The model assumes a heat source in contact with a larger cold plate which is in turn cooled with a convective heat transfer coefficient specified over the sink surface.

Unlike existing models that mostly assume limiting boundary conditions, such as isothermal conditions, at the sink surface, the present solution allows one to accurately determine the constriction and spreading resistances in a plate with a full range of cooling conditions varying from an isothermal condition in one limit to a uniform heat-flux condition in the other limit.

Dimensionless expressions in the form of infinite series are provided for computing the average and maximum constriction resistances as a function of relative contact size, plate thickness and the Biot number.

The results are compared with published numerical data, and the agreement is excellent over a wide range of parameters typically found in microelectronics applications.