Numerical Study of Free Convection in a Doubly Stratified Non-Darcy Porous Medium Using Spectral Quasilinearization Method

2015 ◽  
Vol 16 (3-4) ◽  
pp. 173-183 ◽  
Author(s):  
D. Srinivasacharya ◽  
Sandile S. Motsa ◽  
O. Surender
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Numerical Study ◽  
Saturated Porous Medium ◽  
Nonlinear Partial Differential Equations ◽  
Darcy Number ◽  
Skin Friction Coefficient ◽  
Linearization Method ◽  
Convection Boundary Layer ◽  
Local Skin

AbstractFree convection boundary layer flow past a semi-infinite vertical plate in a doubly stratified fluid-saturated porous medium in the presence of constant suction/injection is analyzed. The flow in the porous medium is described by the Brinkman–Forchheimer-based model. A suitable coordinate transformation is introduced, and the obtained system of non-similar, coupled and nonlinear partial differential equations is solved numerically using the spectral quasi-linearization method. The effects of buoyancy parameter, Darcy number, Forchheimer parameter, suction/injection parameter, thermal and solutal stratification parameters on the dimensionless velocity, temperature and concentration are presented graphically. Further, the local skin friction coefficient, heat and mass transfer rates are presented graphically.

NATURAL CONVECTION BOUNDARY LAYER FLOW ALONG A SPHERE EMBEDDED IN A POROUS MEDIUM FILLED WITH A NANOFLUID

2014 ◽  
Vol 44 (2) ◽  
pp. 149-157
Author(s):  
A. M. RASHAD
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Extended Model ◽  
Local Skin ◽  
Layer Flow

 A boundary-layer analysis is presented for the natural convec tion boundary layer flow about a sphere embedded in a porous medium filled with a nanofluid using Brinkman-ForchheimerDarcy extended model. The model used for the nanofluid incorporates the ef fects of Brownian motion and thermophoresis. The governing partial differential equa tions are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity, temperature, and nanoparticles volume fraction profiles as well as the local skin-friction coefficient, local Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.

scholarly journals Natural Convection from a Permeable Sphere Embedded in a Variable Porosity Porous Medium Due to Thermal Dispersion

2007 ◽  
Vol 12 (3) ◽  
pp. 345-357
Author(s):  
S. M. M. El-Kabeir ◽  
M. A. El-Hakiem ◽  
A. M. Rashad
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Darcy Number ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Thermal Dispersion ◽  
Convective Boundary ◽  
Local Skin ◽  
Variable Porosity ◽  
Permeable Sphere

The laminar natural convection boundary-layer flow of an electricallyconducting fluid from a permeable sphere embedded in a porous medium with variable porosity is considered. The non-Darcy effects including convective, boundary, inertial and thermal dispersion effects are included in this analysis. The sphere surface is maintained at a constant heat flux and is permeable to allow for possible fluid wall suction or blowing. The resulting governing equations are nondimensionalized and transformed into a nonsimilar form and then solved numerically by using the secondlevel local non-similarity method that is used to convert the non-similar equations into a system of ordinary differential equations. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity and temperature profiles as well as the local skin-friction coefficient and the Nusselt number are illustrated graphically to show interesting features of Darcy number, inertia coefficient, the magnetic parameter, dimensionless coordinate, dispersion parameter, the Prantdl number and suction/blowing parameter.

scholarly journals Non-Similar Solutions for Heat and Mass Transfer from a Surface Embedded in a Porous Medium for Two Prescribed Thermal and Solutal Boundary Conditions

2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Abdelraheem Mahmoud Aly ◽  
Ali Chamkha
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Saturated Porous Medium ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Boundary Layer Equations ◽  
Similar Solutions

This work studies the effects of homogeneous chemical reaction and thermal radiation on coupled heat and mass transfer by free convection from a surface embedded in a fluid-saturated porous medium. Two different cases of thermal and solutal boundary conditions, namely the prescribed surface temperature and concentration (PSTC) case and the prescribed heat and mass fluxes (PHMF) case are considered. The governing boundary-layer equations are formulated and transformed into a set of non-similar equations. The resulting equations are solved numerically by an accurate and efficient implicit finite-difference method. The obtained results compared with previously published work and found to be in excellent agreement. A representative set of results is displayed graphically to illustrate the influence of the radiation parameter, chemical reaction parameter and the permeability of the porous medium on the velocity, temperature and concentration fields as well as the local skin-friction coefficient, local Nusselt number and the local Sherwood number.

scholarly journals MHD Free Convection-Radiation Interaction in a Porous Medium - Part I: Numerical Investigation

2020 ◽  
Vol 25 (1) ◽  
pp. 198-218
Author(s):  
B. Vasu ◽  
R.S.R. Gorla ◽  
P.V.S.N. Murthy ◽  
V.R. Prasad ◽  
O.Anwar Bég ◽  
...  
Keyword(s):  
Porous Medium ◽  
Finite Difference ◽  
Free Convection ◽  
Numerical Investigation ◽  
Darcy Number ◽  
Central Difference ◽  
Local Skin ◽  
Finite Difference Equations ◽  
Time Calculation ◽  
Local Skin Friction

AbstractA numerical investigation of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium is presented by taking into account the Soret/Dufour effects. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. We use simple central difference derivatives and averages at the mid points of net rectangles to get finite difference equations with a second order truncation error. We have conducted a grid sensitivity and time calculation of the solution execution. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. The Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. A comparative study between the previously published and present results in a limiting sense is found in an excellent agreement.

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