Numerical simulation of fluid flow and convection heat transfer in sintered porous plate channels

Fluid flow and convective heat transfer of water in sintered bronze porous plate channels was investigated numerically. The numerical simulations assumed a simple cubic structure formed by uniformly sized particles with small contact areas and a finite-thickness wall subject to a constant heat flux at the surface which mirrors the experimental setup. The permeability and inertia coefficient were calculated numerically according to the modified Darcy’s model. The numerical calculation results are in agreement with well-known correlation results. The calculated local heat transfer coefficients on the plate channel surface, which agreed well with the experimental data, increased with mass flow rate and decreased slightly along the axial direction. The convection heat transfer coefficients between the solid particles and the fluid and the volumetric heat transfer coefficients in the porous media predicted by the numerical results increase with mass flow rate and decrease with increasing particle diameter. The numerical results also illustrate the temperature difference between the solid particles and the fluid which indicates the local thermal non-equilibrium in porous media.     

Fully developed natural convection heat and mass transfer in a vertical annular porous medium with asymmetric wall temperatures and concentrations

This work examines the effects of the modified Darcy number, the buoyancy ratio and the inner radius-gap ratio on the fully developed natural convection heat and mass transfer in a vertical annular non-Darcy porous medium with asymmetric wall temperatures and concentrations. The exact solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived by using a non-Darcy flow model. The modified Darcy number is related to the flow resistance of the porous matrix. For the free convection heat and mass transfer in an annular duct filled with porous media, increasing the modified Darcy number tends to increase the volume flow rate, total heat rate added to the fluid, and the total species rate added to the fluid. Moreover, an increase in the buoyancy ratio or in the inner radius-gap ratio leads to an increase in the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid.     

Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall

Double — diffusive natural convection in fluid saturated porous medium has been investigated using a generalised porous medium model. One of the vertical walls of the porous cavity considered is subjected to convective heat and mass transfer conditions. The results show that the flow, heat and mass transfer become sensitive to applied mass transfer coefficient in both the Darcy and non-Darcy flow regimes. It is also observed that the Sherwood number approaches a constant value as the solutal Biot number increases.     

Numerical analysis of convective heat transport in a porous semi‐trapezoidal enclosure with radiation effect

A theoretical and numerical study of natural convection of two‐dimensional laminar incompressible flow in a semi‐trapezoidal porous enclosure in the presence of thermal radiation is conducted. The semi‐trapezoidal enclosure has an inclined left wall that in addition to the right vertical wall is maintained at a constant temperature, whereas the remaining (horizontal) walls are adiabatic. The Darcy‐Brinkman isotropic model is utilized. The governing partial differential equations are transformed using a vorticity stream function and nondimensional quantities and the resulting governing nonlinear dimensionless equations are solved using the finite difference method with incremental steps. The impacts of the different model parameters (Rayleigh number [Ra], Darcy number [Da], and radiation parameter [Rd]) on the thermofluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with the greater Darcy parameter (permeability). The flow is accelerated with the increasing buoyancy effect (Rayleigh number) and heat transfer is also increased with a greater radiative flux. The present numerical simulations are more relevant to hybrid porous media solar collectors.     

Natural convection in an enclosure with localized heating and salting from below

Two-dimensional, double diffusion, natural convection in a rectangular enclosure filled with binary fluid saturating porous media is investigated numerically. Multiple motions are driven by the external temperature and concentration differences imposed across horizontal walls with the simultaneous presence of discrete heat and contaminant sources. The general Brinkman-extended Darcy model is adopted to formulate the fluid flow in the cavity. The fluid, heat and moisture transport through the isotropic porous layer are analyzed using the streamlines, heatlines and masslines, and the heat and mass transfer potentials are also explained by the variations of overall Nusselt and Sherwood numbers. The numerical simulations presented here span a wide range of the main parameters (thermal Rayleigh numbers, strip pitches and Darcy number) in the domain of destabilizing solutal buoyancy forces. It is shown that the heat and mass transfer potential can be promoted or inhibited, depending strongly on the permeability of porous medium, the strip pitch, the thermal and solutal Rayleigh numbers.     

