[show abstract][hide abstract] ABSTRACT: Unsteady two-dimensional stagnation point flow of a nanofluid over a stretching sheet is investigated numerically. In contrast to the conventional no-slip condition at the surface, Navier's slip condition has been applied. The behavior of the nanofluid was investigated for three different nanoparticles in the water-base fluid, namely copper, alumina and titania. Employing the similarity variables, the governing partial differential equations including continuity, momentum and energy have been reduced to ordinary ones and solved via Runge-Kutta-Fehlberg scheme. It was shown that a dual solution exists for negative values of the unsteadiness parameter A and, as it increases, the skin friction Cfr grows but the heat transfer rate Nur takes a decreasing trend. The results also indicated that, unlike the stretching parameter ε, increasing in the values of the slip parameter λ widen the ranges of the unsteadiness parameter A for which the solution exists. Furthermore, it was found that an increase in both ε and λ intensifies the heat transfer rate.
[show abstract][hide abstract] ABSTRACT: In this study MHD effect on natural convection heat transfer in an enclosure filled with nanofluid is investigated. The transport equations used in the analysis took into account the effect of Brownian motion and thermophoresis parameters. The Navier Stokes equations in their vorticity-stream function form are used to simulate the flow pattern, isotherms and concentration. The governing equations are solved via Control Volume based Finite Element Method. The inner and outer circular walls are maintained at constant temperatures while two other walls are thermally insulated. The heat transfer between cold and hot regions of the enclosure cannot be well understood by using isotherm patterns so heatline visualization technique is used to find the direction and intensity of heat transfer in a domain. Effect of Hartmann number (Ha = 0, 30, 60 and 100), buoyancy ratio number (Nr = 0.1–4) and Lewis number (Le = 2, 4, 6 and 8) on streamline, isotherm, isoconcentration and heatline are examined. Also a correlation for Nusselt number corresponding to active parameters is presented. The results indicate that Nusselt number is an increasing function of buoyancy ratio number but it is a decreasing function of Lewis number and Hartmann number. Also it can be concluded that as buoyancy ratio number increases the effects of other active parameters are more pronounced.
[show abstract][hide abstract] ABSTRACT: In this paper the process of solidification and melting of a phase change material is investigated in fin and tube heat exchanger. The shell side including around the tubes and spaces between fins is filled with the material R35 allocated to store energy of water, as heat transfer fluid, which flows inside the tubes. Experimental apparatus is used to investigate the effect of flow rate, inlet temperature and geometrical parameter (fin pitch) on charging and discharging processes of the phase change material. The shell side is a rectangular cube in which a continuous spiry tube creates a heat transfer surface. Results indicate that utilizing fins increases fin average temperature regardless of flow regime. While reduction in fin pitch doesn't affect this parameter sensibly for both regimes. By the increase of inlet temperature from Th = 50 °C to Th = 60 °C, melting time decreases more severally in comparison with the same rise from Th = 60 °C to Th = 70 °C.
International Communications in Heat and Mass Transfer 01/2014; · 2.21 Impact Factor
[show abstract][hide abstract] ABSTRACT: Unsteady motion of a rigid spherical particle in a quiescent shear-thinning power-law fluid was investigated analytically. The accurate series solution was found by coupling the homotopy-perturbation method (HPM) and the variational iteration method (VIM). The results were compared with those obtained from VIM and the established finite difference scheme. It was shown that both methods (VIM and HPM–VIM) gave accurate results; however, the amount of calculations required for HPM–VIM was significantly reduced. In addition to improved efficiency, it was revealed that HPM–VIM leads to completely reliable and precise results. The terminal settling velocity—that is the velocity at which the net forces on a falling particle eliminate—for three different spherical particles (made of plastic, glass and steel) and three flow behavior index n, in two sets of power-law non-Newtonian fluids was investigated, based on the series solution. Analytical results obtained indicated that the time of reaching the terminal velocity in a falling procedure is significantly declined with growing the particle size. Further, with approaching flow behavior to Newtonian behavior from shear-thinning properties of flow (n → 1), the transient time to achieving the terminal settling velocity is decreased.
