Coupled heat and mass transfer by MHD free convection flow along a vertical plate with streamwise temperature and species concentration variations

The problem of steady, laminar, coupled heat and mass transfer by MHD free convective boundary‐layer flow along a vertical flat plate with the combined effects of streamwise sinusoidal variations of both the surface temperature and the species concentration in the presence of Soret and Dufour effects is considered. A suitable set of dimensionless variables is used to transform the governing equations of the problem into a non‐similar form. The resulting non‐similar equations have the property that they reduce to various special cases previously considered in the literature. An adequate and efficient implicit, tri‐diagonal finite difference scheme is employed for the numerical solution of the obtained equations. Various comparisons with previously published work are performed and the results are found to be in excellent agreement. A representative set of numerical results for the velocity, temperature, and concentration profiles as well as the surface shear stress, rate of heat transfer, and the rate of mass transfer is presented graphically for various parametric conditions and is discussed. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21033     

Mixed Convection Over a Vertical Plate in a Doubly Stratified Fluid‐Saturated Non‐Darcy Porous Medium with Cross‐Diffusion Effects

The present article investigates the influence of Dufour and Soret effects on mixed convection heat and mass transfer over a vertical plate in a doubly stratified fluid‐saturated porous medium. The plate is maintained at a uniform and constant wall heat and mass fluxes. The Darcy–Forchheimer model is employed to describe the flow in porous medium. The nonlinear governing equations and their associated boundary conditions are initially transformed into dimensionless forms. The resulting system of nonlinear partial differential equations is then solved numerically by the Keller‐box method. The variation of the dimensionless velocity, temperature, concentration, heat, and mass transfer rates for different values of governing parameters involved in the problem are analyzed and presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21114     

Heat and mass transfer effects on peristaltic flow of an Oldroyd‐B fluid in a channel with compliant walls

This investigation describes the peristaltic motion of a magnetohydrodynamic (MHD) Oldroyd‐B fluid with heat and mass transfer. An incompressible Oldroyd‐B fluid is considered in a channel with flexible walls. The relevant equations are developed by employing equations of continuity, momentum, energy, and concentration. Expressions of stream function, temperature, concentration field, and heat transfer coefficient are presented when the wave number is small. The obtained solutions are graphically discussed for the several interesting parameters entering into the problem. It is found that relaxation and retardation times have opposite effects on the size of the trapped bolus. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20380     

Solutal Dispersion and Viscous Dissipation Effects on Non‐Darcy Free Convection Over a Cone in Power‐Law Fluids

The effects of viscous dissipation and solutal dispersion on free convection about an isothermal vertical cone with a fixed apex half angle, pointing downwards in a power‐law fluid‐saturated non‐Darcy porous medium are analyzed. The governing partial differential equations are transformed into partial differential equations using non‐similarity transformation. The resulting equations are solved numerically using an accurate local non‐similarity method. The accuracy of the numerical results is validated by a quantitative comparison of the heat and mass transfer rates with previously published results for a special case and the results are found to be in good agreement. The effects of viscous dissipation, solutal dispersion, and/or buoyancy ratio on the velocity, temperature, and concentration field as well as on the heat and mass transfer rates are illustrated, by insisting on the comparison between pseudo‐plastic, dilatant, and Newtonian fluids. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 476–488, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21095     

DOUBLE-DIFFUSIVE CONVECTION IN A POROUS ENCLOSURE WITH COOPERATING TEMPERATURE AND CONCENTRATION GRADIENTS AND HEAT GENERATION OR ABSORPTION EFFECTS

The problem of unsteady, laminar double-diffusive convective flow of a binary gas mixture in a rectangular enclosure filled with a uniform porous medium is considered. A temperature-dependent heat source or sink is assumed to exist within the enclosure boundaries. Transverse cooperating gradients of heat and mass are applied on the two opposing vertical walls of the enclosure while the other two horizontal walls are adiabatic and impermeable to mass transfer. A numerical solution based on the finite-difference methodology is obtained. Representative results illustrating the effects of the inverse Darcy number, the heat generation or absorption coefficient, and the buoyancy ratio on the contour maps of the streamline, temperature, and concentration as well as the profiles of velocity, temperature, and concentration at the midsection of the enclosure are reported. In addition, results for the average Nusselt and Sherwood numbers are presented in tabulated form and discussed for various parametric conditions.     

