Non－Darcian and Anisotropic Anisotropic Effects on Natural Convection in Horizontal Porous Media Enclosure

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Analysis of Flow and Heat Transfer in a Parallelogram Non‐Uniformly Heated Enclosure Filled with Porous Medium

The flow and heat transfer in a parallelogram enclosure filled with a porous medium is analyzed numerically. The heated bottom wall has a sinusoidal temperature distribution and side walls cooled isothermally while the upper wall is well insulated. Dimensionless Darcy law and energy equations are solved using the finite difference method along with the corresponding boundary condition. Computations were carried out for four inclination angles of side walls (γ = 45°, 60°, 75°, 90°) with different Rayleigh numbers (100≤Ra≤1000) and their effects on the flow field and heat transfer are discussed. It is found that the inclination angle has a significant effect on flow pattern and heat transfer and an increase in the angle leads to a decrease in the strength of the right vortex. The study also revealed that as the Rayleigh number increases at γ = 45°, another (third) vortex develops along the left wall and its strength enhances with Rayleigh number. At the end, a correlation is extracted from the numerical data which represents the relation between the Nusselt number, inclination angle, and the Rayleigh number. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; 39(7): 497–506, 2010; Published online in Wiley Online Library ( wileyOnlinelibrary.com ). DOI 10.1002/htj.20312     

Natural Convection of Nanofluid in Cylindrical Enclosure Filled with Porous Media

A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq＇s approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within （10≤ Ra ≤ 103）, aspect ratio （1 ≤ As 〈 5） and the volume fraction （0 ≤0 〈 0.2）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as ~ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.     

Numerical Study of Natural Convection in an Enclosure with an Internal Heat Source at Higher Rayleigh Numbers

Natural convection is extensively used in cooling of large scale electrical and electronic equipments. This work involves study of flow and heat transfer characteristics in enclosures with partial openings having an internal heat source at higher Rayleigh number (Ra_h > 10⁶). It involves the numerical simulation of 2D steady state natural convection in enclosures of different aspect ratios (H/W = 2 and 3) for five Rayleigh numbers (Ra_h = 10⁷, 10⁸, 10⁹, 10¹⁰, and 10¹¹). Two different configurations have been considered based on the number and position of vents—diagonal side (DS) and two inlets one outlet (2I1O). The time dependent nature of the flow is characterized by performing a Fast Fourier Transform (FFT) analysis of temperature and velocity at a characteristic location in the enclosure. The global parameters considered are the mass flow rate driven through the cavity by the heater and the average Nu defined over the heater surface. It is seen that with increase in Ra_h, flow becomes more fluctuating and moves towards chaotic regime and this transition is quicker at lower H/W. For the given configuration both the global parameters increases with increase in Ra_h and decrease in H/W.     

Numerical Simulation of Natural Convection in a Parallelogrammic Enclosure Containing Volumetric Heat Source with Non‐uniformly Heated Left Sidewall

The influence of the external Rayleigh number, inclination angle, and internal Rayleigh number on natural convection within an air‐filled parallelogrammic enclosure containing a volumetric source has been investigated numerically. The left sidewall of the enclosure is subjected to a non‐uniformly hot temperature and the right sidewall experiences a uniform cold temperature while the remaining top and bottom walls are kept adiabatic. The physical problems are represented mathematically by various sets of governing equations along with the corresponding boundary conditions. Buoyancy forces are taken into account during the analysis of the present investigation. By using the finite volume method, the dimensionless governing equations are discretized numerically based on a non‐uniform collocated grid system. Results are obtained for a wide range of external Rayleigh numbers varying from 10³ to 10⁶ with internal Rayleigh numbers varying from (0) to (10⁸) while the left sidewall from vertical is varied as 0, 30, –30, 60, and ?60^°, respectively. In the present study, the obtained results are presented in terms of streamlines, isotherms, and average Nusselt number along the hot and cold sidewalls. Two pairs of rotating vortices are observed due to the non‐uniform heating process while the shape of this rotating vortices is sensitive to the inclination angle. Furthermore, the flow field circulation and the average Nusselt number increase remarkably with the increase in the external Rayleigh number. The results of the present work are compared with other published results and give excellent agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 542–560, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21096     

