Vertical Surface In Porous Medium Research Articles

Effects of Radiation and Viscous Dissipation on Transient Free Convection Heat Transfer Flow Past a Hot Vertical Surface in Porous Media

The radiation effects on unsteady transient free convection flow of a viscous incompressible gray, absorbing-emitting but non-scattering, optically-thick fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity taking viscous dissipation onto account has been carried out. Thermal radiation effects are simulated via a radiation-conduction parameter (),rK based on the Rossseland diffusion approximation. We employ a Darcian viscous flow model for the porous medium. The momentum and thermal boundary layer equations are non-dimensionalzed using appropriate transformations and then solved subject to physically realistic boundary conditions using the Ritz finite element method. The computed numerical results for velocity(),u temperature(),θ shear stress function()τ and wall temperature gradient function()Nu are presented through the graphs and tables for air (0.71)rP= and water (7.00).rP= It has been found that increasing thermal radiation parameter ()rKcauses a considerable increase in the flow velocity .u Temperature θ is significantly increased within the boundary layer with a rise in.rK The velocity is found to decrease with an increase in inverse permeability parameter ()pK and increases with increase in the Grashof number ()rG and Eckert number ().

MHD free convection flow of Eyring–Powell fluid from vertical surface in porous media with Hall/ionslip currents and ohmic dissipation

A mathematical study is presented to analyze the nonlinear, non-isothermal, magnetohydrodynamic (MHD) free convection boundary layer flow, heat and mass transfer of non-Newtonian Eyring–Powell fluid from a vertical surface in a non-Darcy, isotropic, homogenous porous medium, in the presence of Hall currents and ionslip currents. The governing nonlinear coupled partial differential equations for momentum conservation in the x, and z directions, heat and mass conservation, in the flow regime are transformed from an (x,y,z) coordinate system to a (ξ,η) coordinate system in terms of dimensionless x-direction velocity (f′) and z-direction velocity (G), dimensionless temperature and concentration functions (θ and ϕ) under appropriate boundary conditions. Both Darcian and Forchheimer porous impedances are incorporated in both momentum equations. Computations are also provided for the variation of the x and z direction shear stress components and also heat and mass transfer rates. It is observed that with increasing ɛ, primary velocity, secondary velocity, heat and mass transfer rates are decreased whereas, the temperature, concentration and skin friction are increased. An increasing δ is found to increase primary and secondary velocities, skin friction, heat and mass transfer rates. But the temperature and concentration decrease. Increasing βe and βi are seen to increase primary velocity, skin friction, heat and mass transfer rates whereas secondary velocity, temperature and concentration are decreased. Excellent correlation is achieved with a Nakamura tridiagonal finite difference scheme (NTM). The model finds applications in magnetic materials processing, MHD power generators and purification of crude oils.

Computational Study of MHD Free Convection Flow of Non-Newtonian Tangent Hyperbolic Fluid from a Vertical Surface in Porous Media with Hall/Ionslip Currents and Ohmic Dissipation

A numerical study is presented to analyze the nonlinear, non-isothermal, magnetohydrodynamic (MHD) free convection boundary layer flows of non-Newtonian tangent hyperbolic fluid past a vertical surface in a non-Darcy, isotropic, homogenous porous medium in the presence of Hall currents and Ionslip currents. The governing nonlinear coupled partial differential equations for momentum conservation in x and z directions, heat and mass conservation in the flow regime are transformed from an (x, y, z) coordinate system to (\(\upxi ,\upeta \)) coordinate system in terms of dimensionless x-direction velocity (\(f^{\prime }\)) and z-direction velocity (G), dimensionless temperature and concentration functions (\(\uptheta \) and \(\upphi \)) under appropriate boundary conditions. Both Darcian and Forchheimer porous impedances are incorporated in both momentum equations. Computations are also provided for the variation of the x and z direction shear stress components and also heat and mass transfer rates. Increasing Weissenberg number (We) is observed to decrease primary and secondary velocity and concentration but increase temperature. It is found that the primary and secondary velocity is increased with increasing power law index (n) whereas the temperature and concentration are decreased. Increasing hall and Ionslip current (\(\beta _{e}\) and \(\beta _{i}\)) is observed to increase primary velocity but decreases secondary velocity, temperature and concentration. Increasing magnetic parameter (\(N_{m}\)) is seen to decrease primary velocity but decreases secondary velocity, temperature and concentration. Increasing Darcy number (Da) is found to increase primary and secondary velocity whereas decreases temperature and concentration. Increasing Forchheimer parameter (Fs) is seen to decrease primary and secondary velocity but increases temperature and concentration. The model finds applications in magnetic materials processing, MHD power generators and purification of crude oils.

