Perturbation analysis of radiative effect on free convection flows in porous medium in the presence of pressure work and viscous dissipation

The effect of thermal radiation with a regular three-parameter perturbation analysis has been studied for the effects in some free convection flows of Newtonian fluid-saturated porous medium. The effects of the thermal radiation, permeability of the porous medium, pressure stress work and viscous dissipation on the flows and temperature fields have been included in the analysis. Four different vertical flows have been analyzed, those adjacent to an isothermal surface, uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source, and, a vertical adiabatic surface. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The numerical results of the perturbation analysis for four conditions are solved numerically by the fourth-order Runge–Kutta integration scheme. Numerical values of the main physical quantities are the skin friction and a heat transfer and total heat and mass convected downstream are presented in a tabular form with the parameters characterizing the radiation, permeability of the porous medium, pressure stress work and viscous dissipation. The obtained results are compared and a representative set is displayed graphically to illustrate the influences of the radiation, permeability of the porous medium, pressure stress work and viscous dissipation on the velocity and the temperature profiles.     

Non-Darcy unsteady mixed convection flow near the stagnation point on a heated vertical surface embedded in a porous medium with thermal radiation and variable viscosity

The unsteady mixed convection boundary layer flow near the stagnation point on a heated vertical plate embedded in a fluid saturated porous medium is studied. It is assumed that the unsteadiness is caused by the impulsive motion of the free stream velocity and by sudden increase in the surface temperature. Both the buoyancy assisting and the buoyancy opposing flow situations are considered with combined effects of the first and second order resistance of solid matrix of non-Darcy porous medium, variable viscosity and radiation. The problem is reduced to a system of non-dimensional partial differential equations, which is solved numerically using the Keller-box method. The features of the flow and the heat transfer characteristics for different values of the governing parameters are analyzed and discussed. The surface shear stress and the heat transfer of the present study are compared with the available results and a good agreement is found.     

Lie group analysis for thermal-diffusion and diffusion-thermo effects on free convective flow over a porous stretching surface with variable stream conditions in the presence of thermophoresis particle deposition

A study has been carried out to obtain the solutions for heat and mass transfer from natural convection flow along a vertical surface with temperature-dependent fluid viscosity embedded in a porous medium due to thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. This paper concerns with a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The impact of thermophoresis particle deposition with chemical reaction in the presence of thermal-diffusion and diffusion-thermo effects plays an important role on the temperature and concentration boundary layer. The results thus obtained are presented graphically and discussed.     

Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.     

Nonsimilar boundary layer analysis of double-diffusive convection from a vertical truncated cone in a porous medium with variable viscosity

This work presents a boundary layer analysis about variable viscosity effects on the double-diffusive convection near a vertical truncated cone in a fluid-saturated porous medium with constant wall temperature and concentration. The viscosity of the fluid is assumed to be an inverse linear function of the temperature. A boundary layer analysis is employed to derive the nondimensional nonsimilar governing equations, and the transformed boundary layer governing equations are solved by the cubic spline collocation method to yield computationally efficient numerical solutions. The obtained results are found to be in good agreement with previous papers on special cases of the problem. Results for local Nusselt and Sherwood numbers are presented as functions of viscosity-variation parameter, buoyancy ratio, and Lewis number. For a porous medium saturated with a Newtonian fluid with viscosity proportional to an inverse linear function of temperature, higher value of viscosity-variation parameter leads to the decrease of the viscosity in fluid flow, thus increasing the fluid velocity as well as the local Nusselt number and the local Sherwood number.     

An analytic solution of an oscillatory flow through a porous medium with radiation effect

Analytical solutions for two-dimensional oscillatory flow on free convective-radiation of an incompressible viscous fluid, through a highly porous medium bounded by an infinite vertical plate are reported. The Rosseland diffusion approximation is used to describe the radiation heat flux in the energy equation. The resulting non-linear partial differential equations were transformed into a set of ordinary differential equations using two-term series. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. The free-stream velocity of the fluid vibrates about a mean constant value and the surface absorbs the fluid with constant velocity. Expressions for the velocity and the temperature are obtained. To know the physics of the problem analytical results are discussed with the help of graph.     

Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating

The combined effect of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid past a vertical permeable surface embedded in a porous medium is analyzed. The heat equation includes the terms involving the radiative heat flux, Ohmic dissipation, viscous dissipation and the internal absorption whereas the mass transfer equation includes the effects of chemically reactive species of first-order. The non-linear coupled differential equations are solved analytically by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field is to decrease the velocity, temperature and concentration profiles in the boundary layer. There is also considerable effect of magnetic field and chemical reaction on skin-friction coefficient and Nusselt number.     