Brownian Motion Effects on Natural Convection of Alumina–Water Nanofluid in 2‐D Enclosure

This article reports a numerical study of natural convection heat transfer in a differentially heated enclosure filled with a Al₂O₃–water nanofluid. Fluent v6.3 is used to simulate nanofluid flow. Simulations have been carried out for the pertinent parameters in the following ranges: the Rayleigh number, Ra = 10⁶, 10⁷, and the volumetric fraction of alumina nanoparticles, ? = 0 ? 4%. The effect of Brownian motion on the heat transfer is considered and examined. The numerical results show a decrease in heat transfer with an increase in particle volume fraction. Similar to experimental results, the Nusselt number increases with the Rayleigh number in the numerical results. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21121     

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     

Numerical Investigation of Double Diffusive Mixed Convection Laminar Flow in Two Sided Lid Driven Porous Cavity

This paper presents the numerical study of mixed convection in a two‐sided lid driven porous cavity due to temperature and concentration gradients. The top and bottom walls are stationary and insulated. The left and right walls are moving at an equal velocity (V_o) in the same direction. The temperature and concentration are kept high at the right wall and low at the left wall. The governing equations are discretized using finite volume method. The pressure–velocity coupling is performed by the SIMPLE algorithm. A third order differed QUICK scheme is applied at the inner nodes and a second order central difference scheme is used at the boundary nodes. The flow behavior and heat transfer are analyzed for different nondimensional numbers, such as, 1 × 10^?4 ≤ Ri ≤ 10, 1 × 10^?4 ≤ Da ≤ 0.1 and 0.7 < Pr < 10. The present numerical results are compared with the literature and are in good agreement. For the above selected nondimensional numbers, the heat and fluid flow behavior is investigated using local and average Nusselt (Nu) and Sherwood (Sh) numbers. Results show that the convection flow is significant up to Da = 0.1, beyond that the effect of porosity is negligible. The effect of Prandtl number (Pr) on average Nu is found to increase significantly.     

Numerical Simulation of Natural Convection in a Triangle Cavity Filled with Nanofluids Using Tiwari and Das' Model: Effects of Heat Flux

In this article, we present a fully higher‐order compact (FHOC) finite difference method to investigate the effects of heat flux on natural convection of nanofluids in a right‐angle triangle cavity, where the left vertical side is heated with constant heat flux both partially and throughout the entire wall, the inclined wall is cooled, and the rest of walls are kept adiabatic. The Darcy flow and the Tiwari and Das’ nanofluid models are considered. Investigations with four types of nanofluids were made for different values of Rayleigh numbers with the range of 100 ≤ Ra ≤ 50,000, size of heat flux as 0.1 ≤ ε ≤ 1.0, enclosure aspect ratio as 0.5 ≤ AR ≤ 2.0, and solid volume fraction parameter of nanofluids with the range of 0% ≤ ? ≤ 20%. Results show that the average heat transfer rate increases significantly as particle volume fraction and Rayleigh numbers increase, and the maximum value of average Nusselt number is obtained by decreasing the enclosure aspect ratio. The results also show that the average heat transfer decreases with an increase in the length of the heater. Furthermore, multiple correlations in terms of the Rayleigh numbers and the solid volume fraction of four types of nanoparticles have been established in a general form.     

Numerical Simulation of Mixed‐Convection Flow in a Lid‐Driven Porous Cavity Using Different Nanofluids

In this study, the effect of mixed convection flow in a lid‐driven porous cavity using different nanoparticles, such as aluminum oxide (Al ₂ O ₃), copper (Cu), silver (Ag), and titanium dioxide (TiO ₂), are investigated. The base fluid is considered as water. The transport equations are solved numerically by finite volume method on a co‐located grid arrangement using quadratic upwind interpolation for convective kinematics (QUICK) scheme. A two‐dimensional square cavity is considered for the present investigation whose horizontal walls are insulated. The cold left wall is moving up and hot right wall is moving down with equal velocities. The variations of temperature distribution, stream function, and Nusselt number (Nu) are analyzed at constant Grashof numbers (Gr), Richardson numbers (Ri), and Darcy numbers (Da) as 1 × 10 ⁴, 100, and 0.1, respectively, for different nanoparticles. The present results are validated by favorable comparison with previously published literature. The predicted results clearly indicate that the presence of nanoparticles inside the porous media enhances the heat transfer significantly. It is observed from the numerical results that the average Nusselt numbers (Nu) were found to increase linearly with an increase in volume fraction (χ). For the given volume fraction, the average Nu is maximum for a silver‐based nanoparticle. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 1–16, 2014; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21075     

