Modeling and CFD Simulation of a Mixed‐Convection Flow of Regular Fluids and Nanofluids in Vertical Porous and Regular Channels

In this article, the problem of combined forced and free convection in vertical porous and regular channels for both regular fluids and nanofluids has been solved using the CFD technique in the entrance regions of momentum and heat transfer taking into account the influences of viscous heating and inertial force. In this regard, various types of viscous dissipation models reported in the literature such as the Darcy model, the power of the drag force model, and the clear fluid‐compatible model were applied. In the case of nanofluid flow, both the Brownian and thermophoresis molecular transfer mechanisms were considered. The dimensionless distributions of velocity, temperature, and the volume fraction of nanoparticles were determined in terms of corresponding dimensionless numbers such as the Grashof, Reynolds, Forchheimer, Brinkman, and Darcy numbers. The predicted results were validated using fully‐developed distributions of velocity and temperature. In addition, the influences of the Grashof number value on the temperature and velocity distributions in the entrance and fully‐developed regions were examined carefully. In addition, temperature and velocity distributions of nanofluids and regular fluids in porous and regular channels were compared. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 243–269, 2014; Published online 30 September 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21079     

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     

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     

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     

Transient and non-Darcian effects on natural convection flow in a vertical channel partially filled with porous medium: Analysis with Forchheimer–Brinkman extended Darcy model

The present study addresses the transient as well as non-Darcian effects on laminar natural convection flow in a vertical channel partially filled with porous medium. Forchheimer–Brinkman extended Darcy model is assumed to simulate momentum transfer within the porous medium. Two regions are coupled by equating the velocity and shear stress in the case of momentum equation while matching of the temperature and heat flux is taken for thermal energy equation. Approximate solutions are obtained using perturbation technique. Variations in velocity field with Darcy number, Grashof number, kinematic viscosity ratio, distance of interface and variations in temperature distribution with thermal conductivity ratio, distance of interface are obtained and depicted graphically. The skin-friction and rate of heat transfer at the channel walls are also derived and the numerical values for various physical parameters are tabulated.     

Numerical Investigation of Nanofluid Mixed‐Convection Flow in the Entrance Region of a Vertical Channel Partially Filled with Porous Medium

In this article, transient two‐dimensional mixed convection of nanofluids in the entrance region of a vertical channel has been studied carefully. The geometry under consideration consisted of a parallel‐plate channel partly filled with a porous medium with a constant wall temperature. In the free flow region, the two‐dimensional flow field has been governed by the Navier–Stokes equations. The general formulation of the momentum equations accounting for the inertial and the viscous effects in the presence of a porous medium has been used. Viscous dissipation effects have also been incorporated in the thermal energy equation. Effects of Brownian diffusion and thermophoresis have also been included for nanoparticles in the nanofluid. The governing equations have been given in terms of the stream function‐vorticity formulation and have been non‐dimensionalized and then solved numerically subject to appropriate boundary conditions. The characteristics of the flow and temperature fields have been presented in the terms of mixed‐convection parameter (GR), Brinkman number (Br), Darcy number (Da), Lewis number (Le), and other important parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 607–627, 2014; Published online 21 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21099     

Flow and heat transfer of couple‐stress permeable fluid sandwiched between viscous fluid layers

The fully developed flow and heat transfer in a horizontal channel consisting of couple‐stress permeable fluid sandwiched between viscous fluid layers is investigated analytically. The channel walls are maintained at two different constant temperatures. The transport properties of the fluids in all regions are assumed to be constant. The governing equations are linear ordinary differential equations and hence closed form solutions are obtained. Effects of physical parameters such as viscosity ratio, thermal conductivity ratio, Eckert number, and Prandtl number on the flow are reported. An interesting and new approach is incorporated to analyze the flow for strong, weak, and comparable porosity with couple‐stress parameter. The variation of rate of heat transfer for different values of couple stress parameter and porosity is also discussed. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21007     

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     

A basic study on humidity recovery by using micro‐porous media (Effects of thermal condition of fluids and geometrical condition of apparatus on transport performance)

Using an experimental apparatus to examine the performance of heat and mass transfer between constant‐temperature water and dry air through a porous plate having extremely small pores, the effects of the thermal conditions in the fluids and the geometric condition of the apparatus on moisture transport were measured. The effects of water temperature, thickness of the porous plate, and channel height of the flowing air on moisture transport are noticeable. However, the effect of air temperature in the channel inlet on moisture transport is slight. In addition, in order to evaluate the degree of air humidity absorption, a parameter called the moisture absorption rate was introduced. The moisture absorption rate was shown to decrease with increasing air velocity and varies only slightly for a plate thickness of 1 mm and decreases for a plate thickness of 3.5 mm with increasing water temperature. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(8): 568–581, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20133     