Oberbeck convection through vertical porous stratum

Natural convection through a vertical porous stratum is investigated both analytically and numerically. Analytical solutions are obtained using a perturbation method valid for small values of buoyancy parameterN and the numerical solutions are obtained using Runge-Kutta-Gill method. It is shown that analytical solutions are valid forN < 1 and several features of the effect of large values ofN are reported. The combined effects of increase in the values of temperature difference between the plates and the permeability parameter on velocity, temperature, mass flow rate and the rate of heat transfer are reported. It is shown that higher temperature difference is required to achieve the mass flow rate in a porous medium equivalent to that of viscous flow.     

Magnetohydrodynamic non-Darcy mixed convection heat transfer from a vertical heated plate embedded in a porous medium with variable porosity

A numerical model is developed to study magnetohydrodynamics (MHD) mixed convection from a heated vertical plate embedded in a Newtonian fluid saturated sparsely packed porous medium by considering the variation of permeability, porosity and thermal conductivity. The boundary layer flow in the porous medium is governed by Forchheimer–Brinkman extended Darcy model. The conservation equations that govern the problem are reduced to a system of non-linear ordinary differential equations by using similarity transformations. Because of non-linearity, the governing equations are solved numerically. The effects of magnetic field on velocity and temperature distributions are studied in detail by considering uniform permeability (UP) and variable permeability (VP) of the porous medium and the results are discussed graphically. Besides, skin friction and Nusselt number are also computed for various physical parameters governing the problem under consideration. It is found that the inertial parameter has a significant influence in increasing the flow field and the rate of heat transfer for variable permeability case. The important finding of the present work is that the magnetic field has considerable effects on the boundary layer velocity and on the rate of heat transfer for variable permeability of the porous medium. Further, the results obtained under the limiting conditions were found to be in good agreement with the existing ones.     

Dynamics of water evaporation fronts

The evolution and shapes of water evaporation fronts caused by long-wave instability of vertical flows with a phase transition in extended two-dimensional horizontal porous domains are analyzed numerically. The plane surface of the phase transition loses stability when the wave number becomes infinite or zero. In the latter case, the transition to instability is accompanied with reversible bifurcations in a subcritical neighborhood of the instability threshold and by the formation of secondary (not necessarily horizontal homogeneous) flows. An example of motion in a porous medium is considered concerning the instability of a water layer lying above a mixture of air and vapor filling a porous layer under isothermal conditions in the presence of capillary forces acting on the phase transition interface.     

Influence of double stratification on MHD free convection with Soret and Dufour effects in a Darcian porous media

The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a doubly stratified saturated porous medium subjected to a magnetic field is studied, taking into account the Dufour and Soret effects. It is found that the similarity solution exists for the case of uniform surface heat and mass flux conditions when the thermal and solutal stratification of the medium are assumed to have power function form x^1/3. The resulting set of ordinary coupled nonlinear differential equations is solved numerically using shooting technique. Nusselt and Sherwood numbers are tabulated for various values of the involved parameters. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Velocity and temperature distribution in a system consisting of a fluid layer overlying a layer of porous medium

The velocity and temperature distribution in a system consisting of a fluid layer overlying a layer of porous medium is investigated in the presence of buoyancy and surface tension forces. The analysis indicates that buoyancy and surface tension forces are additive and aid the flow by counteracting the effect of permeability. The temperature distribution is sensitive to the variation of the aspect ratio, and conductivities of the media. Further, the inclusion of the viscous dissipation term markedly affects the temperature distribution.     

Effects of variable viscosity on non-Darcy MHD free convection along a non-isothermal vertical surface in a thermally stratified porous medium

An analysis is performed for non-Darcy free convection flow of an electrically conducting fluid over an impermeable vertical plate embedded in a thermally stratified, fluid saturated porous medium for the case of power-law surface temperature. The present work examines the effects of non-Darcian flow phenomena, variable viscosity, Hartmann–Darcy number and thermal stratification on free convective transport and demonstrates the variation in heat transfer prediction based on three different flow models. The wall effect on porosity variation is approximated by an exponential function. The effects of thermal dispersion and variable stagnant thermal conductivity are taken into consideration in the energy equation. The resulting non-similar system of equations is solved using a finite difference method. Results are presented for velocity, temperature profiles and local Nusselt number for representative values of different controlling parameters.     

