Effect of Heat Transfer on Newtonian Flow Between Concentric Elliptical Regions

Abstract

In the present study, the slow and steady flow of Newtonian fluid in the presence of heat transfer in annular region formed by two concentric ellipses is considered. The concentric ellipses in z-plane are mapped to concentric circles in ζ-plane using conformal transformation. Analytical solutions for velocity and temperature are obtained in ζ-plane and the same are graphically depicted. The effects of dimensionless parameter such as Grashof number Gr, heat flux β, initial temperature at wall of inner ellipse θ0 and area of cross section of concentric ellipses on velocity, rate of flow and temperature have been studied. The graphical representation shows that the velocity, temperature is enhanced with increase in Gr and area of cross section between ellipses, and decreases with increase in heat flux β.