# International Journal of Thermal Sciences

Published by Elsevier

Print ISSN: 1290-0729

Published by Elsevier

Print ISSN: 1290-0729

Publications

This paper presents a theoretical analysis of transient temperature distribution in metals and composites struck by different lightning currents to simulate objects of interest, especially aircrafts. A computer program based on the finite volume technique is written to compute the transient temperature distributions in three dimensions due to both high-amplitude impulse currents (IC) and the relatively low-amplitude long-duration currents (LDC). Typical waveform of the discharge current during lightning strikes to objects near/on ground (negative downward flash), at high altitudes (negative upward flash) and in-flight (e.g. aircrafts) are simulated with different amplitudes and durations. The simulation considers the IC as first negative, or superimposed or subsequent return strokes with respect to the LDC. Different types of metals and carbon-fiber composites are also investigated to compare their thermal transient responses. Finally, the theoretical results are verified by using a sophisticated high-speed infrared camera to measure the rear-face temperature profiles of metals as a function of the coordinates and time due to both IC and LDC.

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A detailed comparison of flow boiling heat transfer results in a stainless steel tube of 1.1 mm internal diameter with results of a three-zone flow model are presented in this paper. The working fluid is R134a. Other parameters were varied in the range: mass flux 100–600 kg/m2 s; heat flux 16–150 kW/m2 and pressure 6–12 bar.The experimental results demonstrate that the heat transfer coefficient increases with heat flux and system pressure, but does not change with vapour quality when the quality is less than about 50% for low heat and mass flux values. The effect of mass flux is observed to be insignificant. For vapour quality values greater than 50% and at high heat flux values, the heat transfer coefficient does not depend on heat flux and decreases with vapour quality. This could be caused by dryout. The three-zone evaporation model predicts the experimental results fairly well, especially at relatively low pressure. However, the dryout region observed at high quality is highly over-predicted by the model. The sensitivity of the performance of the model to the three optimised parameters (confined bubble frequency, initial film thickness and end film thickness) and some preliminary investigation relating the critical film thickness for dryout to measured tube roughness are also discussed.

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A comment on a recent paper about the combined effects of radiation and viscous dissipation on the convection in an annular porous enclosure has raised the problem of the role played by the viscous dissipation and the pressure work contributions in buoyant flows. The aim of this further comment is to show that the criticism expressed by Costa on the model of the viscous dissipation effect employed in the paper by Badruddin and co-workers is unjustified.

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A three-dimensional steady-state model for predicting heat transfer in a micro heat pipe array is presented. Three coupled models, solving the microregion equations, the two-dimensional wall heat conduction problem and the longitudinal capillary two-phase flow have been developed. The results, presented for an aluminium/ammonia triangular micro heat pipe array, show that the major part of the total heat input in the evaporator section goes through the microregion. In addition, both the apparent contact angle and the heat transfer rate in the microregion increase with an increasing wall superheat. It is also shown that the inner wall heat flux and temperatures as well as the contact angle decrease all along the evaporator section.RésuméInfluence des phénomènes interfaciaux sur les transferts de chaleur par évaporation dans les microcaloducs. Un modèle tridimensionnel a été développé en régime permanent pour prédire les transferts thermiques au sein d'un microcaloduc. Ce modèle, composé de trois sous-modèles couplés, permet de résoudre les équations qui régissent les transferts dans la microrégion, le problème bidimensionnel de conduction thermique dans la paroi et l'écoulement capillaire axial liquide–vapeur. Les résultats, présentés pour une rangée de microcaloducs triangulaires aluminium/ammoniac, montrent qu'une grande partie du flux thermique imposé à l'évaporateur est évacuée par la microrégion. De plus, l'angle de contact apparent et la puissance thermique dissipée dans la microrégion augmentent avec la surchauffe de la paroi. On montre également que la densité de flux, la température de la paroi interne ainsi que l'angle de contact décroissent le long de l'évaporateur.

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A one-dimensional mathematical model of the R744 two-phase ejector for expansion work recovery is presented in this paper. Governing equations were formulated for all passages of the ejector based on the differential equations for mass, momentum, and energy balance as well as a differential representation for the equation of state. For two-flow sections (mixer and diffuser) closing equations for mass, momentum and energy transfer between the primary and secondary flow were introduced. This model utilises the Delayed Equilibrium Model along with the Homogeneous Nucleation Theory for the purpose of the metastable state analysis for a transcritical flow with delayed flashing over the motive nozzle. The thermal properties model was based on a real fluid approach, where the REFPROP 8.0 database was used. Based on the results of experimental tests performed at SINTEF Energi Laboratory, the model was validated for a typical range of operating conditions. The range of available simulation output allowed for the creation of 1D profiles of local values for the flow variables and the computation of the overall indicators, such as pressure lift and expansion work recovery efficiency.Highlights► Double-diffusive natural convection in a porous medium with nanofluid studied. ► Effects of prescribed surface heat, solute and nanoparticle fluxes studied. ► Graphs give velocity, temperature, solute and nanoparticle concentration profiles. ► Data for Nusselt number and two Sherwood numbers also provided.

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This study investigates natural convection heat transfer of water-based nanofluids in an inclined square enclosure where the left vertical side is heated with a constant heat flux, the right side is cooled, and the other sides are kept adiabatic. The governing equations are solved using polynomial differential quadrature (PDQ) method. Calculations were performed for inclination angles from 0° to 90°, solid volume fractions ranging from 0% to 20%, constant heat flux heaters of lengths 0.25, 0.50 and 1.0, and a Rayleigh number varying from 104 to 106. The ratio of the nanolayer thickness to the original particle radius is kept at a constant value of 0.1. The heat source is placed at the center of the left wall. Five types of nanoparticles are taken into consideration: Cu, Ag, CuO, Al2O3, and TiO2. The results show that the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. The results also show that the length of the heater is also an important parameter affecting the flow and temperature fields. The average heat transfer decreases with an increase in the length of the heater. As the heater length is increased, the average heat transfer rate starts to decrease for a smaller inclination angle (it starts to decrease with inclination at 90° for ɛ = 0.25, 60° for ɛ = 0.50, 45° for ɛ = 1.0, respectively).