Nonlinear convection at a porous flat plate with application to heat transfer from a dike

Solutions for a class of coupled nonlinear differential equations, arising in free convection flow at a vertical flat plate embedded in a saturated porous medium at high Reynolds numbers in the presence of heat sources (or sinks) and with nonlinear density temperature variation, are obtained. Further, using the Schauder theory and numerical results, existence and analyticity results are established.     

Effects of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media with radiation

The effect of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media has been studied in the presence of radiation and magnetic field. The plate surface is embedded in a uniform Darcian porous medium in order to allow for possible fluid wall suction or blowing and has a power-law variation of both the wall temperature and concentration. The similarity solution is used to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential equations, and an efficient numerical technique is implemented to solve the reduced system. Numerical calculations are carried out, for various values of the dimensionless parameters of the problem, which include a variable viscosity, chemical reactions, radiation, magnetic field, porous medium and power index of the wall temperature parameters. Comparisons with previously published works are performed and excellent agreement between the results is obtained. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters.     

放/吸热流体在两个充满多孔材料的竖直平行板之间作不稳定的自然对流

在一个由两块无限竖直平行板组成的管道中,充满着多孔的介质材料,使用Darcy模型(Brinkman模型的推广)的动量方程,连同能量方程,计算不可压缩、粘性、放/吸热流体在该管道中的不稳定自然对流,即Couette流动.流动是由于边界平板有不对称的加热,以及作加速运动所引起.选用合理的无量纲参数,对控制方程进行简化,通过Laplace变换进行解析求解,得到闭式的速度和温度分布曲线解,随后导出表面摩擦力和传热率.发现在竖直管道中的不同剖面,流体的流动及温度分布曲线随着时间而增加,且在运动平板附近更高.特别是,流体的速度和温度随着平板间距的增加而增加,但是,表面摩擦力和热传导率随着平板间距的增加而减小.     

各向异性液体-多孔饱和介质在机械荷载作用下的弹性动力分析

将一个各向异性液体-多孔饱和介质的弹性动力分析,归结为一个横观各向同性液体-多孔饱和介质在机械荷载作用下的变形问题.自然界中有些物理问题,仅在一个方向发生变形,例如,与变形结构和变形柱有关的问题.土力学中,通常假设只有竖向沉降,从而归结为一维多孔弹性模型.采用各向异性液体-多孔饱和介质的一维变形模型,研究了在不同时间和距离下扰动的变化.给出了在不同类型荷载作用下,介质的各向异性对位移分布和应力分布的影响.     

Numerical study of viscous dissipation effect on free convection heat and mass transfer of MHD non-Newtonian fluid flow through a porous medium

The problem of free convection heat with mass transfer for MHD non-Newtonian Eyring–Powell flow through a porous medium, over an infinite vertical plate is studied. Taking into account the effects of both viscous dissipation and heat source. The temperature and concentration are of periodic variation. The governing non-linear partial differential equations of this phenomenon are transformed into non-linear algebraic system utilizing finite difference method. Numerical results for the velocity, temperature and concentration distributions as well as the skin friction, heat and mass transfer are obtained and reported in tabular form and graphically for different values of physical parameters of the problem. Also, the stability condition is studied.     

Effect of suction/injection on free convection along a vertical plate in a nanofluid saturated non-Darcy porous medium with internal heat generation

The effect of internal heat generation on free convection along a vertical plate embedded in a nanofluid saturated non-Darcy porous medium in the presence of suction/injection is analyzed. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms by non-dimensional variables. The resulting equations are solved numerically by an accurate, implicit, iterative finite-difference methodology and the obtained results are compared favorably with previously published work. A parametric study is performed to illustrate influence of the temperature exponent, non-Darcy, suction/injection, Brownian motion and thermophoresis parameters on the profiles of the velocity components, temperature and nanoparticle volume fraction. The numerical data for the heat and nanoparticle mass transfer rates have been tabulated for various parametric conditions.     

Flow in a porous medium induced by torsional oscillation of a disk near its surface

Torsional oscillation of an infinite disk in a viscous liquid bounded by a porous medium fully saturated with the liquid has been discussed. It is assumed that the flow between the disk and the porous medium is governed by Navier-Stokes equation and that in the porous medium by Brinkman equation. Flows in the two regions are matched at the interface by assuming that the velocity and stress components are continuous at it. It is found that the depth of penetration of the flow in the porous medium is proportional to the square root of the permeability of the medium. The oscillation of the disk induces a steady radial-axial flow in both the regions in such a way that there is a steady axial flow of the fluid from the porous medium to the free flow region i.e. the fluid is expelled out from the porous medium. The steady flow in the porous medium increases with the increase of the permeability of the medium and with the decrease of the distance between the oscillating disk and porous surface.