Effects of diameter ratio of adiabatic circular cylinder and tilt angle on natural convection from a square open tilted cavity

A numerical analysis is carried out to study the performance of natural convection inside a square open tilted cavity filled with air. An adiabatic circular solid cylinder is placed at the center of the cavity and the sidewall in front of the breathing space is heated by a constant heat flux. The top and bottom walls are kept at the ambient constant temperature. Two‐dimensional forms of Navier–Stokes equations along with the energy equations are solved using the Galerkin finite element method. Results are obtained for a range of Grashof numbers from 10³ to 10⁶ at Pr = 0.71 while the tilt angle varies from 0 to 45° and the diameter ratio of the cylinder is considered to be 0.2, 0.3, and 0.4 with constant physical properties. The parametric studies for a wide range of cylinder diameter ratios and cavity tilt angles show significant features of the present problem in terms of stream functions and temperature profiles. The computational results indicate that the heat transfer coefficient is strongly influenced by the above governing parameters. It is also found that the average Nusselt number decreases when the diameter ratio increases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21001     

Heat and mass transfer effects on MHD flow of a couple‐stress fluid in a horizontal wavy channel with viscous dissipation and porous medium

This paper looks at heat and mass transfer effects on an unsteady MHD flow of a couple‐stress fluid in a horizontal wavy porous space with travelling thermal waves in the presence of a heat source and viscous dissipation. Initially the temperatures of the walls are maintained at different constant temperatures. The analytical expressions for velocity, temperature, and concentration field are obtained by the regular perturbation technique. The results are presented graphically for various values of emerging dimensionless parameters of the problem and are discussed to show interesting aspects of the solution. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21040 PACS: 44.15.+a, 44.30.+f, 44.27.nd, 47.50.Cd     

A Mathematical Study for Laminar Boundary‐Layer Flow,Heat, and Mass Transfer of a Jeffrey Non‐Newtonian Fluid Past a Vertical Porous Plate

In this article, we investigate the nonlinear steady‐state boundary‐layer flow, heat and mass transfer of an incompressible Jeffrey non‐Newtonian fluid past a vertical porous plate. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite‐difference technique. The numerical code is validated with previous studies. The influence of a number of emerging non‐dimensional parameters, namely, Deborah number (De), Prandtl number (Pr), ratio of relaxation to retardation times (λ), Schmidt number (Sc), and dimensionless tangential coordinate (ξ) on velocity, temperature, and concentration evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate, mass transfer rate, and local skin friction are also investigated. It is found that the velocity is reduced with increasing Deborah number whereas temperature and concentration are enhanced. Increasing λ enhances the velocity but reduces the temperature and concentration. The heat transfer rate and mass transfer rates are found to be depressed with increasing Deborah number, De, and enhanced with increasing λ. Local skin friction is found to be decreased with a rise in Deborah number whereas it is elevated with increasing λ. And an increasing Schmidt number decreases the velocity and concentration but increases temperature. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21111     

Melting of a vertical ice cylinder inside a rotating cylindrical cavity filled with binary aqueous solution

The melting of a vertical ice cylinder into a homogeneous calcium chloride aqueous solution inside a rotating cylindrical cavity with several rotating speeds is considered experimentally. The melting mass and temperature are measured on four initial conditions of the solution and four rotating speeds of the cavity. The temperature of the liquid layer becomes uniform by the mixing effect resulting from cavity rotation and it enhances the melting rate of the ice cylinder. As the cavity‐rotating speed increases, the melting rate increases. The dimensionless melting mass is related to the Fourier number and the rotating Reynolds number in each initial condition, therefore an experimental equation that is able to quantitatively calculate the dimensionless melting mass is presented. It is seen that the melting Nusselt numbers increase again in the middle of the melting process. The ice cylinder continues to melt in spite of the small temperature difference between the ice cylinder and the solution. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(6): 359–373, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20211     

Numerical study of ferrofluid flow and heat transfer in the presence of a non‐uniform magnetic field in rectangular microchannels

This paper presents a numerical investigation of the hydro‐thermal behavior of a ferrofluid in rectangular minichannels in the presence of a non‐uniform magnetic field using a two‐phase mixture model and control volume technique. Effects of increasing the diameter of nanoparticles, and channel aspect ratio have also been studied. It is concluded that the magnetic field with a negative gradient increases the Nusselt number and the rate of this increment depends on the channel aspect ratio. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21004     

Effects of an unsteady thermal boundary condition on forced convection heat transfer