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The problem of radiation heat transfer coupled with other modes of heat transfer is important in many engineering applications. Some examples are the heat transfer in glass fabrication and in thermal isolation materials. The angular and spatial discretization of the radiative transport equation in the discrete ordinates method (DOM) plays an important role to obtain accurate numerical results. Two high order spatial discretization schemes are used and compared. One spatial discretization scheme is unidirectional and the other is multidimensional interpolating scheme. Different angular quadratures are selected and tested to obtain accurate results with less computational time. The radiative heat transport equation is solved using the conventional procedure of solution for DOM and the algorithm is validated by comparison with literature exact solutions for different two-dimensional cases. The radiative source term in the energy equation is computed from intensities field. The radiative conductive model is validated by comparison with test cases solutions from the literature. Non-uniform grids are implemented for multidimensional spatial scheme and the results are compared with the result of uniform grid showing agreement. Also, the non-uniform grids are tested in cases of high temperature gradients. To accelerate convergence an adequate relaxation factors in radiative heat transport equation and in energy equation are used. The method can be used to handle cases with reflecting boundaries.

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In the present work, we illustrate a methodology for the reconstruction and modeling of three-dimensional micro-structures of highly anisotropic composite materials. Specifically, we focus on disk-shaped nano-fillers dispersed in a polymer matrix and detailed numerical investigations, based on the lattice Boltzmann method (LBM), are carried out on the global thermal conductivity.

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Heat transfer in fluid flows traditionally is examined in terms of temperature field and heat-transfer coefficients at non-adiabatic walls. However, heat transfer may alternatively be considered as the transport of thermal energy by the total convective–conductive heat flux in a way analogous to the transport of fluid by the flow field. The paths followed by the total heat flux are the thermal counterpart to fluid trajectories and facilitate heat-transfer visualisation in a similar manner as flow visualisation. This has great potential for applications in which insight into the heat fluxes throughout the entire configuration is essential (e.g. cooling systems, heat exchangers). To date this concept has been restricted to 2D steady flows. The present study proposes its generalisation to 3D unsteady flows by representing heat transfer as the 3D unsteady motion of a virtual fluid subject to continuity. This unified ansatz enables heat-transfer visualisation with well-known geometrical methods from laminar-mixing studies. These methods lean on the property that continuity “organises” fluid trajectories into sets of coherent structures (“flow topology”) that geometrically determine the fluid transport. Decomposition of the flow topology into its constituent coherent structures visualises the transport routes and affords insight into the transport properties. Thermal trajectories form a thermal topology of essentially equivalent composition that can be visualised by the same methodology. This thermal topology is defined in both flow and solid regions and thus describes the heat transfer throughout the entire domain of interest. The heat-transfer visualisation is provided with a physical framework and demonstrated by way of representative examples.

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An improved understanding of the heat transfer in materials consisting of two layers (splat and substrate) is essential for many industrial applications. We are interested in the deposition, rapid cooling and solidification of metal droplets (known as splats) brought into contact with a cold substrate. We therefore need to understand the temperature history in both the splat and the substrate, including phase change phenomena. A new model of the thermal contact resistance based on a random distribution of contact points, rather than the uniform distribution commonly used, is presented in this paper.Phase change has been also considered, using the enthalpy-porosity formulation. Simulations have been conducted with the commercial package CFX-4. The computational results for the cooling rate of the splat obtained using the random contact distribution model are in good agreement with available experimental results. In addition, results obtained from the random model provide information on the inhomogeneity affecting the temperature at the interface between the splat and the substrate.

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An accurate WSGGM-based narrow band (WNB) model is investigated in the CO2 4.3 mu m band for use in inverse radiative instrumentation. The WNB model of Kim and Song is tested first with 24 gray gases for all of the narrow bands and it shows significant error compared with the line-by-line (LBL) results for two typical non-isothermal layers. A modification of this model is proposed using the concept of correlated k-distribution (CK) and assuming that the scaling approximation may be justified. With only seven gray gases taken independently for each narrow band (optimised and tabulated), this model shows less than 1 % deviation from the LBL results for most of the important narrow bands around 4.3 mu m. Further extension of the WNB model is tried by applying the CK fictitious gases (CKFG) concept by taking, independently for each narrow band, three fictitious gases for each of which three gray gases are taken. This results in 3(3) gray gases which are spectrally overlapped with each other in a random fashion. Despite the complexity and labour, the test of the CKFG-based WNB model reveals greater error (a few percent or more) than the previous CK-based modification for the CO2 4.3 mu m band. Therefore, use of the CK-based WNB model or accurate and economical computations is recommended, (C) Elsevier, Paris.

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Spectral remote sensing (SRS) method for determining the temperature profile along a line-of-sight is investigated experimentally. Quartz tube, within which combustion gas flows, is used as the test section. The inversion procedure is carried out with a line-by-line (LBL) method and a CK-based WNB model. The optimal gas temperature profile that minimizes the error between the measured narrow band intensities around the CO2 4.3 μm band and the calculated ones is obtained as the result of the inversion process. The gas temperature is also measured with a shielded thermocouple and corrected for the error. The results show that the front, center and back temperatures are within errors of 1%, 4% and 12%, respectively. SRS technique shows poor performance in measuring cold gas temperatures behind a hot layer. The reconstructed temperature profile in the front region is, however, in good agreement with the thermocouple reading. The potential applicability of SRS is positively demonstrated and current technical limitations are also discussed.