Onset of Darcy‐Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer with Internal Heat Source

The onset of Darcy‐Brinkman convection in a binary viscoelastic fluid‐saturated sparsely packed porous layer with an internal heat source is studied using both linear and nonlinear stability analyses. The Oldroyd‐B model is employed to describe the rheological behavior of binary fluid. An extended form of the Darcy‐Oldroyd law incorporating Brinkman's correction and time derivative is used to describe the flow through a porous layer. The onset criterion for stationary, oscillatory, and finite amplitude convection is derived analytically. There is a competition between the processes of thermal diffusion, solute diffusion, and viscoelasticity that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effect of internal Rayleigh number, relaxation and retardation parameters, solute Rayleigh number, Darcy number, Darcy‐Prandtl number, and Lewis number on the stability of a system is investigated and is shown graphically. The nonlinear theory based on the truncated representation of the Fourier series method is used to find heat and mass transfer. The transient behavior of the Nusselt and Sherwood numbers is obtained using numerical methods. Some known results are recovered for the particular cases of the present study. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(8): 676–703, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21056     

Thermosolutal convection from a discrete heat and solute source in a vertical porous annulus

Double-diffusive convection in a vertical annulus filled with a fluid-saturated porous medium is numerically investigated with the aim to understand the effects of a discrete source of heat and solute on the fluid flow and heat and mass transfer rates. The porous annulus is subject to heat and mass fluxes from a portion of the inner wall, while the outer wall is maintained at uniform temperature and concentration. In the formulation of the problem, the Darcy–Brinkman model is adopted to the fluid flow in the porous annulus. The influence of the main controlling parameters, such as thermal Rayleigh number, Darcy number, Lewis number, buoyancy ratio and radius ratio are investigated on the flow patterns, and heat and mass transfer rates for different locations of the heat and solute source. The numerical results show that the flow structure and the rates of heat and mass transfer strongly depend on the location of the heat and solute source. Further, the buoyancy ratio at which flow transition and flow reversal occur is significantly influenced by the thermal Rayleigh number, Darcy number, Lewis number and the segment location. The average Nusselt and Sherwood numbers increase with an increase in radius ratio, Darcy and thermal Rayleigh numbers. It is found that the location for stronger flow circulation is not associated with higher heat and mass transfer rates in the porous annular cavity.     

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     

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     

The role of porous media in modeling flow and heat transfer in biological tissues

Flow and heat transfer in biological tissues are analyzed in this investigation. Pertinent works are reviewed in order to show how transport theories in porous media advance the progress in biology. The main concepts studied in this review are transport in porous media using mass diffusion and different convective flow models such as Darcy and the Brinkman models. Energy transport in tissues is also analyzed. Progress in development of the bioheat equation (heat transfer equation in biological tissues) and evaluation of the applications associated with the bioheat equation are analyzed. Prominent examples of diffusive applications and momentum transport by convection are discussed in this work. The theory of porous media for heat transfer in biological tissues is found to be most appropriate since it contains fewer assumptions as compared to different bioheat models. A concept that is related to flow instabilities caused by swimming of microorganisms is also discussed. This concept named bioconvection is different from blood convection inside vessels. The works that consider the possibility of reducing these flow instabilities using porous media are reviewed.     

