Axial temperature distributions in concentric cooling channels surrounding a heat generating source

Abstract

A set of simultaneous differential equations is established to describe the temperature distribution for coolant flow in three concentric channels separated by walls of finite thermal conductivity and surrounding a cylindrical heat source. The solution of this set of differential equations is dependent on the heat source function Q(z) which must be known or specified. An assumed function Q(z) ~ constant is taken as being a representative case and the resultant solutions are applied to several geometric arrangements. The system of three channel flow reduces to two channel flow when there is zero heat flow across the outer intermediate wall. This condition may arise if the wall is a perfect insulator, or if the flow in the third channel is zero. For the former case the temperature in the third channel is constant over its length, and in the second the stationary coolant assumes the temperature of the coolant in the middle channel. From the set of differential equations established for two channel flow, treatment similar to that used for three channel flow is adopted and the resultant solutions are applied to several geometric arrangements. Brief mention is made of single channel flow. By assuming that the heat source is zero in the case of two channel flow, expressions are derived for the temperature distribution in parallel flow heat exchangers.