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A numerical investigation has been carried out to examine laminar flow and heat transfer characteristics in a three-dimensional isothermal wall square channel with 45°-angled baffles. The computations are based on the finite volume method, and the SIMPLE algorithm has been implemented. The fluid flow and heat transfer characteristics are presented for Reynolds numbers based on the hydraulic diameter of the channel ranging from 100 to 1000. To generate a pair of mainstreamwise vortex flows through the tested section, baffles with an attack angle of 45° are mounted in tandem and inline arrangement on the lower and upper walls of the channel. Effects of different baffle heights on heat transfer and pressure loss in the channel are studied and the results of the 45° inline baffle are also compared with those of the 90° transverse baffle and the 45° staggered baffle. It is apparent that in each of the main vortex flows, a pair of streamwise twisted vortex (P-vortex) flows created by the 45° baffle exist and help to induce impinging flows on a sidewall and wall of the baffle cavity leading to drastic increase in heat transfer rate over the channel. In addition, the rise in the baffle height results in the increase in the Nusselt number and friction factor values. The computational results reveal that numerical results of both the 45° inline and staggered baffles are nearly the same. The optimum thermal enhancement factor is at the 45° baffle height of 0.2 times of the channel height for both arrays. The maximum thermal enhancement factor of the 45° baffle in the Re range studied is found to be about 2.6 or twice higher than that of the 90° transverse baffle.

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This experimental study investigated heat-transfer physics of forced convection in a reciprocating square duct fitted with 45° crossed ribs on two opposite walls. The parametric conditions involved several Reynolds, pulsating and buoyancy numbers, respectively, in the ranges of 600–10 000, 0–10, and 0–0.14 with five different reciprocating frequencies tested, namely, 0.67, 1, 1.33, 1.67 and 2 Hz. The rib-induced flows in the static duct produced an augmentation of heat transfer in the range of 260–300% compared to the smooth-walled situation. The reciprocating heat-transfer data reconfirmed the appearance of large-scale wavy-like axial heat transfer distribution that differed significantly from the stationary results. The manner in which the pulsating force and convective inertia, with and without buoyancy interaction, interactively affected the local heat transfer along the rib-roughened surface was illustrated using a number of experimentally based observations and extrapolations. The buoyancy interaction in the reciprocating duct reduced heat transfer, which effect was enhanced by increasing the pulsating number, but appeared to be a weak function of Reynolds number. When the Reynolds and pulsating numbers were relatively low, a range of heat transfer impediments, that could lead the spatial-time averaged heat-transfer to levels about 71% of nonreciprocating values, was observed. A further increase of pulsating number resulted in a subsequent heat-transfer recovery, which tendency could lead to heat-transfer improvement from the nonreciprocating level. An empirical correlation to evaluate the spatial-time averaged heat transfer over the reciprocating ribbed duct was developed to assist the design activity. The possibility to further enhance heat-transfer via the use of angled ribs in a reciprocating duct is confirmed, but it is important to ensure that the range of reciprocating flow parameters produced does not create heat-transfer impediment in order to avoid overheating situations.

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Experiments are performed to study the transient forced convection heat transfer from a four-in-line chip module that are flush-mounted to on one wall of a vertical rectangular channel using FC-72 as coolant. The flow covers the wide range of laminar flow regime with Reynolds number based on heat source length, from 800 to 2625. The heat flux ranges from 1 to 7 W⋅cm−2. The heat transfer characteristics are studied and correlations are presented. The transient correlation for overall data recommended is . Finally the data obtained from FC-72 are compared with the data from water coolant and found that the Nusselt number data from FC-72 are higher than those from water.

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Pool boiling heat transfer from finned copper surfaces immersed in a saturated dielectric fluid (Fluorinert FC-72) has been experimentally studied. Twelve extended surfaces with different geometrical configurations were tested. Each extended surface consisted of an array of pin fins with square cross-section. Fins were 3 or 6 mm long and their width varied from 0.4 to 1.0 mm. Fins were uniformly or non-uniformly spaced on the base surface: starting from the uniform configuration, in which the width and the spacing of fins were equal, non-uniform surfaces were obtained by regularly removing some rows of fins. For each extended surface, boiling curves were obtained at three different saturation pressures: 0.5, 1.0 and 2.0 bar. The effects of fin dimensions, spacing and pressure on heat transfer in saturated pool boiling were examined. In particular, the effect which the non-uniform distribution of fins produces on boiling behaviour was analysed. When fins thin out, the overall heat transfer coefficient based on the total area of the extended surface increases, but the heat transfer rate does not improve, even in the boiling region close to the maximum heat flux. The better wetting of the boiling surface by the liquid refrigerant, as a result of the sparser grouping of fins, is apparently offset by the reduction in the heat transfer area. If pressure is increased, the boiling curves of finned surfaces move towards lower wall superheats, as already observed in previous studies with regard to both plane and finned surfaces.

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In this work, the rising velocities of gas bubbles in a still liquid are measured and compared with available theories. In order to separate the mechanical effects from the thermal and mass exchange ones in bubble dynamics, adiabatic two-phase flow conditions were established by injecting gas (nitrogen) bubbles in a fluoroinert liquid (FC-72) at ambient temperature and pressure through an orifice (about 0.1 mm diameter) drilled on a generatrix of a horizontal tube. Bubble size, aspect ratio, detachment frequency, velocity and frequency of shape oscillations were measured by processing of high speed video images (at 1500 fps). A sensible steady oscillation of velocity, with a amplitude up to 20% of the mean value, was evidenced after the initial acceleration region. This oscillation was well correlated with the one in aspect ratio, thus providing evidence of the separate influence of this last parameter on drag coefficient. Available correlations did not give fully satisfactory results in predicting the mean rising velocity, showing a general tendency to underprediction. Sensible wake effects were excluded. Finally, the frequency of shape oscillation and the mean aspect ratio were compared with available models, evidencing their limitations.

