Thermal Spreading Resistance in a Multilayered Orthotropic Circular Disk With Interfacial Resistance and Variable Heat Flux

Thermal spreading resistance in a multilayered orthotropic disk is considered. Interfacial resistance between each layer is prescribed by means of a contact conductance h_c using a Robin type boundary condition. Orthotropic properties are considered by transforming the orthotropic system into an equivalent isotropic system using stretched coordinates. A recursive modeling approach is presented to account for the effects of two or more layers in the structure from the simple case of a single isotropic layer. This approach simplifies the analysis considerably. Finally, variable heat flux distribution is considered for three special cases: uniform, parabolic, and inverse parabolic. Numerous special cases can be derived from the general result including perfect interfacial contact and perfect sink plane conductance. Additional issues are also discussed in detail. The expressions for the total thermal resistance and spreading resistance can be easily implemented in any mathematical software or coded in Fortran, C, or BASIC. Since the method is strictly analytical, thermal analysts can quickly assess changes in layer properties, material sequence, heat flux distribution, and effects of interfacial contact resistance, with little extra effort.