Spatial and Temporal Resolution of Conjugate Conduction-Convection Thermal Resistance

A transient, 3-D solution to the heat conduction equation with a small square heat source on an adiabatic surface and Newtonian convection on the opposite side was obtained using Green´s functions. The geometry conservatively models conduction spreading resistance encountered by small, concentrated heat sources such as light-emitting diodes and integrated circuits in general, mounted to larger substrates such as the base of a heat sink experiencing Newtonian convection. The solution is presented for a range of nondimensional parameters. Superposition techniques can also be used to extend the applicability of the current solution to the temperature prediction of arbitrary heat flux patterns in certain cases. This technique only holds for applications where the heat transfer coefficient is not a function of temperature, such as thermal management strategies designed to rely on forced convection with air.