Heat flow through conical constructions in vacuum and in conducting media

Heat conduction through a long cylinder terminating in the frustrum of a cone which is surrounded by a vacuum or a conducting fluid is investigated. The problem is analyzed numerically by finite differences using an energy balance technique to obtain the finite difference network and solved by the Gauss-Siedel method with successive overrelaxation. The results show that the constriction resistance, defined as the ratio of the temperature drop due to the constriction to the temperature gradient in the undisturbed field, decreases significantly in the presence of a conducting fluid and as the cone semiangle increases. It is found that the disk constriction resistances can be used in the analysis of heat flow through joints formed by nominally flat rough surfaces in vacuum. Experimental tests on a notched specimen verify the results of the analysis.