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The expansion of the plasma plume created during the interaction between an excimer laser and a copper target is studied by a Monte-Carlo simulation. The global shape of the plume is followed in time using a three dimensional algorithm, allowing the simulation of the expansion both under vacuum and background gas. The laser energy absorption by the plume of evaporated particles is found to have dominant effects on the plume shape. An approximation of these effects is made by taking into account a kinetic energy transfer in the plume through the recombination of ionized and excited particles by collisional recombinative processes. Results of the simulation of the expansion under vacuum are compared with experimental results obtained by fast photography of the plume and time of flight measurements. First results of the simulation by a Monte-Carlo method of the plasma plume expansion under residual pressure show clearly the snowplow of the leading edge of the plume and the background particles deficiency in the dense region of the plume.

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An original model describing non-equilibrium heat transfer in ablative composite layers has been studied. The model is obtained as an extension of previous work involving the use of the volume averaging method to upscale the micro-scale equations. Using this methodology, it is shown that non-equilibrium models existing in the literature may lead to equilibrium conditions for typical aerospace applications. The new model presented in this paper takes into account two separate macro-scale “phases”, but, contrary to previous models, they are constituted of the inert part of the material, on one side, and the mixture of gas and pyrolysable part of the material on the other side. The theoretical development allows to estimate the transport properties in the macro-scale model from micro-scale unit cell characteristics. They are obtained for different types of unit cells: simple stratifed unit cells, and unit cells characteristic of woven composites. Quantitative indications are given for the estimates of the macro-scale thermal diffusivity tensors, and for the volume heat exchange coefficient.

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On a vapor film, floating drops with volumes of several cm3 are disk-like on horizontal plates, while in contrast, drops with volumes smaller than 0.5 mm3 are spherical. Most of the drops have a volume, and thus a form, between these two boundary shapes. The evaporation time of disk-like drops is represented in a dimensionless manner on the basis of well-known analytical solutions, whereby two newly defined characteristic numbers are introduced. For spherical drops an analytical solution is developed. It is shown that with these characteristic numbers the evaporation time of disks as well as of spheres can be described. However, as a result of changed drop geometry, other values for the exponents of the numbers occur. The evaporation times of intermediate drops, which were determined experimentally by ourselves and taken from the literature, can likewise be described by these characteristic numbers. Their exponents change with the volume between the limit values of the two shapes, sphere and disk.

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Coupled heat transfers in hollow structures uniformly heated from below or from above are numerically investigated. Discussions of the results are for structures formed by a range of 3 identical rectangular cavities with end vertical side walls of the structure assumed adiabatic or submitted to periodic conditions. The Boussinesq approximation is invoked and the flows are considered laminar and two-dimensional for the whole range of parameters considered. Conduction heat transfer in the solid partitions and surface radiation amongst grey diffuse surfaces are accounted for. The conservation equations are solved by a finite difference method and the pressure–velocity coupling solved by the SIMPLE algorithm.

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This paper presents a detailed analysis of an ammonia–water vertical tubular absorber cooled by air. The absorption process takes place co-currently upward inside the tubes. The tubes are externally finned with continuous plate fins and the tube rows are arranged staggered in the direction of the air flow. The air is forced over the tube bank and circulates between the plain fins in cross flow with the ammonia–water mixture. The analysis has been carried out by means of a mathematical model developed on the basis of mass and energy balances and heat and mass transfer equations. The model takes into account separately the churn, slug and bubbly flow patterns experimentally forecasted in this type of absorption processes inside vertical tubes and considers the simultaneous heat and mass transfer processes in both liquid and vapour phases, as well as heat transfer to the cooling air. The model has been implemented in a computer program. Results based on a representative design and nominal operating conditions of an absorber for a small capacity ammonia–water absorption refrigeration system are shown. A parametric analysis was realised to investigate the influence of the design parameters and operating conditions on the absorber performance. The noteworthy results that have effect on practical design of the absorber are presented and commented.

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This paper presents a detailed analysis of the heat and mass transfer processes during the absorption of ammonia into water in a co-current vertical tubular absorber. The absorber configuration is of the shell and tubes type. The absorption process progresses as the vapour and liquid contact inside the tubes. Water is used as the absorber cooling medium. A differential mathematical model has been developed on the basis of mass and energy balances and heat and mass transfer equations, in order to provide further understanding of the absorber behaviour. The model takes into account separately for the churn, slug and bubbly flow patterns experimentally forecasted in this type of absorption processes inside vertical tubes and considers the simultaneous heat and mass transfer processes in both liquid and vapour phases, as well as heat transfer to the cooling medium. The model equations have been solved using the finite-difference method. Results obtained for specific data are depicted to show local values of the most important variables all along the absorber length. Parametric analyses have been performed to show the influence of design parameters and operating conditions on the absorber performance. The effect of the heat and mass transfer coefficients has also been evaluated.

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The effect of the presence of molecular water impurity of various concentrations in absorbing and scattering glass media on the temperature field in a layer subjected to thermal infrared radiation is investigated. The analysed medium is treated as a multicomponent medium consisting of glass matrix and water impurity. The effect of radiation on the medium is expressed by heat sources in each component due to absorption of radiation. It is shown that the presence of water impurity in the glass medium should be accounted for in order to predict the temperature distribution during radiation action. The effect of scattering of radiation by water molecules on thermal and diffusive processes in the analysed medium is shown to be insignificant.

