Abstract
This work revisited the mixed convection flow formation in a uniformly heated vertical porous channel filled with porous material as discussed by Chandrasekhara and Nayrayanan [11]. Using perturbation method as well as numerical solution, Chandrasekhara and Nayrayanan [11] discussed the behavior of the fluid as well as rate of heat transfer. This methods are known not to be exact solution. In this work, we derived an exact solution using D’Alembert’s method and corrected some results obtained in [11]. To justify the accuracy of the present method, we used the implicit finite difference method (IFDM). Result shows that D’Alembert’s method is more efficient, effective and thus a promising tool for finding exact solution for coupled equations.
Highlights
The analysis of heat and mass transfer in porous media has become an interesting area of research due to its varied applications both in industrial and scientific applications such as extrusion of polymers, cooling of metallic plates, aerodynamics plastic extrusion, geothermal reservoirs, glass blowing and fiber spinning, drying of porous solids, thermal insulation, petroleum resources and many others
A review of the literature shows that laminar free convection in vertical channel has been studied by several authors: Elenbaas [1] led the first experimental study which was used in the follow as reference solution
In order to increase the cooling requirements, researches for methods to improve the heat transfer parameters or to analyze standard configurations to carry out optimal geometrical parameters for a better heat transfer rate are crucial [3,4,5,6,7,8,9]
Summary
The analysis of heat and mass transfer in porous media has become an interesting area of research due to its varied applications both in industrial and scientific applications such as extrusion of polymers, cooling of metallic plates, aerodynamics plastic extrusion, geothermal reservoirs, glass blowing and fiber spinning, drying of porous solids, thermal insulation, petroleum resources and many others. Fluid flow nested with porous medium is a common phenomenon in nature such as transport of water in living plants, trees and fertilizers or wastes in soil. This problem is motivated by its engineering applications as: convection in the Earth crust, flows in soils, aquifers, storage of agriculture products and so on. Bodoï and Österle [2] obtained the first numerical solution of the natural convection in vertical channel. In order to increase the cooling requirements, researches for methods to improve the heat transfer parameters or to analyze standard configurations to carry out optimal geometrical parameters for a better heat transfer rate are crucial [3,4,5,6,7,8,9]
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