Convection Heat Transfer on a Vertical Surface in Porous Media

Free convection on a vertical surface with Newtonian heating of the form proposed by Merkin (1994) in the fluid-filled porous medium is considered on the basis of the full equations of a viscous liquid. Using dimensional analysis a set of criteria that define the characteristics of flow and heat transfer was derived. Asymptotic analysis of the full equations allowed us to determine the region of applicability of the boundary layer approximation, which was used in the previous studies of this problem. Darcy parameter influence was studied; the composite numerical and analytical solution for stream function and temperature was derived.

Asymptotic Model of Free Convection Flow on a Vertical Surface in Porous Media with Newtonian Heating

The mathematical model based on system of momentum and energy equations for free convection flow along a vertical surface in porous media under boundary conditions of the third sort is solved analytically using the method of matched asymptotic expansions. The region of validity for boundary layer model and expansions for stream function and temperature with parameter of perturbations were defined. The dependence of characteristic flow from governing dimensionless parameters and was analyzed numerically. The influence of viscous and convective terms of momentum equation in the proposed mathematical model significantly increases the rate of heat transfer on plate in porous media in comparison with Darsy flow model.

Effect of Viscous Dissipation, Soret and Dufour Effect on Free Convection Heat and Mass Transfer from Vertical Surface in a Porous Medium

In the present approach, a two dimensional steady free convection flow of heat and mass transfer from a vertical surface in porous media with viscous dissipation has been analyzed numerically considering Soret and Dufour effects. The governing non linear partial differential equations have been transformed by a similar transformation in to a system of ordinary differential equations, which are solved numerically by using implicit finite difference scheme. The dimensionless velocity, temperature and concentration profiles are displayed graphically showing the effects for the different values of the Lewis number, soret number and viscous dissipation parameter.

Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet in the presence of the radiation and buoyancy effects

The homotopy analysis method is employed to examine free convective heat and mass transfer in a steady two-dimensional magnetohydrodynamic fluid flow over a stretching vertical surface in porous medium. In this study thermal radiation and non-uniform magnetic field are taken into consideration. The two-dimensional boundary-layer governing partial differential equations are derived with considering Boussinesq and boundary-layer approximations, and the ordinary differential nonlinear forms of momentum, energy and concentration equations, obtained by the similarity solution, are solved analytically in the presence of buoyancy forces. The effects of different involved parameters such as magnetic field parameter, suction parameter, Prandtl number, buoyancy parameter, Schmidt number, Biot number and radiation parameter on velocity, temperature and concentration profiles are plotted and discussed in the paper.

Unsteady MHD double-diffusive convection boundary-layer flow past a radiate hot vertical surface in porous media in the presence of chemical reaction and heat sink

This paper presents an analytical study of the unsteady MHD free convective heat and mass transfer flow of a viscous, incompressible, gray, absorbing-emitting but non-scattering, optically-thick and electrically conducting fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity. We employ a Darcian viscous flow model for the porous medium the Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The homogeneous chemical reaction of first order is accounted in mass diffusion equation. The governing equations are solved in closed form by Laplace-transform technique. A parametric study of all involved parameters is conducted and representative set of numerical results for the velocity, temperature, concentration, shear stress function \(\frac{\partial u}{\partial y} \vert_{y=0}\), temperature gradient \(\frac{\partial \theta }{ \partial y}\vert_{y=0}\), and concentration gradient \(\frac{ \partial \phi }{\partial y}\vert_{y=0}\) is illustrated graphically and physical aspects of the problem are discussed.