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This work is focused on the study of unsteady heat and mass transfer by mixed convection flow over a vertical permeable cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field and heat generation or absorption effects. The cone surface is maintained at variable temperature and concentration. Fluid suction or injection is assumed to occur at the cone surface. The coupled nonlinear partial differential equations governing the thermosolutal mixed convective flow have been solved numerically using an implicit, iterative finite-difference scheme. Comparisons with previously published work have been conducted and the results are found to be in excellent agreement. A parametric study showing the effects of the buoyancy parameter, suction or injection velocity and heat generation or absorption coefficient on the local tangential and azimuthal skin friction coefficients, and the local Nusselt and Sherwood numbers is conducted. These are illustrated graphically to depict special features of the solutions. It is found that the local tangential and azimuthal skin-friction coefficients and local Nusselt and Sherwood numbers increase with the time when the angular velocity of the cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. Increasing the buoyancy ratio is predicted to increase the skin-friction coefficients and the Nusselt and Sherwood numbers. Also, increases in the heat generation or absorption coefficient increase the local tangential skin-friction coefficient and Sherwood number and decrease the local Nusselt number. On the other hand, the azimuthal skin-friction coefficient and the Nusselt and Sherwood numbers increase (decrease) with the increase in the suction (injection) parameter.

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This paper presents a detailed study on the ammonia–water vapour rectification process in absorption systems using a helical coil rectifier. A differential mathematical model has been developed on the basis of mass and energy balances and heat and mass transfer equations. The differential volume has been defined in each coil turn by a differential angle on the turn and a second differential angle on the coiled tube cross section. It contains the corresponding differential portion of coolant, coiled tube wall, condensate film and vapour. Simultaneous heat and mass transfer processes have been taken into account in the vapour and liquid phases. The model equations have been solved using the finite-difference method. Results have been obtained for characteristic data from an ammonia–water absorption refrigeration system. Most significant calculated variable profiles along the coil height as well as in the coiled tube cross section are presented and discussed. The influence of the heat and mass transfer coefficients on the rectifier performance has also been considered.

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An endoreversible four-heat-reservoir absorption heat pump cycle model with a generalized heat transfer law Q∝Δ(Tn) is established. The general relation between the coefficient of performance (COP) and the heating load with Q∝Δ(Tn) is deduced. The fundamental optimal relation, the optimal temperatures of working substance, as well as the optimal heat transfer surface area distributions with linear phenomenological heat transfer law are derived. Moreover, the effects of heat transfer law on the performance of absorption heat pump are analyzed and the performance comparison before and after optimizing the distribution of the total heat transfer surface area is performed by numerical example.

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A solar absorption air-conditioner is simulated with an air-to-air heat exchanger to evaluate the feasibility of a compact solar air-conditioning ventilator module. The air-to-air heat exchanger considered in this study is a membrane type total exchanger and the absorption air-conditioner is a single-effect LiBr-water machine with air-coil heat exchangers. All components are modeled in effectiveness-NTU methods including a dehumidifying DX evaporator coil and a cross-flow absorber allowing the whole system to be described by a set of simultaneous algebraic equations, which are then solved easily by a matrix solver. It is predicted that the baseline air-conditioner would produce cooling power in 1.4–5 kW from hot water in 50–100 °C with a COPthrm over 0.7 without the risk of crystallization and that the heat transfer coefficients of the air-coils and the pressure losses would greatly influence the performance. Total cooling power of the baseline system at 80 °C hot water temperature condition is found 19.2 kW, of which 15.7 kW is attributable to AHX and 3.5 kW to the absorption air-conditioner. Corresponding total COPelec is 76, to which the contributions of AHX and the absorption air-conditioner are 62 and 14, respectively. Air flow rates are found to greatly influence the overall performance and should be carefully chosen. It is concluded that the proposed idea is technically feasible and worth further development as an alternative solution.

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This work is focused on the study of combined heat and mass transfer by natural convection of a micropolar, viscous and heat generating or absorbing fluid flow near a continuously moving vertical permeable infinitely long surface in the presence of a first-order chemical reaction. The governing equations for this investigation are formulated and solved numerically using the fourth-order Runge–Kutta method. Comparisons with previously published work on special cases of the problem are performed and found to be in excellent agreement. A parametric study illustrating the influence of the micro-gyration parameter, vortex viscosity parameter, chemical reaction parameter, Schmidt number, heat generation or absorption parameter on the fluid velocity as well as the skin-friction coefficient and the Nusselt and Sherwood numbers is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.

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This paper presents a study on the NH3–H2O distillation process using a packed column with liquid reflux from the condenser in an absorption refrigeration system. A differential mathematical model has been developed on the basis of mass and energy balances and the heat and mass transfer equations. A net molar flux between the liquid and vapour phases has been considered in the mass transfer equation, which obviates the need to assume equimolar counter-diffusion. The model equations have been solved using the finite-difference method. Results obtained for a specific application are shown, including parameter distributions along the column length. The influence of rectifying and stripping lengths, mass and heat transfer coefficients and volumetric heat rejection from the column, on the distillate ammonia concentration has been analysed.

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In this paper an improved quadrature scheme based on the reverse Monte Carlo method implemented using Sobol sequences to generate ray orientations is presented. This has the property that a more uniform pattern of rays on the unit hemisphere is produced compared to the usual implementation of the reverse Monte Carlo method. The use of Sobol sequences gives a ray convergence rate for the incident heat flux that is asymptotically equivalent to . The generation of ray directions using Sobol sequences means that the Central Limit Theorem no longer holds. In its place a Gaussian variable is formulated from the incident intensity distributions calculated using Sobol sequences. This makes it possible to calculate confidence limits for a prediction of incident heat flux and the confidence limits contract with ray number at a rate of . An extension to the Monte Carlo method combined with Sobol sequences is also presented that exploits the shape of the incident intensity distribution to a receiver. The new methodology is relatively simple to implement and shows some promising improvements in computational efficiency.

