Mixed convection heat and mass transfer over a vertical plate in a power‐law fluid‐saturated porous medium with radiation and chemical reaction effects

Mixed convection heat and mass transfer from a vertical plate embedded in a power‐law fluid‐saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using the shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21058     

Soret and Dufour Effects on Non‐Darcy Free Convection in a Power‐Law Fluid in the Presence of a Magnetic Field and Stratification

In this article, effects of Soret and Dufour on free convection heat and mass transfer along a vertical plate embedded in a doubly stratified power‐law fluid‐ saturated non‐Darcy porous medium in the presence of a magnetic field is considered. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations, with the location along the plate as a parameter and then solved numerically. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated by insisting on the comparison between pseudo‐plastic, dilatant, and Newtonian fluids. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 592–606, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21098     

Nonsimilar solutions for mixed convection of water at 4°C over a vertical surface with a convection boundary condition in a porous medium

A boundary layer analysis has been presented for the mixed convection of water at 4°C over a vertical plate embedded in a porous medium. The Robin or convective boundary condition at the surface has been considered where the heat lost from the surface is the product of a heat transfer coefficient and the temperature difference between the surface and the free stream. The governing non‐similar boundary layer equations for both the forced and free convection dominated regimes were solved numerically by means of an implicit finite difference method. The friction factor and dimensionless heat transfer rate (Nusselt number) are presented for several values of the dimensionless heat transfer coefficient and buoyancy parameter. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21022     

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21083     

Similarity Solution to Hydromagnetic Flow Past a Continuously Moving Semi‐infinite Vertical Porous Plate with Large Suction

The problem of a two‐dimensional free convective mass transfer flow of an incompressible, viscous, and electrically conducting fluid past a continuously moving semi‐infinite vertical porous plate with large suction in the presence of a magnetic field applied normal to the plate is studied. The non‐linear partial differential equations governing the flow have been transformed by a set of similarity transformations into a system of non‐linear ordinary differential equations. The resulting system of the similarity equations are solved analytically adopting the perturbation technique. The expressions for the velocity field, temperature field, concentration field, induced magnetic field, drag coefficient, and the coefficient of the rate of heat and mass transfer at the plate are obtained. The results are discussed in details through graphs and tables to observe the effect of various physical parameters involved in the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21097     

MHD flow over an inclined radiating plate with the temperature‐dependent thermal conductivity,variable reactive index,and heat generation

We study the effects of higher‐order chemical reaction and heat generation on coupled heat and mass transfer by MHD mixed convection from a permeable radiating inclined plate with the thermal convective boundary condition. The governing boundary layer equations are formulated and transformed into a set of similarity equations using dimensionless similarity variables developed by Lie group analysis. The resulting equations are then solved numerically using Maple 13 which uses a fourth–fifth order Runge–Kutta–Fehlberg algorithm for solving nonlinear boundary value problems. A representative set of numerical results are displayed graphically and discussed to show some interesting aspects of the parameters: convective heat transfer (γ), the angle of inclination (α), generation order of chemical reaction (n), reaction rate (λ), the Prandtl number (Pr), and the Schmidt number (Sc) on the dimensionless axial velocity, the temperature, and the concentration profiles. Also effects of pertinent parameters on the skin friction factor, the rate of heat, and the rate of mass transfer are obtained and displayed in tabular form. Good agreement is found between the numerical results of the present paper with the earlier published works under some special cases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20409     

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     

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     

MHD Flow of a Couple‐Stress Fluid and a Viscous Fluid in a Vertical Wavy Porous Space with Traveling Thermal Waves and Temperature‐Dependent Heat Source

In this article, the heat transfer analysis is investigated for magnetohydrodynamic (MHD) flow in a vertical wavy porous space with one region filled with couple‐stress fluid and the other region with a viscous fluid in the presence of a temperature‐dependent heat source. The flow is generated by the periodic thermal waves prescribed at the wavy walls of the channel and the transport properties of both fluids are assumed constant. The resulting dimensionless coupled nonlinear equations are assumed into a mean (zeroth‐order) part and a perturbed part, using amplitude as a small parameter. The perturbed quantities are obtained by using the regular perturbation method. The results are graphically presented and the role of pertinent parameters on the heat transfer characteristics of the fluid flow is discussed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 134‐147, 2014; Published online 3 September 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21068     

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     

Free Convective Flow of Pseudo‐Plastic and Newtonian Fluid Past a Convectively Heated Vertical Plate in a Darcian Porous Medium with Heat Generation/Absorption

We study the effect of thermal convective boundary condition and yield stress on free convection heat transfer for a pseudo‐plastic and Newtonian fluid past a permeable vertical flat plate which is embedded in a Darcian porous medium in the presence of heat generation/absorption numerically. Instead of using similarity transformations available in the literature, we have developed them by one point transformation and hence transform the governing boundary layer equations into corresponding similarity equations. The resulting similarity equations were solved using Runge–Kutta–Fehlberg fourth fifth (RKF45) order numerical method. The effect of the governing parameters, namely the power index of pseudo‐plastic fluids n, the rheological parameter Ω, heat generation/absorption parameter Q, suction/injection parameter , and the convective heat parameter B on the dimensionless velocity, the temperature and the heat transfer rates were investigated. A close agreement is found between our results and published results. Our present study finds application in printing and polymer industries and fluid phenomena associated with concentrated suspensions.     