A numerical analysis based on adjoint formulation of unsteady forced convection heat transfer is proposed to generally evaluate effects of the thermal boundary condition on the heat transfer characteristics. A numerical solution of the adjoint problem enables us to predict the heat transfer characteristics, such as the total heat transfer rate or the temperature at a specific location, when the thermal boundary conditions change arbitrarily with time. Moreover, using the numerical solution of the adjoint problem, we can obtain the optimal thermal boundary conditions in both time and space to maximize the heat transfer at any arbitrary time. Numerical solutions of the adjoint problem in a lid‐driven cavity are presented to illustrate the capability of the present method. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(3): 237–247, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10032     

Lattice Boltzmann simulation of natural convection and heat transfer from multiple heated blocks

This study is aimed to investigate the natural convection heat transfer from discrete heat sources (similar to heated microchips) using Bhatnagar‐Gross‐Krook lattice Boltzmann method via graphics process unit computing. The simulation is carried out separately for three and six heated blocks model for different Rayleigh numbers and fixed Prandtl number, $Pr=0.71$ (air). The uniformly heated blocks are placed at the bottom wall inside a rectangular enclosure. The enclosure is maintained by the cold temperature at its left and right walls. The top and bottom surface is maintained by adiabatic conditions apart from the regions where blocks are attached to the bottom wall. The numerical code is validated with the benchmark heat transfer problem of side‐heated square cavity as well as with an experimental study for one discrete heat source. The rate of heat transfer is presented in terms of the local Nusselt and average Nusselt number for each block. It is found that the heat transfer rate becomes maximized in the leftmost and rightmost blocks due to the adjacent cold walls. It is found that the number of blocks and their positions play a substantial role in determining their collective performance on the heat transfer rate.     

Simulating magnetohydrodynamic natural convection flow in a horizontal cylindrical annulus using the lattice Boltzmann method

A numerical study is presented about the effect of a uniform magnetic field on free convection in a horizontal cylindrical annulus using the lattice Boltzmann method. The inner and outer cylinders are maintained at uniform temperatures and it is assumed the walls are insulating with a magnetic field. Detailed numerical results of heat transfer rate, temperature, and velocity fields have been presented for Pr=0.7, Ra=10³ to 5 × 10⁴, and Ha=0 to 100. The computational results show that in a horizontal cylindrical annulus the flow and heat transfer are suppressed more effectively by a radial magnetic field. It is also found that the flow oscillations can be suppressed effectively by imposing an external radial magnetic field. The average Nusselt number increases by increasing the radius ratio while it decreases by increasing the Hartmann number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21008     

Optimal homotopy asymptotic method for heat transfer in hollow sphere with robin boundary conditions

In this article, we have investigated heat transfer from a hollow sphere using a powerful and relatively new semi‐analytic technique known as the optimal homotopy asymptotic method (OHAM). Robin boundary conditions are applied on both the inner and outer surfaces. The effects of Biot numbers, uniform heat generation, temperature‐ dependent thermal conductivity, and temperature parameters on the dimensionless temperature and heat transfer are investigated. The results of OHAM are compared with a numerical method and are found to be in good agreement. It is shown that the dimensionless temperature increases with an increase in Biot number at the inner surface and temperature and heat generation parameters, whereas it decreases with an increase in the Biot number at the outer surface and the dimensionless thermal conductivity and radial distance parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 124‐133, 2014; Published online 20 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21067     

MHD boundary‐layer flow over a stretching surface with internal heat generation or absorption

This article is concerned with the steady laminar magnetohydrodynamic boundary‐layer flow past a stretching surface with uniform free stream and internal heat generation or absorption in an electrically conducting fluid. A constant magnetic field is applied in the transverse direction. A uniform free stream of constant velocity and temperature is passed over the sheet. The effects of free convection and internal heat generation or absorption are also considered. The governing boundary layer and temperature equations for this problem are first transformed into a system of ordinary differential equations using similarity variables, and then solved by a new analytical method and numerical method, by using a fourth‐order Runge–Kutta and shooting method. Velocity and temperature profiles are shown graphically. It is shown that the differential transform method solutions are only valid for small values of independent variables but the results obtained by the DTM‐Padé are valid for the entire solution domain with high accuracy. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21054     

Heat and mass transfer in a MHD non‐Darcian micropolar fluid over an unsteady stretching sheet with non‐uniform heat source/sink and thermophoresis

