A Rigorous Series Solution for a Thermal Dissipation System with a Diamond Heat Spreader on an Infinite Slab Heat Sink

Abstract

We consider the problem of conductive heat dissipation from an infinite stripe of constant heat flux, through an infinitely-long rectangular rod diamond heat spreader and an infinite slab heat sink. Using the Fourier cosine series and the Fourier transform, we have developed series solutions for both the temperature distributions in the system and the average temperature over the heating stripe. The series coefficients are determined through an infinite set of linear algebraic equations. Considering the case of diamond heat spreader and copper heat sink, we have investigated the effects of the geometrical dimensions and the thermal conductivity of the spreader on the thermal behavior of the system for a given sink thickness. The main results are: (1) there exists a spreader thickness for achieving the minimum temperature at the top spreader surface; (2) the commonly-used assumption of isothermal spreader-sink interface is valid for a relatively thicker spreader compared to the heating-stripe width; (3) increasing the ratio of the heat spreader width to the heating-stripe width beyond 30 does not reduce the average temperature significantly, indicating the existence of an effective spreader width; (4) for lowering the surface temperature, the spreader width is the most effective and practical design parameter over the thickness and the thermal conductivity.