A numerical solution of developing temperature for laminar developing flow in eccentric annular ducts

The energy equation expressed in bipolar coordinates is used to determine the temperature distribution in the thermal entrance region of an eccentric annular duct. An implicit alternating-direction method is used in the numerical solution. The analysis of the hydrodynamic entrance region, which provides the velocity distributions needed for the thermal solution, was obtained from a published solution by the present authors. A published Graetz solution for an eccentric annulus and a published combined thermal and hydrodynamic entrance region solution for the circular tube are used in the verification of the present solution. In the present analysis 17 combinations of fundamental thermal boundary conditions, Prandtl number, and annular geometry are considered. The annular geometry with equal relative eccentricity and radius ratio of 0.5 is used to study the effects of eccentricity and Prandtl number on the fluid temperature and surface heat flux distributions.