Analysis of fluid flow and heat transfer in a channel with staggered porous blocks

Fluid flow and heat transfer characteristics in a channel with staggered porous blocks were numerically studied in this paper. The Navier–Stokes and Brinkman–Forchheimer equations were used to model the fluid flow in the open and porous regions, respectively. Coupling of the pressure and velocity fields was resolved using the SIMPLER algorithm. The local thermal equilibrium model was adopted in the energy equation to evaluate the solid and fluid temperatures. The effect of Darcy number, Reynolds number, porous block height and width on the velocity field were studied. In addition, the effects of the above parameters as well as the thermal conductivity ratio between the porous blocks and the fluid on the local heat transfer were analyzed. The pressure drops across the channel for different cases were discussed. The results show that the flow behavior and its associated local heat transfer are sensitive to the variation of the above parameters. It is predicted by the present study that an increase in the thermal conductivity ratio between the porous blocks and the fluid results in significant enhancement of heat transfer at the locations of the porous blocks.     

Thermo‐solutal convection in an inclined porous cavity with various aspect ratios under mixed thermal and species boundary conditions

The problem of laminar thermo‐solutal convective flow of a binary fluid mixture in an inclined rectangular cavity filled with a uniform porous medium is considered. Mixed heat and mass fluxes and uniform temperature and concentration conditions are applied on two opposing walls of the cavity while the other two walls are kept adiabatic and impermeable to mass transfer. The problem is put in terms of the stream function‐vorticity formulation. A numerical solution based on the finite‐difference methodology is obtained. Representative results illustrating the effects of the inclination angle of the cavity, buoyancy ratio, Darcy number, and the cavity aspect ratio on the contour maps of the streamline, temperature, and concentration as well as the profiles of velocity, temperature, and concentration at mid‐section of the cavity are reported. In addition, numerical results for the average Nusselt and Sherwood numbers as well as some useful correlations are presented for various parametric conditions and discussed. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20369     

Mixed convection of a permeable fluid in a vertical channel with boundary conditions of a third kind

Numerical investigation of a steady mixed convective flow through a fluid‐saturated porous media in a vertical channel with boundary conditions of the third kind including the effects of viscous dissipation and Darcy dissipation has been studied. The plates exchange heat with an external fluid. Both conditions of equal and of different reference temperatures of the external fluid are considered. First, the simpler cases of either negligible Brinkman number or negligible Grashof number are addressed with the help of analytical solutions. The combined effects of buoyancy forces and viscous dissipation are analyzed by a perturbation series method valid for small values of perturbation parameter. To relax the conditions on the perturbation parameter, the governing equations are also evaluated numerically by a shooting technique that uses the classical explicit Runge–Kutta method of four slopes as an integration scheme and the Newton–Raphson method as a correction scheme. The problem is analyzed for different values of mixed convection parameters, porous parameter for equal and unequal Biot numbers, keeping the wall temperatures symmetric or asymmetric. The graphical results illustrating the effects of various parameters on the flow as well as average velocity and Nusselt numbers are presented. Further the analytical and numerical solutions agree very well for small values of the perturbation parameter. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21019     

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     

Effect of Darcy,Reynolds, and Prandtl Numbers on the Performance of Two‐Phase Flow Heat Exchanger Filled with Porous Media

Experimental investigation of two‐phase laminar forced convection in a single porous tube heat exchanger is presented. The effect of Darcy, Reynolds, and Prandtl numbers on the performance of this heat exchanger during the condensation process of carbon dioxide at different test conditions were investigated. Gravel sand with different porosities is used as a porous medium. The flow in the porous medium is modeled using the Brinkman–Forchheimer‐extended Darcy model. Parametric studies are also conducted to evaluate the effects of porosity and Reynolds and Prandtl numbers on the heat transfer coefficient and the friction factor. A dimensionless performance parameter is developed in order to be used in evaluating the porous tube heat exchanger based on both the heat transfer enhancement and the associated pressure drop. The study covers a wide range of inlet pressure (P_in), mass flow rate (), porosity of gravel sand (ε), and Darcy number (Da) which ranged: 34.5 ≤ P_in ≤ 43 bars, 8 * 10^{? 5} ≤ ≤ 16 * 10^{? 5} kg/s, 34.9% ≤ ε ≤ 44.5%, 1.6 * 10^{? 6} ≤ Da ≤ 5 * 10^{? 6}, respectively. The study predicted the combined effect of the Reynolds number, Darcy number, porosity, and Prandtl number on the heat transfer and pressure drop of carbon dioxide during the condensation process in a porous medium. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21117     

