FINITE ELEMENT ANALYSIS OF DOUBLE DIFFUSIVE CONVECTIVE HEAT TRANSFER THROUGH A POROUS MEDIUM IN A CONCENTRIC CYLINDRICAL ANNULUS

Abstract

We discuss the non-Darcy free and forced convection flow through a porous medium in a Co-axial 
cylindrical duct where the boundaries are maintained at constant concentration. The inner cylinder is 
maintained at constant temperature and the outer cylinder is maintained at constant heat flux. The Brinkman 
Forchhimer extended Darcy equations which takes into account the boundary and inertia effects are used in 
the governing linear momentum equation. The effect of density variation is combined to the buoyancy term 
under Boussineq approximation. The momentum, energy and diffusion equations are coupled equations. In 
order to obtain a better insight into this complex problem, we make use of Galerkin finite element analysis 
with Quadratic Polynomial approximations. The Galerkin finite element analysis has two important features. 
The first is that the approximation solution is written directly as a linear combination of approximation 
functions with unknown nodal values as coefficients. Secondly, the approximation polynomials are chosen 
exclusively from the lower order Piecewise polynomials restricted to contiguous elements. The behaviour of 
velocity, temperature and concentration is analyzed at different axial positions. The shear stress and the rate of 
heat and mass transfer have also been obtained for variation in the governing parameters.