On the thermal flow through a porous annular region

Abstract

This paper reports the analytical results on the non-isothermal stationary fluid flow inside thin vertical annular region formed by two co-axial cylinders. The annulus is packed with the fluid-saturated sparsely packed porous medium which is cooled through the side wall. The flow is governed by the prescribed pressure drop between the top and bottom walls which are maintained at uniform, but different temperatures. The main objective of this work is to propose the approximate model describing the effective flow using rigorous asymptotic analysis with respect to the thickness of the annular region. Starting from the dimensionless Darcy-Brinkman-Boussinesq system endowed with the appropriate boundary conditions, we derive the explicit asymptotic approximation clearly showing the effects of the porous structure and thermal transfer. We also provide the theoretical error analysis in order to indicate the order of accuracy of the proposed model and justify its usage.