Forced convection heat transfer in rectangular ducts—general case of wall resistances and peripheral conduction for ventilation cooling of nuclear waste repositories

Abstract

A numerical solution for laminar flow heat transfer between a flowing gas and its containing rectangular duct has been obtained for many different boundary conditions which may arise in nuclear waste repository ventilation corridors. The problem has been solved for the cases of insulation on no walls, one wall, two walls, and three walls with various finite resistances on the remaining walls. Simplifications are made to decouple the convective heat transfer problem from the far field conduction problem, but peripheral conduction is retained. Results have been obtained for several duct aspect ratios in the thermal entrance and in the fully developed regions, including the constant temperature cases. When one wall is insulated and the other three are at constant temperature, the maximum temperature occurs in the fluid rather than on the insulated wall. This maximum moves toward the insulated wall with increasing axial distance. Nusselt numbers for the same constant flux on all four walls with peripheral conduction lie in a narrow band bounded by zero and infinite peripheral conduction cases. A dimensionless wall conduction group of four can be considered infinite for the purpose of estimating fully developed Nusselt numbers to within an accuracy of 3%. A decrease in wall and bulk temperatures by finite wall conduction has been demonstrated for the case of a black body radiation boundary condition. Nusselt numbers for the case of constant temperature on the top and bottom walls and constant heat flux on the side walls exhibited unexpected behavior.