Double diffusive LTNE porous convection with Cattaneo effects in the solid

The impact of Cattaneo heat flux law in the solid on the onset of double‐diffusive Darcy porous convection with local thermal nonequilibrium temperatures is investigated. The Fourier law of heat transfer is invoked for the fluid, whereas the Cattaneo heat flux law used to transfer heat in solid skeleton alters the temperature equation from parabolic to hyperbolic. The results are obtained for porous skeletons of aluminum and copper oxides. Both Cattaneo and solute concentration effects reinforce in controlling the onset of oscillatory convection and some novel consequences are observed. Compared with the results perceived in the absence of solute concentration, a manifestation of oscillatory convection with scaled‐interphase heat transfer coefficient as well as solid thermal relaxation time parameter initiates earlier in its presence. The effect of increasing interphase heat transfer coefficient and the Lewis number is to delay and hasten the onset of stationary and oscillatory convection. Besides, the increase in the value of solid thermal relaxation time parameter advances the oscillatory onset. Although the increase in the solute Darcy–Rayleigh number is to delay the stationary onset, it shows a twofold behavior on the onset of oscillatory convection. Before the onset of oscillatory convection, the size of the convection cell gets narrower and after which it becomes much wider. The existing results are retrieved as limiting cases from the current study.     

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

By adopting a perturbation method and a local thermal nonequilibrium model, nonlinear thermal convection in an anisotropic porous layer saturated by an elasticoviscous fluid is investigated. An elasticoviscous fluid is modeled by a modified Darcy‐Oldroyd‐B model, and the fluid and solid phase temperatures are represented using a two‐field model for the heat transport equation. Anisotropy in permeability and fluid and solid thermal conductivities are considered. A cubic Landau equation is derived separately to study the stability of bifurcating solution of both stationary and oscillatory convection, and the results of linear instability theory are delineated. The boundary between stationary and oscillatory convection is demarcated by identifying codimension‐two points in the viscoelastic parameters plane. It is found that the subcritical instability is not possible, and the linear instability analysis itself completely captures the behavior of the onset of convection. Heat transfer is obtained in terms of Nusselt number, and the effect of governing parameters on the same is discussed. The results of the Maxwell fluid are obtained as a particular case from the present study.     

The effect of rotation on the onset of convection in a horizontal anisotropic porous layer

The effect of rotation and anisotropy on the onset of convection in a horizontal porous layer is investigated using a linear theory and a weak nonlinear theory. The linear theory is based on the usual normal mode technique and the nonlinear theory on the truncated Fourier series analysis. Darcy model extended to include time derivative and Coriolis terms with anisotropic permeability is used to describe the flow through porous media. A modified energy equation including the thermal anisotropy is used. The effect of rotation, mechanical and thermal anisotropy parameters and the Prandtl number on the stationary and overstable convection is discussed. It is found that the effect of mechanical anisotropy is to allow the onset of oscillatory convection instead of stationary. It is also found that the existence of overstable motions in case of rotating porous medium is not restricted to a particular range of Prandtl number as compared to the pure viscous fluid case. The steady finite amplitude analysis is performed using truncated Fourier series to find the Nusselt number. The effect of various parameters on heat transfer is investigated.     

Natural convection in fluid–superposed porous layers heated locally from below

A numerical study of two-dimensional natural convection in fluid–superposed porous layers heated locally from below is reported based on the one-domain formulation of the conservation equations. The effects of five dimensionless parameters on overall Nusselt number are investigated: Rayleigh number based on overall layer height, heater-to-cavity length ratio, porous layer-to-cavity height ratio, domain aspect ratio, and Darcy number. Streamline and isotherm patterns indicate that convective motion is restricted to the overlying fluid layer with some penetration into the porous layer. Nusselt numbers increase with a decrease in the heater length and height ratio, and increase with the Darcy number. The size of the heat source does not affect the dependence of the heat transfer coefficient on height ratio and Darcy number. For domains with large aspect ratios, complex flow restructuring is observed with an increase in Rayleigh number. The present results represent an extension of the well studied problem of buoyant convection in fluid–superposed porous layers with a fully heated lower surface.     

