Numerical Simulation of Transient Free Convection Flow and Heat Transfer in a Porous Medium (original) (raw)
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Frontiers in Heat and Mass Transfer
A numerical investigation is performed to analyze the transient laminar free convection over an isothermal inclined plate embedded in a saturated porous medium with the viscous dissipation effects. The flow in the porous medium is modeled with the Darcy-Brinkman-Forchheimer model, taking into account the convective term. The dimensionless nonlinear partial differential equations are solved numerically using an explicit finite difference method. The effects of different parameters: (1 ≤ Re ≤ 10 ; 10 −2 ≤ Da ≤ 10 ; 0 ≤ Gr ≤ 50 ; 0 ≤ F r ≤ 3 ; 0 ≤ Ec ≤ 1 ; 0 ≤ φ ≤ 90 0 and P r = 0.71) that enter into the problem on the dimensionless streamlines of the velocity field, the isothermal lines distributions and the local Nusselt number are examined. Also, the physical aspects of the problem are discussed in details. It is found that the viscous dissipation and the inertial forces have a significant effect on the temperature field whereas the wall heat transfer rate is optimal for the vertical position of the plate.
Journal of Porous Media, 2014
In this article, the nonlinear steady state boundary layer flow and heat transfer of an incompressible Eyring-Powell non-Newtonian fluid from a vertical porous plate in a non-Darcy porous medium is investigated. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a secondorder versatile, implicit finite-difference Keller box technique. The numerical code is validated with previous studies. The influence of a number of emerging nondimensional parameters, namely, Eyring-Powell rheological fluid parameters (ε), the local non-Newtonian parameter based on length scale (δ), Prandtl number (Pr), Darcy number (Da), Biot number (Bi), Forchheimer parameter (Λ), and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented, and excellent correlation is achieved. It is found that the velocity is reduced with increasing fluid parameter (ε) and Forchheimer parameter (Λ). But temperature is enhanced with increasing fluid parameter and Forchheimer parameter. Increasing fluid parameter δ is the local non-Newtonian parameter based on length scale x, and the Darcy parameter, Da, enhances the velocity but reduces the temperature. The increasing Biot number, Bi, is observed to enhance both velocity and temperature, and an increasing Prandtl number decreases the velocity and temperature.
Journal of the Egyptian Mathematical Society, 2012
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.
The unsteady free convection and mass transfer flow past an exponentially accelerated infinite vertical plate with variable viscosity and thermal conductivity has been investigated in this work. The plate temperature is raised linearly with time and the concentration level near the plate is raised to C .The governing boundary layer equations of momentum, temperature and concentration are the second order couple linear partial differential equation. Mathematical formulation of boundary layer equations have been non-dimensionalized by using dimensionless variables. These non-dimensional boundary layer equations are non-linear and partial differential equations and are solved by finite difference method. For the different physical parameters the results of velocity, temperature and concentrations are displayed in the form of level curves. Skin friction and Nusselt number are also described in graphically.
Numerical Study on Unsteady Free Convection and Mass Transfer Flow past a Vertical Porous Plate
The unsteady free convection and mass transfer boundary layer flow past an accelerated infinite vertical porous plate by taking into account the viscous dissipation is considered when the plate accelerates in its own plane. The dimensionless momentum, energy and concentration equation are solved numerically by using explicit finite difference method with the help of a computer programming language Compaq visual FORTRAN 6.6. The obtained results of this study have been discussed for different values of well-known parameters with different time steps. The flow phenomenon has been identified with the help of flow parameters such as Porosity parameter (P), Grashof number for heat transfer (Gr), Modified Grashof number for mass transfer (Gc), Scmidth number (Sc), Prandtl number (Pr) and Eckert number (Ec). The effect of these parameters on the velocity field, temperature field and concentration field has been studied and results are presented graphically also skin friction and Nusselt number is represented by the tabular form
The objective of the paper is to analyze the unsteady free convective flow and mass transfer through a viscous, incompressible, electrically conducting fluid along a porous vertical isothermal non-conducting uniformly moving plate in the presence of exponentially decaying heat generation and transverse magnetic field with variable suction and viscous dissipation. The governing equations of motion, energy and concentration are transformed into ordinary differential equations using similarity parameter method. The ordinary differential equations are then solved numerically using Runge – Kutta method along with shooting technique. Numerical results for velocity, temperature and concentration are obtained for various values of physical parameter and presented graphically. Also the numerical values of skin-friction coefficient, Nusselt number and Sherwood number are obtained for various values of physical parameters discussed and presented through tables.
