Performance analysis and optimization of a radiating fin array

Abstract

Space radiators are used to reject waste heat from power units, electronic devices, and various equipment in space vehicles. It is important that radiators can achieve the heat desired to be dissipated into space with the least mass. With a view to ensuring this aim, the heat transfer calculations that must be performed must be highly accurate. Therefore, the variation of conductivity with temperature should also be taken into account in the mathematical model. This paper presents heat transfer performance and optimization of a fin array consisting of straight fins put axially on a tube and radiating heat into deep space. The mathematical model yields the governing equation as a highly nonlinear integro-differential equation which is solved by the variation of parameters method (VPM). By applying an appropriate optimization procedure, the conduction-radiation parameter, N-c, providing maximum heat transfer is obtained for a given fixed fin profile emissivity, epsilon, opening angle among the fins, gamma, and thermal conductivity parameter describing the variation of thermal conductivity, beta. For the range of suitable problem parameters, optimum values of the dimensionless conduction-radiation parameter N-c, which is a combination of thermal and geometric quantities, are expressed in epsilon and gamma for a given beta. The correlation equations are expected to provide remarkable benefits to the designer.