The effect of heat and mass transfer in a MHD non‐Darcian flow of a micropolar fluid over an unsteady stretching sheet with thermophoresis and non‐uniform heat source/sink is discussed. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The arising nonlinear problem is solved by the Keller box method. The effects of various physical parameters on skin friction, local Nusselt number, and Sherwood number are presented graphically and in tabular form. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21018     

Modeling of a Solar Water Collector with Water‐Based Nanofluid Using Nanoparticles

The pressure‐velocity form of the Navier–Stokes equations, energy equation, and concentration equation are used to represent the mass, momentum, energy, and concentration conservations of the nanofluid medium in the solar collector. The governing equations and corresponding boundary conditions are converted to dimensionless form and solved numerically by the finite element method. The physical domain is discretized by triangular mesh elements with six nodes. The working fluid is water‐based nanofluid with two nanoparticles, namely, silver (Ag) and copper oxide (CuO). The study includes computations for different values of buoyancy ratio (Nr) and Schmidt number (Sc). Flow, heat, and mass transfer characteristics are presented in the forms of streamlines, isotherms, and iso‐concentrations. In addition, results for the average radiative, convective heat and mass transfer, mean temperature and concentration of nanofluid, mid‐height horizontal‐vertical velocities, and subdomain average velocity field are offered and discussed for the above‐mentioned parametric conditions. Results show that the effects of Nr and Sc on the convective‐radiative heat and mass transfer phenomenon inside the collector are significant for all values of Nr and Sc studied. Comparison and validation with the standard experimental/numerical data is given in brief. The variation of the obtained result is presented as 34% with the result of experimental data. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 270–287, 2014; Published online 30 September 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21080     

Application of radially varying magnetic field on a peristaltic flow of non‐Newtonian fluid in the presence of heat and mass transfer

This article deals with the variable MHD effects on the peristaltic flow of a non‐Newtonian fluid in the presence of heat and mass transfer. The walls of annulus are maintained at different temperatures. Continuity, momentum concentration, and energy equations are utilized in the mathematical analysis. Two types of solutions, namely, the exact and numerical, are derived. These solutions are compared and discussed. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20314     

Free Convective Flow in an Open‐Ended Vertical Porous Wavy Channel with a Perfectly Conductive Thin Baffle

The problem of steady two‐dimensional free convective flow of a Walters fluid (model B ′) in a porous medium between a long vertical wavy wall and parallel flat wall in the presence of a heat source is discussed. The channel is divided into two passages by means of a thin, perfectly conductive plane baffle and each stream will have its own pressure gradient and hence the velocity will be individual in each stream. The governing equations of the fluid and the heat transfer have been solved subject to the relevant boundary conditions by assuming that the solution consists of two parts: a mean part and disturbance or perturbed part. Exact solutions are obtained for the mean part and the perturbed part is solved using long wave approximation. Results are presented graphically for the distribution of velocity and temperature fields for varying physical parameters such as Grashof number, wall temperature ratio, porous parameter, heat source/sink parameter, product of non‐dimensional wave number, and space‐coordinate and viscoelastic parameter at different positions of the baffle. The relevant flow and heat transfer characteristics, namely, skin friction and the rate of heat transfer at both walls, has been discussed in detail. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21118     

Mixed convective flow of two immiscible viscous fluids in a vertical wavy channel with traveling thermal waves

The problem of fully developed laminar mixed convection flow in a vertical wavy channel filled with two immiscible viscous fluids is studied analytically. Non‐linear equations governing the motion have been solved by linearization technique, wherein the flow is assumed to be in two parts; a mean part and a perturbed part. Exact solutions are obtained for the mean part and a perturbed part is solved using long wave approximation. Separate solutions are matched at the interface using suitable matching conditions. Numerical results are presented graphically for the distribution of velocity and temperature fields for varying physical parameters such as Grashof number, viscosity ratio, width ratio, and conductivity ratio. The effect of these parameters on the physical characteristics such as Nusselt number and skin friction at the walls is studied. It is found that Grashof number, viscosity ratio, width ratio, and conductivity ratio enhance the velocity parallel to the flow direction. Reversal effect is observed on the velocity which is perpendicular to the flow direction. The Nusselt number remains invariant on Grashof number. As the width ratio decreases, the Nusselt number decreases at the right wall and increases at the left wall and reversal effect is observed for variations of conductivity ratio. The skin friction increases at the left wavy wall and decreases at the right wavy wall as the Grashof number increases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20379