Control of turbulent channel flow over a backward‐facing step by suction or injection

Experiments have been performed for turbulent channel flow over a backward‐facing step. The backward‐facing step is controlled by equipping a slit at the bottom corner of the step. Low momentum fluids in the recirculation region are sucked or high momentum fluids are injected from the slit. The width of the slit is changed between 2, 3, and 5 mm, and the flow ratio is varied from 0.00 to 0.15. The wall static pressure and local heat transfer coefficient are measured behind the backward‐facing step. The wall shear stress is measured using a micro flow sensor. In addition, the velocity profiles and turbulent intensities are measured by a split hot film probe. It is found that the heat transfer and pressure drop characteristics are controlled by the flow ratio. When the suction flow ratio is 0.06, the highest performance is obtained. Enhancement of the heat transfer is related to the increase of turbulence intensity. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(8): 490–504, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20036     

Numerical simulation of mixed convection in a porous medium filled with water/Al2 O3 nanofluid

The present work encloses the application of a Brinkman–extended Darcy model in a problem concerning mixed convection ina lid–driven porous cavity using nanofluids. The transport equations are solved numerically by the finite volume method on a co–located grid arrangement using the Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme. The effects of governing parameters, namely, Grashof number (Gr), Darcy number (Da), and solid volume fraction $(\chi )$ , on the streamlines and the isotherms are studied. The present results are validated by favorable comparisons with previously published results and are in good agreement with them. The present numerical results show that the addition of nanoparticles to a base fluid has produced an augmentation of the heat transfer coefficient and it is found to increase significantly with an increase of the particle volume concentration. It is observed from the results that at the higher value of the Grashof number (Gr = 10⁴ ), the average Nusselt number increases with an increase in the Darcy number for a constant solid volume fraction. The detailed results are reported by means of streamlines, isotherms, and Nusselt numbers. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21029     

Non‐Darcy assisted flow along a channel with an open cavity filled with water–TiO2 nanofluid

Numerical investigation on forced (assisted) convection heat transfer in a two‐dimensional horizontal porous channel with an open cavity is studied in this article. A non‐uniform heat flux is considered to be located on the bottom surface of the cavity. The rest of the surfaces are taken to be perfectly insulated. The physical domain is filled with a water‐based nanofluid containing TiO₂ nanoparticles. The fluid enters from the left and exits from the right with initial velocity U_i and temperature T_i. Governing equations are discretized using the penalty finite element method. The simulation is carried out for a wide range of Reynolds number Re (= 10–500) and Darcy number Da (= 10^?5–∞). Results are presented in the form of streamlines, isothermal lines, local and average Nusselt numbers, average temperatures of the fluid, horizontal and vertical velocities at mid‐height of the channel and mean velocity fields for various Re and Da. The enhancement of heat transfer rate is caused by the increasing Re and falling Da. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21046     

Transient free convective flow through a vertical cylinder filled with a porous material

This article aims to explore the impressive impact of emerging parameters on transient fully evolved free convective flow inside a vertical cylinder containing a porous material. The mathematical formulation of the model related to the considered physical circumstance is presented under compatible boundary conditions. Closed‐form solutions are received for the velocity field, the temperature distribution, mass flux, skin friction, and the Nusselt number in terms of Bessel functions and modified Bessel functions of the first kind. Impressive effects of parameters such as the Darcy number $Da$, Prandtl number $\text{Pr}$, viscosity ratio $M$, and also time $t$ on both the velocity and temperature distribution have been explored employing graphs and tables. It is irradiated by analysis that flow erection, heat transfer rate, skin friction, and mass flux are admirably impacted by the Prandtl number, the Darcy number, viscosity ratio parameter, and time. It is found that both the velocity and temperature field profiles rise with the rising value of time and ultimately attain their steady state. Moreover, the Prandtl number and the viscosity ratio parameter reduce the velocity profiles, while the reverse phenomenon occurs with the Darcy number.     

Effects of Thermal‐Diffusion,Diffusion‐Thermo,and Space Porosity on MHD Mixed Convective Flow of Micropolar Fluid in a Vertical Channel with Viscous Dissipation

This paper examines thermal‐diffusion and diffusion‐thermo effects on the fully developed MHD flow of a micropolar fluid through a porous space in a vertical channel with asymmetric wall temperatures and concentrations. The homotopy analysis method (HAM) is adopted to obtain the approximate analytical solution for the velocity, micro‐rotation, temperature, and concentration field. The convergence and the accuracy of the solutions are discussed. The role of pertinent parameters on the heat and mass transfer characteristics of the flow are presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 561–576, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21100     

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