Magnetohydrodynamic Effect on Free Convection of Three Dimensional Laminar Flow in Porous Annulus

A numerical study has been carried out to investigate heat transfer by free convection under the effect of MHD （magnetohydrodynamic） for steady state three-dimensional laminar flow in horizontal and vertical cylindrical annulus filled with saturated porous media （sand silica） with fins attached to the inner cylinder. A single electric coil placed around the inner cylinder to generate a magnetic field. The governing equations which used are continuity, momentum （using Darcy＇s law） and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using Fortran 90 program. The parameters affected on the system are Rayleigh number ranging within （102 ~ Ra＊ 〈 104）, and MHD （Mn） （0 〈_ Mn 〈_ 100） and radius ratio Rr （0.225, 0.338 and 0.435）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that heat transfer decrease with the increase of magnetohydrodynamic. It was found that the average Nusselt number increase with Ra＊ and decrease with H~ Mn and Rr. A correlation for the average Nusselt number in terms of Ra＊ and Mn, has been developed for the inner cylinder.     

非均匀竖直平板自然对流耦合边界的数值研究

以板管式换热器为应用背景,采用SIMPLEC算法求解了竖直薄平板温度不均匀时边界导热与自然对流的耦合传热。数值计算结果表明,对自然对流而言,在≤108,采用铝平板已经可以获得足够好的传热性能,再增加平板的导热性能对传热几乎没有影响;而在≤104的情况下,采用钢平板可以获得跟铝平板几乎一致的传热效果;平板温度不均匀,明显增加了自然对流边界层厚度,但在顶端和底端加热盘管之间的平板区域其局部数与等壁温情况相差不大;对在104～107的范围内提出一个非均匀平板自然对流平均数计算公式,其误差约为5%。     

Thermophoretic Deposition Effect on Transient Free Convection Hydromagnetic Flow Along an Accelerated Inclined Permeable Surface with Time‐Dependent Temperature and Concentration

This work investigates the thermophoretic deposition effect on a transient free convection hydromagnetic flow along an accelerated infinite inclined permeable surface in the presence of heat generation, suction (or injection), thermal diffusion, and diffusion‐thermo taking into account that the surface temperature and concentration are time dependent. The governing partial differential equations are transformed into a set of nonlinear coupled ordinary differential equations, which are then solved numerically by applying the shooting method with a sixth‐order Runge–Kutta integration scheme. Graphical results for the dimensionless velocity, temperature, concentration distributions as well as wall thermophoretic velocity are reported and examined for the pertinent parameters showing the interesting aspects of the obtained solutions. The local skin‐friction coefficient, the local Nusselt number, and the local Sherwood number are also computed. The results show that higher flow rates can be obtained when the temperature and concentration are time independent. Smaller buoyancy is observed for higher temperature indexes. Wall thermophoretic velocity is decreased with the increasing values of the Prandtl number, the thermophoretic parameter, as well as heat generation parameter. The results further show that the presence of thermal diffusion and diffusion‐thermo intensify the shear stress but reduce the rate of heat as well as mass transfer. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 352–367, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21081     

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     

Natural convection MHD mass transfer through an infinite vertical porous plate in the existence of radiation embedded in porous medium

This research focuses on studying the effects of heat and mass transfer convective flow passing through an infinite vertical plate embedded in porous media under radiation and chemical reaction with constant heat and mass flux. A magnetic field of strength is functional throughout the fluid region. The novelty of the present work is to examine the heat and mass transfer magnetohydrodynamics flow in the presence of thermal radiation. The equations governing the flow, heat and mass transfer are solved analytically using the perturbation technique. Expressions for velocity, temperature, concentration, skin-friction, Nusselt, and Sherwood numbers are obtained. The influence of physical parameters on the flow domain is described graphically and in tabular form. It is found that increase in radiation parameter reduces the velocity and temperature. Moreover, internal friction of the plate decreased with increasing values of radiation parameter.     