管内填充多孔介质强化换热的数值研究

管内填充多孔介质强化换热的基本原理是构造热边界层,增大壁面附近流体的温度梯度,并且流动阻力增幅不大。本文运用数值模拟的方法,模拟填充多孔介质管内的流场和温度场,探讨填充比例φ、渗透率Da以及空隙率ε对管内对流换热的影响规律。研究表明,提高填充比例φ和减小渗透率Da都能明显提高换热效果,但也增加了管内流动阻力。空隙率ε对强化换热作用不大,但高空隙率可以明显降低管内流动阻力,在实际中应选用空隙率较大的多孔介质。     

Computational unsteady flow analysis for third‐grade fluid from an isothermal vertical cylinder through a Darcian porous medium

The present study describes a mathematical model for free‐convective laminar incompressible boundary layer flow of a third‐grade fluid of the Reiner‐Rivlin differential type, external to an evenly heated semi‐infinite vertical cylinder through a two‐dimensional porous medium. Assuming a homogenous‐isotropic porous medium, simulation of bulk drag effects at low Reynolds number is conducted with the Darcy model. The resulting partial differential equation boundary value problem is normalized using suitable transformation variables. The highly nonlinear time‐dependent coupled conservation equations along with boundary conditions are resolved computationally with an optimized Crank‐Nicolson finite difference code. Validation with previous studies is included. The heat transport and skin‐friction coefficients are computed for different values of emerging nondimensional parameters. Furthermore, steady‐state and transient fluid flow variables are shown graphically. An enhanced fluid velocity is observed for increased Darcy number and the reverse trend is computed for higher values of third‐grade viscoelastic parameter. Also, the rate of heat transfer is observed to increase with greater Darcy number and a reduction in third‐grade viscoelastic parameter. A key observation which is drawn from the present study is that for third‐grade fluid the flow variables deviate significantly from a hot cylindrical wall as compared with a Newtonian fluid. The study is relevant to thermal polymer coating applications in aerospace materials processing.     

About enhancement of heat transfer over a circular cylinder embedded in a porous medium

Studies of the steady viscous flow and heat transfer past a circular cylinder are presented for some fluid saturated fibrous porous media. Numerical results have been obtained according to the Darcy-Brinkman model by means of the finite element method. Forced convection is analyzed by assuming a solid matrix of constant porosity and permeability in a Péclet number range without any effect of thermal dispersion. Analysis of the influence of the Darcy number on isotherms, streamlines, and velocity contours shows the conditions of the enhancement of heat transfer from the cylinder to the surrounding porous medium.     

Transient forced convection heat transfer from a circular cylinder embedded in a porous medium

Studies of the transient heat transfer past a circular cylinder in a steady-state viscous flow are presented for some fluid saturated fibrous porous media. Numerical results have been obtained according to the Darcy-Brinkman model by means of the finite element method. Analysis of the influence of the Darcy and Peclet numbers on the mean Nusselt number exhibits the successive conduction, transition and convection regimes. The duration necessary to reach the steady-state convection heat transfer appears as a function of the Peclet and Darcy numbers.     

热质渗透壁面饱和多孔介质通道流动与热质传递的数值模拟

利用数值模拟方法研究了多孔介质中存在温度梯度、浓度梯度并具有热质渗透壁面时的受迫对流对传热传质的影响。采用有限容积法在同位网格上离散控制多孔介质内流体流动与热质传递方程守恒方程(即N-S)，对流项采用二阶精度的QUICK格式，扩散项采用中心差分格式。利用SIMPLE算法求解压力和速度耦合问题。利用所发展的程序研究了在不同孔隙率，不同的温度、浓度边界条件下，流场、温度场和浓度场以及Nu和Sh的变化规律。     

Transient natural convection and heat transfer during the storage of granular media

Transient heat transfer in an originally isothermal cylinder filled with a porous medium after sudden change of wall temperature is studied experimentally and computationally. Lab-scale experiments with water as the interstitial fluid are used in order to imitate the conditions prevailing in large, air-filled industrial silos. The proposed model assumes isotropy of the porous medium, local thermal equilibrium between the phases, Darcy flow and applicability of the Boussinesq approximation. Its predictions are in satisfactory agreement with the experimental results. Simulations reveal the role of dimensionless parameters like the modified porous media Rayleigh number and the cylinder aspect ratio. A criterion for neglecting the influence of natural convection on heat transfer is established.