Forced and mixed convection in the annulus between two horizontal confocal elliptical cylinders

Abstract

This study presents a numerical simulation of the three dimensional laminar mixed convection between two elliptical horizontal cylinders using temperature dependent physical properties. The inner cylinder is uniformly heated whereas the outer cylinder is adiabatic. The flow and thermal fields are modeled by the continuity, momentum and energy equations with appropriate initial and boundary conditions using an elliptical coordinate system. The model equations are numerically solved by a finite volume numerical method with a second order accurate spatiotemporal discretization. For the considered geometric, dynamic and thermal controlling parameters, it is found that the realistic consideration of the mixed convection with variable physical properties gives physically sound flows and thermal fields that are qualitatively and quantitatively different from those of forced convection with temperature dependent properties and those of mixed convection with constant properties; the obtained Nusselt number is also higher in this case. The heat transfer enhancement obtained by considering natural convection within mixed convection with temperature dependent physical properties increases with the increased Grashof number which is proportional to the heat flux imposed at the surface of the inner cylinder.