Thermal resistance in conductive constructal designs of arbitrary configuration: A new general approach

Constructal networks cooling a heat generating body has been the subject of many investigations in the last decade. Various configurations have been proposed and optimized deterministically. However, the analytical solutions are quite different for each class of geometries. Also, deductions based on numerical simulations cannot be generalized. Therefore, a general method to calculate the thermal resistance of a constructal network with arbitrary configuration is provided in the present study. The formulation is based on analytical solution of temperature distribution in a high conductivity link collecting the heat generated in a volume of arbitrary shape. It is shown that the thermal resistance of a link can be written in the form of conventional one dimensional resistance if an effective length is considered. The thermal resistance of the whole network could then be obtained by a weighted summation of all thermal resistances. Results of the present formulation for configurations of various geometries show that this method is completely consistent with the available analytical and numerical solutions.