable, several different approximation strategies are then described. These approaches include the extended Kalman filter and particle filters. For a particular problem, if the assumptions of the Kalman filter hold, then no other algorithm can out-perform it. However, in a variety of real scenarios, the assumptions do not hold and approximate techniques must be employed. The extended Kalman filter approximates the models used for the dynamics and measurement process, in order to be able to approximate the probability density by a Gaussian. Particle filtering approximates the density directly as a finite number of samples. A number of different types of particle filter exist and some have been shown to outperform others when used for particular applications. However, when designing a particle filter for a particular application, it is the choice of importance density that is critical. These notes are of a tutorial nature and so, to facilitate easy implementation, 'pseudo-code' for algorithms are included at relevant points.

Increasingly, for many application areas, it is becoming important
to include elements of nonlinearity and non-Gaussianity in order to
model accurately the underlying dynamics of a physical system. Moreover,
it is typically crucial to process data on-line as it arrives, both from
the point of view of storage costs as well as for rapid adaptation to
changing signal characteristics. In this paper, we review both optimal
and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking
problems, with a focus on particle filters. Particle filters are
sequential Monte Carlo methods based on point mass (or "particle")
representations of probability densities, which can be applied to any
state-space model and which generalize the traditional Kalman filtering
methods. Several variants of the particle filter such as SIR, ASIR, and
RPF are introduced within a generic framework of the sequential
importance sampling (SIS) algorithm. These are discussed and compared
with the standard EKF through an illustrative example

The integral transform method in thermal and fluids sciences and engineering

- Rm Cotta

Hybrid Methods and Symbolic Computations Handbook of numerical heat transfer

- Rm Cotta
- Md Mikhailov

Conjugated heat transfer in microchannels NATO science for peace and security series A: chemistry and biology, microfluidics based microsystems: fundamentals and applications

- Js Nunes
- Rm Cotta
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Transient conjugated heat transfer in external compressible laminar flow over plates with internal heat generation. VII National congress of mechanical engineering

- K M Lisboa
- Jrb Souza
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Lisboa KM, Souza JRB, Cotta RM, Naveira-Cotta CP (2012)
Transient conjugated heat transfer in external compressible laminar flow over plates with internal heat generation. VII National
congress of mechanical engineering, CONEM 2012, São Luis,
pp 1-10, 31st July-3rd August, 2012

Conjugated heat transfer analysis of heated Pitot tubes: wind tunnel experiments, infrared thermography and lumped-differential modeling

- Jrb Souza
- Jlz Zotin
- Jbr Loureiro
- C P Naveira-Cotta
- Silva Freire
- A P Cotta

Souza JRB, Zotin JLZ, Loureiro JBR, Naveira-Cotta, CP, Silva
Freire AP, Cotta RM (2011) Conjugated heat transfer analysis of
heated Pitot tubes: wind tunnel experiments, infrared thermography and lumped-differential modeling. 21st International congress of mechanical engineering, COBEM-2011, ABCM, Natal,
October 2011