2015
This is an Open Access Journal / article distributed under the terms of the Creative Commons Attribution License (CC BY-NC-ND 3.0) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. All rights reserved. This paper presents a numerical analysis of the MHD free convection flow and mass transfer of a dissipative fluid along a vertical porous plate with thermal conductivity and viscosity depending on temperature and mass transfer, the surface of which is exposed to a constant heat flux. The non-linear system of partial differential equations is numerically solved by the implicit finite difference scheme of Crank–Nicolson’s type. Velocity, temperature and concentration profiles, local skin-friction, local Nusselt and local Sherwood numbers are plotted for air. The influence of the Suction rate parameter, buoyancy ratio parameter, dissipation number, viscosity variation parameter, thermal conductivity variation param...
Non-Darcy Free Convective Heat Transfer from a Plate in a Porous Medium
International Journal of Fluid Mechanics Research, 2005
In this article, the problem of buoyancy-induced flow over a horizontal or a vertical flat plate embedded in a fluid-saturated non-Darcy porous medium is studied. Forchheimer extension is considered in the flow equations. Similarity solutions for the transformed governing equations are obtained, with a prescribed variable surface temperature or variable surface heat flux, for each position of the plate. Values of the slip velocity, Nusselt number for variable surface temperature as well as excess surface temperature for variable surface heat flux, and the total heat transfer as well as the momentum flux, which are plotted in figures, have been presented for different values of the given parameters for the two cases of horizontal and vertical plates.
Flow Turbul Combust, 1993
Transient non-Darcy free convection between two parallel vertical plates in a fluid saturated porous medium is investigated using the generalized momentum equation proposed by Vafai and Tien. The effects of porous inertia and solid boundary are considered in addition to the Darcy flow resistance. Exact solutions are found for the asymptotic states at small and large times. The large time solutions reveal that the velocity profiles are rather sensitive to the Darcy number Da when Da < 1. It has also been found that boundary friction alters the velocity distribution near the wall, considerably. Finite difference calculations have also been carried out to investigate the transient behaviour at the intermediate times in which no similarity solutions are possible. This analytical and numerical study reveals that the transient free convection between the parallel plates may well be described by matching the two distinct asymptotic solutions obtained at small and large times.
Chemical Engineering Journal, 2011
This paper focuses on the thermo-diffusion (Soret) and diffusion-thermo (Dufour) effects on a steady laminar free convection heat and mass transfer flow past a semi-infinite vertical plate in the presence of suction and injection. Soret and Dufour effects are significant when density differences exist in the flow regime. For example, when species are introduced at a surface in fluid domain, with different (lower) density than the surrounding fluid, both Soret and Dufour effects can be influential. The governing boundary layer equations are normalized with appropriate transformations. The resulting system of nonlinear partial differential equations is solved numerically using the efficient Keller-box implicit finite difference method. A parametric study of the influence of Soret number, Dufour number, suction/ blowing parameter, buoyancy parameter, Prandtl number and Schmidt number on the velocity, temperature and concentration in the boundary layer regime is presented. The behavior of skin-friction, Nusselt number and Sherwood number are also presented. It is found that increasing Soret number with simultaneously decreasing Dufour number enhances the local heat transfer rate (local Nusselt number) at the plate, whereas the opposite effect is sustained for the mass transfer rate (local Sherwood number). This model finds applications in metallurgical materials processing, chemical engineering flow control, etc.