A novel analytical solution of heat transfer of a micropolar fluid through a porous medium with radiation by DTM‐Padé

In this paper, the differential transform method (DTM) was applied to heat transfer of a micropolar fluid through a porous medium with radiation. The governing equations can be written as a system of nonlinear ordinary differential equations. The approximate solutions of these equations were obtained in the form of series with easily computable terms. Then, Padé approximant was applied to increase the convergence rate of the series. The results obtained in this study were compared with the numerical results (fourth‐order Runge–Kutta method). © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res, 39(8), 575–589, 2010; Published online 26 July 2010 in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20317     

A study on heat transfer in a second‐grade fluid through a porous medium with the modified differential transform method

This study investigates the boundary‐layer flow and heat transfer characteristics in a second‐grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM‐Padé. The DTM‐Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary‐layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM‐Padé with numerical solution (fourth‐order Runge–Kutta with shooting method) illustrates that the DTM‐Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030     

Effect of double stratification on mixed convection heat and mass transfer from a vertical surface in a fluid‐saturated porous medium

This paper presents the mixed convection heat and mass transfer near a vertical surface in a stratified porous medium using an integral method. The conservation equations that govern the problem are reduced to a system of coupled non‐linear ordinary differential equations, which is then reduced into a single algebraic equation using exponential profiles for the temperature and concentration. The results for heat and mass transfer rates in terms of Nusselt and Sherwood number are presented for a wide range of governing parameters like the buoyancy ratio (N), Lewis number (Le), flow driving parameter (Ra/Pe), in addition to both thermal and solutal parameters (S and R). The results indicate that the stratification effects have considerable influence on both the heat and mass transfer rates. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20300     

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     

Cross–diffusion effects on mixed convection from an exponentially stretching surface in non–Darcy porous medium

The Soret and Dufour effects on mixed convection flow and heat and mass transfers from an exponentially stretching surface in a quiescent fluid–saturated non–Darcy porous medium is studied. Stretching velocity, wall temperature, and wall concentration are assumed to have specific exponential function forms. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using an implicit finite difference scheme known as the Keller–box method. The present results are found to be in excellent agreement with previously published work on various special cases of the problem. The influence of buoyancy, Soret and Dufour numbers, and Darcy and non–Darcy parameters on the convective transport in the boundary layer region is analyzed. Also, the numerical values of the skin friction, heat, and mass transfer coefficients for different values of governing parameters are also tabulated. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21032     

Forced convection and entropy generation inside a channel with a heat‐generating porous block

The flow pattern and heat transfer in a composite system containing a porous region has received considerable attention due to its importance in many engineering applications. In this study a thermal lattice Boltzmann model with nine velocities, D2Q9, is employed to investigate the fluid flow, heat transfer, and entropy generation inside a channel with a heat‐generating porous block. The effects of the porous block's length, porosity, and the Reynolds number, overflow pattern, heat transfer, and entropy generation were studied. The mentioned parameters have different effects on heat transfer and conjugate phenomena. By increasing the block length, Reynolds number, and porosity the dimensionless entropy generation will reduce. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21017     

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     

MHD nonlinear natural convection from a uniformly moving porous vertical plate with constant heat and mass flux in the presence of thermal radiation,diffusion-thermo,heat sink,and chemical reaction

An attempt has been made to investigate the problem of nonlinear free convection heat and mass transfer flow past an infinite vertical porous plate embedded in a porous medium by taking into account thermal radiation and heat sink with constant heat and mass flux. Transversely oriented and of uniform strength $B_0$, a magnetic field has been introduced to the fluid area. The nonlinear density variation with temperature as well as concentration are the basis for the current physical situation, which is explained by this mathematical model. Exact solutions are derived for momentum equation, energy equation, and species continuity equation under the relevant boundary conditions. The dimensionless governing equations are analytically solved. The influence of various physical parameters, such as Dufour number, Schmidt number, thermal Grashof number, magnetic parameter, mass Grashof number, heat sink, thermal radiation, Prandtl number, chemical reaction parameter on the flow, and transport characteristic, has been presented graphically and in tabular form. The novelty of the present investigation is that here both constant heat and mass flux at the plate are taken into account in addition to thermal radiation and heat sink. The findings of the mathematical study demonstrate that velocity, temperature, and skin friction intensify with a rise in the Dufour number this is due to the fact that the convection current becomes stronger as the Dufour number rises. Fluid's concentration declines as the Schmidt number grows, or the concentration rises as the mass diffusivity rises. Fluid temperature is enhanced with high thermal diffusivity. Frictional resistance on the plate hikes due to thermal buoyancy force.     

Mixed convective heat and mass transfer on a peristaltic flow of a non‐Newtonian fluid in a vertical asymmetric channel

In the present analysis we discuss the effects of mixed convective heat and mass transfer on the peristaltic flow of a non‐Newtonian fluid in a vertical asymmetric channel. The flow is investigated in a wave frame of reference moving with the velocity c away from the fixed frame. The governing equations for the present flow problem are first modeled and then discussed. The analytical solution of the present flow problem is discussed using regular perturbation technique. The graphical results are discussed to see the effects of various physical parameters of interest. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21020