Thermal Resistance Approach Of Transient Heat Conduction In Constructal Geometries

This paper, presents a new approach to an analytical solution for the time-dependent heat conduction problems. Many of transient heat conduction problems are solved with method of separation of variables which is time-consuming. Thus the main objective of this article is converting a partial differential equation to an ordinary differential equation that it can be solved easier and faster. This can be happen with scale analysis which assuming that in semi-infinite bodies x = √αt , so time domain changes to space domain and in this way it can be solve a transient problem to a steady state one; however, the analytical solutions are quite different for each class of geometries. Also, deductions based on numerical simulations cannot be generalized. Therefore, a new method to calculate the thermal resistance of a constructal network with arbitrary configuration is needed which in this paper the formulation for transient mode has been provided. Keywords- Analytical Solution, Constructal Geometries, Transient Heat Conduction