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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.v33.i1-2.140
17 pages

Natural Convection in a Porous Rectangular Duct - the Brinkman Model

D. V. Krishna
Department of Mathematics, Sri Krishnadevaraya University, Anantapur, India
D. V. Prasada Rao
Department of Mathematics, Sri Krishnadevaraya University, Anantapur, India

ABSTRACT

The study of buoyancy driven convection How and heat transfer in a porous medium has gained importance owing to its application in the development of geothermal technology, drying technology, insulation technology and many other technological fields. Convective heat transfer in a rectangular porous duct with differentially heated sidewalls is a problem, which has received attention by many investigators. In this paper we discuss the said problem using finite element analysis. The governing nonlinear coupled equations for the momentum and temperature under the Brinkman's model are obtained in terms of the stream function and the temperature. The Galerkin method with eight node serendipity elements is used to obtain the coupled global matrices. These coupled matrices are solved using iterative procedure. The behavior of velocity, temperature and the Nusselt number is discussed computationally for different values of governing parameters, viz., the Grashof number, the Darcy parameter, and the Prandtl number. It is observed that in a two-dimensional convection now through a sparsely packed porous medium, the resultant velocity at any position in the given duct enhances with in crease in either the permeability of the medium or the thermal buoyancy acting on the fluid. In a given duct the influence of the thermal buoyancy exhibits a critical value for G. It is also interesting to know that irrespective of the aspect ratio of the duct, the values of Nusselt number exhibit in variance for all G in low-permeable media. In all ducts with moderate permeability the Nusselt number exhibits a hysteresis behavior for G greater than a critical value.


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