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This paper presents the thermodynamic model used in the numerical simulation of ice accreted on an airfoil surface in wet and dry regimes developed at AMIL (Anti-Icing Materials International Laboratory), in a joint project with CIRA (Italian Aerospace Research Center). The thermodynamic model combines mass and heat balance equations to an analytical representation of water states over the airfoil to calculate the surface roughness and masses of remaining, runback, and shedding liquid water. The water state on the surface is represented in the form of beads, film or rivulets, each situation corresponding to a particular roughness height which has a major impact on the heat transfer coefficients necessary for the heat and mass balances. The model has been tested for severe icing conditions at six different temperatures corresponding to dry, mixed and wet accretion. Water mass, roughness and heat transfer convection coefficients over the airfoil surface are presented. The thermodynamic model combined with an air flow, water trajectory, and geometric model provides accurate results. It generates the complex ice shapes observed on the wing profile, and the numerical ice shapes profiles agree well with those obtained in wind tunnel experiments.

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The β-pdf has been widely assumed for the probability distribution of the mixture fraction in many turbulent mixing and turbulent non-premixed combustion models in the literature. The numerical integration of the β-pdf often encounters the singularity difficulties and only few publications have addressed this issue. An efficient, accurate and robust numerical treatment of the β-pdf integration was proposed. The present treatment of the β-pdf integration was implemented into a flamelet model to calculate turbulent methane–air combustion in a model gas turbine combustor. Numerical results obtained using the present β-pdf integration method and those based on the properties of the beta and gamma functions were compared to illustrate the accuracy of the present method. Effect of assuming the β-pdf to the mass-weighted pdf and unweighted pdf of the mixture fraction on the calculated density field was also investigated.

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The Neumann (or insulated) boundary condition is often encountered in engineering applications. The conventional finite difference schemes are either first-order accurate or second-order accurate but need a ghost point outside the boundary. Compact finite difference schemes are difficult to apply for multi-dimensional cases or for cylindrical and spherical coordinate cases. In this study, we present a kind of new and accurate finite difference schemes for the Neumann (insulated) boundary condition in Cartesian, cylindrical, and spherical coordinates, respectively. Combined with the Crank–Nicholson finite difference method or other higher-order methods, the overall scheme is proved to be unconditionally stable and provides much more accurate numerical solutions. The numerical errors and convergence rates of the solution are tested by several examples. Results show that the new method is promising.

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A simplified method based on Rayleigh's criterion is developed for evaluating thermoacoustic power conversion in transverse-pin and tortuous stacks. Heat transfer and viscous losses are approximated by steady-flow correlations valid at large acoustic displacements with respect to a longitudinal pitch of a pin stack or a characteristic pore size of a random stack. A Lagrangian approach is employed to calculate temperature fluctuations of oscillating gas parcels inside the stack. A computational example is presented for a stack with an inline pin arrangement placed in a standing acoustic wave. Power conversion and efficiencies are evaluated for conditions relevant to a small-scale system. An indirect comparison is also made between theoretical results and experimental data for a prime mover with a wire mesh stack.

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A simplified calculus model to investigate on the transverse heat transport near the edges of a thermally isolated thermoacoustic stack in the low acoustic Mach number regime is presented. The proposed methodology relies on the well-known results of the classical linear thermoacoustic theory which are implemented into an energy balance calculus-scheme through a finite difference technique. Details of the time-averaged temperature and heat flux density distributions along a pore cross-section of the stack are given. It is shown that a net heat exchange between the fluid and the solid walls takes place only near the edges of the stack plates, at distances from the ends not exceeding the peak-to-peak particle displacement amplitude. The structure of the mean temperature field within a stack plate is also investigated; this last results not uniform near its terminations giving rise to a smaller temperature difference between the plate extremities than that predicted by the standard linear theory. This result, when compared with experimental measurements available in literature, suggests that thermal effects localized at the stack edges may play an important role as sources of the deviations found between linear theory predictions and experiments at low and moderate Mach numbers.

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The paper describes the theory and application of opto-acoustics to determine thermal diffusivities of gases. An experimental device, already described in previous papers of the authors [Internat. J. Thermophys. 19 (1998) 1099; Proc. 2nd European Thermal Science and 14th UIT National Heat Transfer Conf., 1996, pp. 1071–1078] permitted the detection of thermal diffusivities of gases at moderate pressures with an experimental uncertainty of about ±1.25%.Based on the experience gained with this device, a comprehensive error analysis is presented in this paper. It shows how the experimental uncertainties can be considerably reduced to about −0.45 to +0.35%. The parameters for optical cell design are dealt with, as well as the appropriate characteristics, such as frequencies of the modulated laser beam, and the microphone used in the experiment.

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The aim of our ongoing research is to propose a forest fire simulator. To this end, we have developed a semi-physical model of fire spread that has been validated experimentally thanks to laboratory-scale pine needle bed fires under both slope and low wind conditions. This model described the physical phenomena in a simple manner while providing the main characteristics of spread. However, it did not allow to describe accurately the experimental tendency of an increasing spread rate with increasing wind velocity, particularly because of the strong assumption of considering a constant wind over the entire spreading zone. In the present study, we propose a simplified description of the flow that is coupled to our model. To proceed, we carry out the reduction of a multiphase model of reference. This reduction of the complete equations that describe the flow allows us to develop a simplified flow by considering mainly the buoyancy effect induced by combustion in the flaming zone. The results are subsequently compared to laboratory experiments under varying wind and slope conditions. A substantial improvement of the predicted rates of spread is provided.

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Cross-stream buoyancy-induced formation of VS (vortex shedding) past a rotating cylinder maintained at constant wall temperature is studied at Re = 40 and 100. The non-dimensional rotational velocity (α) is varied from 0 to 8 and Richardson number from 0 to 1 with air as the working fluid. Semi-explicit finite-volume method code implemented on colocated Cartesian multi-block grid is used. Buoyancy-induced onset of vortex shedding is found for stationary/rotating cylinder at sub-critical Re = 40. Steady-VS flow transition map is shown for the different rotational velocity and Ri; and reasoned using vorticity dynamics. At higher rotational velocity, origin of buoyancy-induced secondary frequency for Re = 40 at α = 6 and for 100 at α = 5 is discussed using spectral analysis and phase portrait technique. The VS frequency is much smaller at higher as compared to lower rotational velocity and increases with increasing Ri. A monotonic increase in the downward lift force and a reversal in the direction of drag force is found with increasing rotational velocity. Rotation can be used as a drag reduction and heat transfer suppression technique.