Effect of mass transfer on the free convective flow through a porous medium with variable permeability in slip flow regime with couple stresses

This paper examines the problem of mass transfer on MHD unsteady free convective flow of a polar fluid through a porous medium of variable permeability bounded by an infinite horizontal porous plate in slip flow regime. The permeability of the porous medium decreases exponentially with time about a constant mean. Using perturbation technique the expressions for the velocity distribution, mean angular velocity of rotation of particles, concentration distribution and skin friction are obtained. The effects of permeability parameter K0, Magnetic parameter M, Prandtl number Pr , Schimdt number Sc ,and Grashof number Gr ,Modified Grashof number Gm entering into the problem on velocity, temperature distribution and concentration distribution are shown graphically and discussed numerically. It can be observed that this velocity decreases with the increase in M, Pr, Sc and increases with the increase in K0, Gr, Gm. Temperature and Concentration decreases with the increase in the value of Pr and Sc respectively. INTRODUCTION The convection problem in a porous medium has important application in geothermal reservoirs and geothermal energy extractions. It is obvious that in order to utilize the geothermal energy to maximum, one should have a complete and precise knowledge about the amount of perturbations needed to generate convection current in geothermal fluids. Also the knowledge of the quantity of perturbation is essential to entreat convection current in mineral fluids that is found in the earth’s crust helps one to utilize minimal energy to extract the minerals. Cheng and Lau[1] and Cheng and Teckchandani [2] obtained numerical solutions for the convective flow in a porous medium bounded by two isothermal parallel plates in the presence of withdrawl of the fluid. All the above mentioned studies treat the permeability and the conductivity or thermal resistance of the medium as constant or neglect the effect of porosity. Lai and Kulacki [6] studied Coupled heat and mass transfer by natural convection from vertical surfaces in porous media. Lin and Wu[7] discussed Coupled heat and mass transfer by laminar natural convection from vertical plate. Malasetty and Gaikwad[8] investigated effect of cross diffusion on double diffusion convection in the presence of horizontal gradients. Yan et. al [11] have discussed Simultaneous heat and mass transfer in laminar mixed convection flows between vertical parallel plate with asymmetric heating. Yan[12] studied Turbulent mixed convection heat and mass transfer past a vertical porous plate. Mazumdar and Deka[9] investigated MHD flow past an impulsively started infinite vertical plate in presence of thermal radiation. In geothermal region situation may arise when the flow becomes unsteady and sliping at the boundary may take place as well. In such situation of slip flow, ordinary continuum approach fails to yield satisfactory results. Many authors have solved problems taking slip conditions at the boundary. Jain and Teneja [3] solved the problem of magnetopolar flow through a porous medium in slip flow regime. Khandelwal et al [5] have studied effect of couple stresses on the flow through a porous medium with variable permeability in slip flow regime. Varshney et. al.[10] have discussed effect of heat transfer on the flow through a porous medium with variable permeability in slip flow regime with couple stress. Our problem under study is an extension of the problem of Varshney et. al.[10] with mass transfer. The effects of different parameter entering into the problem viz. Permeability parameter Ko, Magnetic Am. J. Sci. Ind. Res., 2011, 2(3): 469-477 470 parameter M, Prandtl number Pr , Schimdt number Sc ,and Grashof number Gr ,Modified Grashof number Gm entering into the problem on velocity, temperature distribution and concentration distribution are shown graphically and discussed numerically FORMULATION AND SOLUTION OF THE PROBLEM Let us consider the unsteady flow of a polar fluid through a porous medium of variable permeability in slip flow regime past an infinite horizontal porous plate in presence of a transverse magnetic field. The external velocity of the fluid is assumed as nt 0 U [1 e ] − + e . The flow is chosen to be at small magnetic Reynolds number which enables us to neglect the induced magnetic field. The x-axis is taken along the plate and y-axis normal to it. Under these conditions the equations which govern the flow are: v 0 y ∂ = ∂ (1)

Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect

The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are presented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ, the order of the chemical reaction parameter m, the Soret number Sr, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.