Journal of Molecular Liquids 01/2014; · 1.68 Impact Factor
[show abstract][hide abstract] ABSTRACT: In this study, entropy generation minimization (EGM) was employed to optimize fluid flow and heat transfer over a moving wedge. Governing partial differential equations including continuity, momentum and energy are reduced to ordinary ones using similarity variables and solved numerically. The novelty of this study is to consider the effects of the moving wedge parameter λ, to find the stable system via entropy generation minimization (EGM) method. The results indicated that as the slope of the wedge increases, the absolute values of the optimum moving wedge parameter λo grow as well. Moreover, it was found that the minimum value of entropy generation happens for the negative values of λo which gets smaller as Falkner–Skan power law parameter m increases.
[show abstract][hide abstract] ABSTRACT: This paper deals with the mixed convective heat transfer of nanofluids through a concentric vertical annulus. Because of the non-adherence of the fluid-solid interface in the presence of nanoparticle migrations, known as slip condition, the Navier’s slip boundary condition was considered at the pipe walls. The employed model for nanofluid includes the modified two-component four-equation non-homogeneous equilibrium model that fully accounts for the effects of nanoparticles volume fraction distribution. Assuming the fully developed flow and heat transfer, the basic partial differential equations including continuity, momentum, and energy equations have been reduced to two-point ordinary boundary value differential equations and solved numerically. Two cases including constant heat flux at the outer wall and insulated inner wall (Case A) and constant heat flux at the inner wall with insulated outer wall (Case B) have been considered. Results indicate that the buoyancy has negative effects on the efficiency of the system; however, slip velocity at the surface enhances both the heat transfer rate and the efficiency.
[show abstract][hide abstract] ABSTRACT: The aim of this paper is to find a general mathematical expression for amperometric enzyme
kinetics problems. The variational iteration method coupled with Padé approximation (VIM-Padé) is used to attain a reliable mathematical expression based on the rational functions. The
accuracy of the results is shown in two cases of the electrochemical polymerization on the
electrode surfaces. The comparisons indicated that the presented mathematical expression is not
only a general model—which could be used in most amperometric enzyme kinetics problems—
but also gives more accurate results than the mathematical expressions previously developed for
Journal of electroanalytical chemistry 12/2013; In Press. · 2.67 Impact Factor
[show abstract][hide abstract] ABSTRACT: In this paper, heat transfer and flow analysis for a non-Newtonian third grade nanofluid flow in porous medium of a hollow vessel in presence of magnetic field are simulated analytically and numerically. Blood is considered as the base third grade non-Newtonian fluid and gold (Au) as nanoparticles are added to it. The viscosity of nanofluid is considered a function of temperature as Vogel's model. Least Square Method (LSM), Galerkin method (GM) and fourth-order Runge-Kutta numerical method (NUM) are used to solve the present problem. The influences of the some physical parameters such as Brownian motion and thermophoresis parameters on non-dimensional velocity and temperature profiles are considered. The results show that increasing the thermophoresis parameter (Nt) caused an increase in temperature values in whole domain and an increase in nanoparticles concentration just near the inner wall of vessel. Furthermore by increasing the MHD parameter, velocity profiles decreased due to magnetic field effect.
Computer methods and programs in biomedicine 11/2013; · 1.14 Impact Factor
[show abstract][hide abstract] ABSTRACT: This work aims to focus on the study of natural convection heat transfer characteristics in a vertical wall embedded in a non-Darcy porous medium filled with nanofluids.
International Journal of Numerical Methods for Heat and Fluid Flow 11/2013; 23. · 1.09 Impact Factor
[show abstract][hide abstract] ABSTRACT: Combustion process for iron particles burning in the gaseous oxidizing medium is investigated using the Boubaker polynomial expansion scheme (BPES) and the differential transformation method (DTM). Effects of thermal radiation from the external surface of burning particle and alterations of density of iron particle with temperature are considered. The solutions obtained using BPES technique and DTM are compared with those of the fourth-order Runge-Kutta numerical method. Results reveal that BPES is more accurate and reliable method than DTM. Also the effects of some physical parameters that appeared in mathematical section on temperature variations of particles as a function of time are studied.