Entropy Generation Analysis of the MHD Flow of Couple Stress Fluid between Two Concentric Rotating Cylinders with Porous Lining

An attempt has been made to study the entropy generation analysis of couple stress fluid flow in an annulus between two concentric rotating vertical cylinders. There is a porous lining attached to the inside of an outer cylinder. The flow is under the influence of a radial magnetic field. The flow in the annular gap is caused by rotation of the cylinders. The Stokes couple stress flow model is employed. The flow in the porous sleeve is governed by Darcy's law. The velocity, temperature, entropy generation number, Bejan number, wall shear stress and heat transfer rate at the inner and outer cylinders are obtained numerically by employing a finite difference scheme with vanishing of couple stresses on the boundary. The effect of relevant parameters on the flow and entropy generation rate are discussed and depicted through graphs.     

Heat and mass transfer on MHD convective flow over an infinite vertical porous plate with the heat source and chemical reaction

It is considered that the magnetohydrodynamic free convective flow of an incompressible electrically conducting fluid through a porous medium past a vertical absorbent surface. The homogeneous transverse magnetic field is considered in the existence of heat source and chemical reaction in the rotating frame. The accurate solutions of the velocity, temperature, and concentration are acquired systematically making use of the perturbation method. The consequences of a variety of governing flow parameters on the velocity, temperature, and concentration are analyzed through graphical profiles. Computational outcomes for the skin friction, Nusselt number, and Sherwood number through the tabular format were also examined.     

Effects of Nanofluid on Peristaltic Flow of a Carreau Fluid Model in an Inclined Magnetic Field

In the present article we talk about the influence of a nanofluid on the peristaltic flow of a Carreau fluid model in the presence of an inclined channel and magnetic field. The mathematical modeling of the proposed problem is given for the two‐ dimensional and directional flow. The governing highly nonlinear coupled equations are simplified by means of the assumptions of long wavelength and low Reynolds number approximation. The solutions of the simplified coupled nonlinear equations are calculated using an analytical approach. At the end, graphical results are displayed to show the effects of various emerging parameters of interest. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 368–383, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21082     

Numerical Investigation of the Magnetic Field Effects on the Entropy Generation and Heat Transfer in a Nanofluid Filled Cavity with Natural Convection

This paper presents a numerical investigation of the entropy generation and heat transfer in a ferrofluid (water and 4% Fe₃O₄ nanoparticles) filled cavity with natural convection using a two phase mixture model and control volume technique. The effect of applying a nonuniform magnetic field on the entropy generation and heat transfer in the cavity and also the interaction of magnetic force and the buoyancy force are investigated. Based on the obtained results, applying a magnetic field will enhance the heat transfer mechanism. Furthermore, by applying the nonuniform magnetic field on the ferrofluid filled cavity with natural convection, the total entropy generation is decreased considerably at higher Rayleigh numbers. Therefore, applying a magnetic field can be considered as a suitable method for entropy generation minimization in order to have high efficiency in the system.     

Thermal Radiation and Heat Source Effects on a MHD Nanofluid Past a Vertical Plate in a Rotating System with Porous Medium

This article studies the effect of thermal radiation on a MHD free convection flow of a nanofluid bounded by a semi‐infinite vertical plate with a constant heat source in a rotating frame of reference. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The dimensionless governing equations for this investigation are solved analytically using the regular perturbation method. The effect of various important parameters entering into the problem on velocity and temperature fields within the boundary layer are discussed for three different water‐based nanofluids such as Cu, Al₂O₃, and TiO₂ with the help of graphs. The predicted results clearly indicate that the presence of nanoparticles in the base fluid enhances the heat transfer process significantly. The present work shows the need for immediate attention in next‐generation solar film collectors, heat‐exchanger technology, material processing exploiting vertical surface, geothermal energy storage, and all those processes which are greatly exaggerated by heat‐enhancement concepts. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21101