The Effects of Thermal Radiation, Hall Currents, Soret, and Dufour on MHD Flow by Mixed Convection over a Vertical Surface in Porous Media

The study sought to investigate the influence of a magnetic field on heat and mass transfer by mixed convection from vertical surfaces in the presence of Hall, radiation, Soret (thermal-diffusion), and Dufour (diffusion-thermo) effects. The similarity solutions were obtained using suitable transformations. The similarity ordinary differential equations were then solved by MATLAB routinebvp4c. The numerical results for some special cases were compared with the exact solution and those obtained by Elgazery (2009) and were found to be in good agreement. A parametric study illustrating the influence of the magnetic strength, Hall current, Dufour, and Soret, Eckert number, thermal radiation, and permeability parameter on the velocity, temperature, and concentration was investigated.

Theoretical Analysis of Radiative Effects on Transient Free Convection Heat Transfer past a Hot Vertical Surface in Porous Media

The purpose of the present investigation deals with the unsteady free convective flow of a viscous incompressible gray, absorbing-emitting but non-scattering, optically-thick fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity. We employ a Darcian viscous flow model for the porous medium. The momentum and thermal boundary layer equations are non-dimensionalized using appropriate transformations and then solved subject to physically realistic boundary conditions using the Laplace transform technique. Thermal radiation effects are simulated via a radiation-conduction parameter, Kr, based on the Rosseland diffusion approximation. The influence of Grashof (free convection) number, radiation-conduction parameter (Kr), inverse permeability parameter (Kp) and dimensionless time (t) are studied graphically. We observe that increasing thermal radiation parameter causes a noticeable increase in the flow velocity, u. Temperature, θ, is significantly increased within the boundary layer with a rise in Kr since the latter represents the relative contribution of thermal radiation heat transfer to thermal conduction heat transfer. Increased radiation therefore augments heat transfer, heats the fluid and increases the thickness of the momentum and thermal boundary layers. Velocity is found to decrease with an increase in Kp (inverse permeability parameter) as are shear stress function ( ∂u/∂y | y=0) magnitudes owing to greater resistance of the porous medium for lower permeabilities, which decelerate the flow. An increase in Kr however boosts the shear stress function magnitudes i.e. serves to accelerate the flow. Temperature gradient, ∂θ/∂y | y=0 is also positively affected by an increase in thermal radiation (Kr) and with time. The present study has applications in geological convection, forest fire propagation, glass heat treatment processes at high temperature, metallurgical processing etc.

Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects

The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a saturated porous medium subjected to a chemical reaction is numerically analyzed, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion (Soret) effects. The transformed governing equations are solved by a very efficient numerical method, namely, a modified version of the Keller-box method for ordinary differential equations. The parameters of the problem are Lewis, Dufour and Soret numbers, sustentation parameter, the order of the chemical reaction n and the chemical reaction parameter γ. Local Nusselt number and local Sherwood number variations and dimensionless concentration profiles in the boundary layer are presented graphically and in tables for various values of problem parameters and it is concluded that γ and n play a crucial role in the solution.

Influence of a magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects

The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a saturated porous medium subjected to a magnetic field is numerically studied, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion (Soret) effects. The governing partial differential equations are transformed into a set of coupled differential equations, which are solved numerically using a finite difference method. Dimensionless velocity, temperature and concentration profiles are presented graphically for various values of the magnetic number M and Lewis number Le, and for fixed values of the Dufour number D f, Soret number S r and buoyancy number N. Three cases are considered and presented in tables, for the local Nusselt number and local Sherwood number corresponding to Le=1 and various values of M, N, D f and S r. Increasing the value of M increases the local Nusselt number and local Sherwood number.

Transient non-Darcy mixed convection along a vertical surface in porous medium with suction or injection

Transient non-Darcy mixed convection from a semi-infinite, isothermal vertical plate embedded in a homogeneous porous medium, in the presence of surface suction or injection has been numerically investigated. Forchheimer extension is considered in the flow equations. Appropriate transformations are employed to transform the governing partial differential equations to a non-similar form. The transformed equations have been solved numerically using an implicit finite difference scheme. Numerical results illustrating the effects of all involved parameters on the transient velocity and temperature profiles, the local Nusselt number and the friction coefficient are presented and discussed.