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Flow boiling was investigated under unstable boiling conditions in three different micro-pin fin heat sinks using water and R-123 as working fluids. Once boiling was initiated severe temperature fluctuations were recorded for all the tested (three) micro-pin fin heat sinks.Flow images and fast-Fourier transform (FFT) of pressure signals during flow boiling were used to explain experimental results. The boiling instability mechanisms behind unstable boiling were discussed for both water and R-123. Accordingly, no significant pressure fluctuations with respect to time averaged pressure drop were evident for the tested micro-pin fin heat sinks before and after flow boiling instability initiates. However, a step change in the pressure signals were recorded with the inception of unstable boiling, and a sharp increase in the magnitude peaks of the FFT profiles was observed in the device operated with R-123, while there was no significant change in the FFT profiles in the devices operated with water. According to complementary flow visualization studies, the oscillation frequency of the periodic flow patterns for the device operated with R-123 was higher (f∼80 Hz) than that of the devices operated with water (f∼20 Hz).

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Thermal actuators are extensively used in microelectromechanical systems (MEMS). Heat transfer through and around these microstructures are very complex. Knowing and controlling them in order to improve the performance of the micro-actuator, is currently a great challenge. This paper deals with this topic and proposes a dynamic thermal modelling of thermal micro-actuators. Thermal problems may be modelled using electrical analogy. However, current equivalent electrical models (thermal networks) are generally obtained considering only heat transfers through the thickness of structures having considerable height and length in relation to width (walls). These models cannot be directly applied to micro-actuators. In fact, micro-actuator configurations are based on 3D beam structures, and heat transfers occur through and around length. New dynamic and static thermal networks are then proposed in this paper. The validities of both types of thermal networks have been studied. They are successfully validated by comparison with finite elements simulation and analytical calculations.

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This study proposes a modification of the well-known FLASH method in order to adapt it measurements on liquids or pasty materials. The new experimental procedure requires a suitable cylindrical receptacle filled with the sample to analyze. A classical FLASH measurement is applied to this receptacle. However, as the presence of the container disturbs the conductive transfer during the transient heating of the sample, we have recourse to an identification procedure, which takes into account the disturbing influence of the receptacle to compute the thermal conductivity of the material. The modified experimental apparatus as well as the identification procedure are described in detail. Thereafter, an exhaustive estimation of the measurement accuracy is performed. The measurement uncertainty proves to be lower than 4%. Finally, we applied our method to different liquid or pasty media. A good agreement is found between the experimental results obtained and the thermal conductivity indicated in the literature for these materials.

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The aim of this study is to demonstrate the usefulness of an adaptive neuro-fuzzy inference system (ANFIS) for the prediction of transient heat transfer. An ANFIS has been applied for the transient heat transfer in thermally and simultaneously developing circular duct flow, subjected to a sinusoidally varying inlet temperature. The experiments covered Reynolds numbers in the 2528⩽Re⩽4265 range and inlet heat input in the 0.01⩽β⩽0.96 Hz frequency range. The accuracy of predictions and the adaptability of the ANFIS were examined, and good predictions were achieved for the temperature amplitudes of the transient heat transfer in thermally and simultaneously developing circular duct flow. The results show that the neuro-fuzzy can be used for modeling transient heat transfer in ducts. The results obtained with the ANFIS are also compared to those of a multiple linear regression and a neural network with a multi-layered feed-forward back-propagation algorithm.

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This paper proposes a simple change of dependent variables that guarantees positivity of turbulence variables in numerical simulation codes. The approach consists in solving for the natural logarithm of the turbulence variables which are known to be strictly positive. The approach is valid for any numerical scheme be it a finite difference, a finite volume, or a finite element method. The paper presents the turbulence equations in logarithmic variables for two popular turbulence models: the standard k-epsilon model and the k-omega model of Wilcox. The advantages of the proposed formulation and the associated numerical difficulties are discussed within the framework of an adaptive finite element method. Error estimation and mesh adaptation procedures are described. The approach is applied to flows for which analytical solution or experimental measurements are available: a shear layer and the flow over a backward facing step. The proposed approach results in a robust adaptive algorithm. Predictions compare well with measurements. (C) Elsevier, Paris.

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When analyzing the transient characteristics of solidification processes, choosing appropriately-sized time steps is difficult. Accordingly, the current study develops a modified local time truncation error (LTE)-based strategy designed to adaptively adjust the size of the time step during the simulated solidification procedure in such a way that the time steps can be adapted in accordance with the local variations in latent heat released during phase change or the effects of pure conduction in a single solid or liquid phase. In the approach presented in this work, the LTE-based time-step evaluation procedure is applied not only after a convergent temperature field is obtained at each time step, but also during the nonlinear iterations performed at each time step whenever a convergence problem is encountered. The computational accuracy and efficiency of the proposed method are demonstrated via the simulation of the one-dimensional and two-dimensional solidification problems and compared with those of other adaptive time step and the uniform time step methods. Furthermore, the performance of these approaches has also been demonstrated using fully-implicit and semi-implicit schemes.

