Analytical Investigation of Nanofluid Natural Convection in a Shallow Cavity with Differentially Heated End Walls in Presence of Electromagnetic Forces

Ahmad Jamali Keikha

Abstract

The present study deals with the effect of electromagnetic forces on the problem of natural convection in a cavity of small aspect ratio with differentially heated end walls. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes: a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A→ 0, are derived.