Transient heat and mass transfer by natural convection from verticalsurfaces in porous media

A study on the transient heat and mass transfer from verticalplates embedded in fluid saturated porous media is conducted. The walltemperature and concentration are power functions of the dimensionlessstreamwise coordinate. Results for the heat and mass transfer rates areobtained for different values of the Lewis number, the buoyancy ratio, thepower-law exponent and the ratio of porosity and heat capacity ratio. Thetransient local Nusselt number at X = 1 is found to be almost independentof the ratio of porosity and heat capacity ratio, while the transient localSherwood number at X = 1 tends to increase as the ratio of porosity andheat capacity ratio is increased. Moreover, increasing the power-lawexponent increases the transient local Nusselt and Sherwood numbers.

The effect of longitudinal surface waves on free convection from vertical surfaces in porous media

In this paper we consider the effect of longitudinal surface waves on the thermal boundary layer flow induced by a vertically aligned heated surface embedded in a porous medium. The full governing equations are considered and the boundary layer equations are derived in a systematic way. It is found that, for a wide range of values of x, the distance from the leading edge, the boundary layer equations for the three—dimensional flowfield are satisfied by a two-dimensional similarity solution.

Non-Darcy mixed convection along nonisothermal vertical surfaces in porous media

An analysis is performed for mixed convective flow through a fluid-saturated porous medium adjacent to a vertical surface with the heating condition of power-law variation in the wall temperature. The entire mixed convection regime is covered by the single parameter χ = [1+( Ra x/ Pe x) 0.5] −1 from the pure forced convection limit ( χ = 1) to the pure free convection limit ( χ = 0). In modeling the flow through porous media, non-Darcy effects such as high-flow-rate inertia forces, no-slip boundary condition, near-wall porosity variation and thermal dispersion are taken into consideration. Because of the porosity variation in the near wall region, the stagnant thermal conductivity also varies accordingly. The aims of the present work are to examine the effects of non-Darcian flow phenomena on mixed convective transport and to demonstrate the variation in heat transfer predictions based on different flow models. A finite difference scheme was used to solve the transformed system of equations. Numerical results show that non Darcian and thermal dispersion effects have significant influences on velocity profiles, temperature profiles and heat transfer rates from the vertical surface.

Nonsimilarity solutions for mixed convection from vertical surfaces in porous media: variable surface temperature or heat flux

Nonsimilarity solutions for mixed convection from a vertical flat plate embedded in a porous medium are reported for two surface heating conditions: variable wall temperature (VWT) and variable surface heat flux (VHF) of the power-law form. The entire mixed convection regime is divided into two regions. One region covers the forced convection dominated regime and the other one covers the free convection dominated regime. The governing equations are first transformed into a dimensionless form by the nonsimilar transformation and then solved by a finite-difference scheme. Four nonsimilarity parameters are introduced. The parameters Ra x/Pe x and Ra x */Pe x 3/2 characterize the effect of buoyancy forces on the forced convection for the VWT and VHF cases, respectively; while the parameters Pe x/Ra x and Pe x/Ra x *2/3 characterize the effect of forced flow on the free convection for VWT and VHF cases, respectively. Numerical results for both heating conditions are presented. Correlation equations for the local and average Nusselt numbers are also presented.

Coupled heat and mass transfer by natural convection from vertical surfaces in porous media

Similarity solutions for buoyancy induced heat and mass transfer from a vertical plate embedded in a saturated porous medium are reported for (1) constant wall temperature and concentration, (2) constant wall heat and mass flux. In addition, the effect of flow injection on the heat and mass transfer has also been considered. Governing parameters for the problem under study are the buoyancy ratio, N, and Lewis number, Le. Depending on the sign of the buoyancy ratio, inclusion of a concentration gradient may either assist or suppress the flow induced by thermal buoyancy. The Lewis number is found to have a more pronounced effect on the concentration field than it does on the flow and temperature fields. Results for Nusselt and Sherwood numbers cover a wide range of the governing parameters, −1 < N < 10 and 0.1 ⩽ Le ⩽ 100, and a comparison is made with the results of Bejan and Khair ( Int. J. Heat Mass Transfer 28, 909–918 (1985)).