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This paper presents numerical models of radiative heat transfer in glass manufacturing that can be performed on normal workstations, yet are sufficiently accurate for many practical applications. Since many of the glass production processes are so complex that a complete simulation is still unthinkable at present, there is a great interest for such models in order to optimise final glass products. We use simplified approximations of spherical harmonics to obtain approximate solutions of high accuracy in optically thick regimes. The arising systems of partial differential-algebraic equations of mixed parabolic–elliptic type are numerically solved by a self-adaptive discretization method based on an error-controlled finite element method in space and a one-step method of Rosenbrock-type with variable step sizes in time. The method itself judges the quality of the numerical solutions and determines adaptive strategies to keep the discretization error below a user-prescribed tolerance. Multilevel techniques based on reliable and efficient a posteriori error estimators and time embedding are used to improve the spatial discretization by local refinement and to steer the step size selection routine. We present numerical results for a typical step in glass manufacturing, the cooling of a glass cube. Our approximate solutions are validated with solutions to the full radiative transport equation and compared to Rosseland approximations widely used in the engineering practice. The results show that simplified approximations of spherical harmonics are efficient and sufficiently accurate. They are a significant improvement of the classical diffusion models.

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This paper documents a computational investigation of the film cooling effectiveness of a 3-D gas turbine endwall with one fan-shaped cooling hole. The simulations were performed for adiabatic and conjugate heat transfer models. Turbulence closure was investigated using three different turbulence models: the realizable k–ε model, the SST k–ω model, as well as the v2–f turbulence model. Results were obtained for a blowing ratio of one, and a coolant-to-mainflow temperature ratio of 0.54. The simulations used a dense, high quality, O-type, hexahedral grid with three different schemes of meshing for the cooling hole: hexahedral-, hybrid-, and tetrahedral-topology grid. The computed flow/temperature fields are presented, in addition to local, two-dimensional distribution of film cooling effectiveness for the adiabatic and conjugate cases. Results are compared to experimental data in terms of centerline film cooling effectiveness downstream cooling-hole, the predictions with realizable k–ε turbulence model exhibited the best agreement especially in the region for (2 ≤ x/D ≤ 6). Also, the results show the effect of the conjugate heat transfer on the temperature (effectiveness) field in the film cooling hole region and, thus, the additional heating up of the cooling jet itself.

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The adiabatic film cooling effectiveness and flow characteristics for a new hybrid scheme and a circular hole were investigated numerically. The new film cooling scheme is proposed for high temperature gas turbine engines in aerospace and electric power generation applications. The hybrid scheme included two consecutive film hole configurations with interior bending to direct the secondary flow in stream-wise direction. The film cooling performance with flow-field analysis for the hybrid scheme and the circular hole were investigated at blowing ratio of 0.5, 1.0 and 2.0 for 0.95 density ratios. The results showed that the hybrid scheme provided a superior local and average film cooling effectiveness performance that was enhanced for further increase in blowing ratio. Moreover, the new scheme enhanced the downstream overall area-average film cooling effectiveness compared to the circular film hole. Subsequently, film cooling and conjugate heat transfer were combined to investigate the cooling effectiveness of the hybrid scheme at Br = 0.5 and 1.0 for different flow arrangements, specifically: parallel flow and jet impingement with two different gap heights (0.8 d and 1.2 d). The hybrid scheme presented a high cooling effectiveness by combining film cooling and conjugate heat transfer. The jet impingement configuration enhanced the upstream flow circulation which has a significant effect on convective heat transfer. Furthermore, a large gap height with jet impingement enhanced the downstream cooling effectiveness compared to other conjugate and adiabatic cases studied. The conjugate configuration with large gap height provided the highest overall laterally averaged cooling effectiveness compared to other conjugate and adiabatic cases studied.As a result, the hybrid scheme is able to minimize the cooling flow rate significantly since it provided superior cooling effectiveness at a lesser secondary flow rate, thus increasing overall engine efficiency.

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A non-adiabatic capillary tube in a transcritical CO2 heat pump cycle has been simulated to investigate the effect of parameters such as gas cooler and evaporator temperature, capillary tube diameter and heat exchanger length on various performance indicators. The homogeneous flow model is employed to simulate two-phase flow in the non-adiabatic capillary tube. Fundamental equations of mass, energy and momentum are solved simultaneously through an iterative process. Single and two-phase heat transfer coefficients are calculated by employing appropriate empirical correlations. Subcritical and supercritical thermodynamic and transport properties of CO2 are calculated employing an in-house precision property code.Lowering evaporator temperature is found to be more effective for heat transfer from the capillary tube compared to the gas cooler temperature. Heat transfer rate variation with respect to gas cooler temperature in case of CO2 is distinctly different compared to conventional refrigerants due to its transcritical nature and is influenced by initial quality, mass flow rate of the refrigerant and the prevailing temperature difference at the gas cooler. Increase in gas cooler temperature causes the heat transfer rate to first increase and then to decrease. Lowering evaporator and gas cooler temperature increases the cooling capacity. Throttling effect decreases rapidly as internal tube diameter becomes larger leading to higher mass flow rate of the refrigerant. Shorter inlet adiabatic capillary length with larger heat exchanger length is better for heat transfer. This study is an attempt to allay the scepticism prevailing in the parlance of CO2 based transcritical systems overemphasising the need for a throttle valve to control the optimum discharge pressure.

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A fibre optical probe is used to measure the radial distribution of void fraction and bubble frequency of adiabatic water-air two-phase flow in an inclined tube. Three typical void fraction distributions can be established for vertical two-phase flow: sliding bubble flow, coring bubble flow, and an intermediate type. These typical distributions are influenced by the angle of inclination in different ways. In case of coring bubble flow, the void fraction maximum near the tube axis moves to the upper part of the cross-section when the vertical tube changes to the horizontal position. In case of sliding bubble flow, one of the void fraction maxima near the tube wall is increased (upper part of cross-section) and the other one is decreased (lower part of cross-section) when the inclination changes from vertical to horizontal. The flow pattern transition can also be seen in the change of equivalent bubble diameters. (C) Elsevier, Paris.

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