[show abstract][hide abstract] ABSTRACT: A numerical investigation is carried out to study the effect of splitter’s inclination angle behind an inclined square cylinder on the forced convection heat transfer in a plan channel using the lattice Boltzmann method (LBM). The simulations are conducted for the pertinent parameters in the following ranges: the Reynolds number Re=50–300, the gap ratio G/d = 2, and the splitter’s inclination angle θ = 0°−90°. The results show that with the increase in the angle of the splitter, the drag coefficient initially decreases and then increases. Moreover, the time-averaged Nusselt number at a certain angle increases noticeably.
Applied Mathematics and Mechanics 05/2013; 34(5). · 0.65 Impact Factor
[show abstract][hide abstract] ABSTRACT: The present article solves the couple equations of a spherical solid particle’s motion in plane coquette fluid flow by using the HPM-Padé technique which is a combination of the Homotopy Perturbation Method (HPM) and Padé approximation. The series solutions of the couple equations are developed. Generally, the truncated series solution is adequately in a small region and to overcome this limitation, the Padé techniques which have the advantage of turning the polynomial approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. The current results compared with those derived from HPM and the established fourth order Runge–Kutta method in order to ascertain the accuracy of the proposed method. It is found that this method can achieve more suitable results in comparison to HPM.
[show abstract][hide abstract] ABSTRACT: In the present work attempts are made to enhance the heat transfer rate in shell and coiled tube heat exchangers experimentally. Hot water flows in helical tube and cold water flows in the shell side. Tube and shell side heat transfer coefficients are determined using Wilson plots. Experimental apparatus and Taguchi method are used to investigate the effect of fluid flow and geometrical parameters on heat transfer rate. After experiments, Taguchi method is used for finding the optimum condition for the desired parameters in the range of 0.0813 < Dc < 0.116, 13 < Pc < 18, tube and shell flow rates from 1 to 4 LPM. Then the optimum condition according to the overall heat transfer coefficient for the whole heat exchanger is found. Results indicate that the higher coil diameter, coil pitch and mass flow rate in shell and tube can enhance the heat transfer rate in these types of heat exchangers. Contribution ratio obtained by Taguchi method shows that shell side flow rate, coil diameter, tube side flow rate and coil pitch are the most important design parameters in coiled heat exchangers.
[show abstract][hide abstract] ABSTRACT: The steady two-dimensional boundary layer flow over a wedge, which is called Falkner-Skan flow is studied numerically to analyze the entropy generation inside the boundary layer. Constant wall temperature with no-slip boundary condition for velocity has been considered. Applying the transformation of governing equations including continuity, momentum and energy via similarity variables, a dimensionless equation for entropy generation inside the boundary layer is obtained for the first time. Analyzing the Bejan number, it is found that as Falkner-Skan power law parameter increases, the share of generated entropy due to fluid friction in total entropy generation increases. Finally, the effects of different parameters on the entropy generation are discussed and the physical interpretations of the results are explained in details. Introduction Boundary layers are thin regions next to the wall in the flow where viscous forces are important. The so called wall can be in various geometrical shapes. Blasius  studied the simplest boundary layer over a flat plate. The boundary layer flow over a static or a moving wedge in a viscous fluid (regular fluid) has been considered by Riley and Weidman  and Yacob et al. , which is an extension of the flow over a static wedge considered by Falkner and Skan . They employed a similarity transformation that reduces the partial differential boundary layer equations to a nonlinear third-order ordinary differential equation before solving it numerically. A large amount of literatures on this problem has been cited in the books by Schlichting and Gersten  and Leal . Beside the boundary layers, Entropy plays an essential role in our understanding of many diverse phenomena in many fields. It also form the basis of most modern formulations of both equilibrium and nonequilibrium thermodynamics. Entropy generation can be viewed as a measure of disorder or disorganization generated during a process, in other words it represents the addition thermodynamic irreversibility in a process which can causes more energy and power losses in the system so it is necessary to monitor this concept in each process to have a stable system. Bejan presented a method named Entropy Generation Minimization [EGM] in 1996  to solve this problem. Other scientists have done some researches in this field too. Sahina et al.  investigated entropy generation in straight pipes and recently Tandiroglu  studied entropy generation for turbulent flow in a circular tube with baffle. In this paper, for the first time, we have presented an equation for entropy generation inside the boundary layer for a wedge. Momentum, energy and entropy generation equations over a wedge are solved with Shooting method as a powerful numerical technique. Moreover, Diagrams are plotted and the physical interpretations of the results are discussed in details.
[show abstract][hide abstract] ABSTRACT: In this paper the lattice Boltzmann method (LBM) is employed to simulate deformation and breakup of a falling drop under gravity and electric field. First the two-phase LBM is applied to verify the Laplace law for static drops. Then relaxation of a square droplet is conducted. Furthermore a comparison is made with Taylor theoretical results for different electrical capillary number, permittivity and conductivity ratio. It is seen that with permittivity ratio larger than conductivity, droplet takes an oblate and for lower ratio takes prolate shape. It is seen that for relatively low Eotvos number where the surface tension is a dominant factor and for high Ohnesorge number where the viscosity plays an important role shear breakup occurs. On the other hand it is also found that by increasing the Eotvos number and decreasing Ohnesorge number drop distorts more and back breakup happens in addition to shear breakup.
[show abstract][hide abstract] ABSTRACT: In this paper, entropy generation minimization (EGM) was employed in order to achieve a thermodynamic optimization of fluid flow and heat transfer over a flat plate. The basic boundary layer equations including continuity, momentum, energy, and entropy generation have been reduced to a two-point boundary value problem via similarity variables and solved numerically via Runge–Kutta–Fehlberg scheme. The novelty of this study was to consider the effects of velocity ratio λλ – which represents the ratio of the wall velocity to the free stream fluid velocity – in a thermodynamic system. Focusing on the velocity ratio as a pivotal parameter, in view of minimizing the entropy generation, the optimum value of λ=λoλ=λo was achieved. Moreover, considering Bejan number, it was shown that the region, in which the maximum entropy generates, gets closer to the plate as λλ increases.
[show abstract][hide abstract] ABSTRACT: Temperature distribution equation and refrigeration efficiency for fully wet circular porous fins with variable sections are introduced in this study by a new modified wet fin parameter presented by Sharqawy and Zubair. This parameter can be calculated without knowing the fin tip condition by considering the temperature and humidity ratio differences for the driving forces of heat and mass transfer, respectively. It’s assumed that heat and mass convective coefficients vary with fin temperature and heat transfer through porous media is simulated using passage velocity from the Darcy's model. After presenting the governing equation, Least Square Method (LSM) and fourth order Runge-Kutta method (NUM) are applied for predicting the temperature distribution in the sample aluminum porous fins. After that, effects of porosity, Darcy number, Rayleigh number, Lewis number and etc. on fin efficiency are examined. As a main outcome, for reaching to high values of fin efficiency, rectangular fin should be used instead of convex and triangular sections.
International Journal of Refrigeration 01/2013; · 1.79 Impact Factor
[show abstract][hide abstract] ABSTRACT: The steady two-dimensional boundary layer flow of nanofluids over a flat plate is studied analytically to analyze the generated entropy inside the boundary layer at a constant wall temperature. Applying the transformation of the PDE equations of continuity, momentum and energy to ODE ones by similarity variables, a dimensionless equation for entropy generation inside the boundary layer is presented. The most accurate series solution was found by coupling the homotopy-perturbation method (HPM) and the variational iteration method (VIM), which provides an effective technique for solving strongly nonlinear ordinary differential equations. The analytical results indicated that the generated entropy strongly depends on the nanoparticle volume fraction (ϕ), Prandtl, Eckert and Reynolds numbers. Based on the series solution, the effects of ϕ on velocity, temperature and entropy generation were explained in details and the related figures are plotted.