TITLE:
A Simple Closed Form Solution to Single Layer Heat Spreading Angle Appropriate for Microwave Hybrid Modules
AUTHORS:
Rick L. Sturdivant, Astacian J. Bogdon, Edwin K. P. Chong
KEYWORDS:
Heat Transfer, Thermal Analysis, Microwave, Hybrid, Reliability
JOURNAL NAME:
Journal of Electronics Cooling and Thermal Control,
Vol.6 No.2,
June
15,
2016
ABSTRACT: A simple equation for heat spreading angle is derived which is useful for
cases with a single layer thermal spreader. The derivation starts with
Fourier’s heat transfer law. Heat spreading in two dimensions is then
introduced which results in a quadratic equation relative to spreading angle.
The result is a closed form equation for heat spreading angle. Calculations
using the equation are compared to 3D finite element simulations which show agreement
acceptable for most practical applications and over a wide range of physical
dimensions and thermal conductivities. A norma-lized dimensional parameter is
defined which is used to generate a curve fit equation of the spreading angle.
A three step procedure is then presented which allows the calculation of the
spreading angle and temperature rise in the thermal spreader. The result has
application for initial calculations of temperature rise in microwave hybrid
modules and electronic packages such as heat sinks for high power amplifiers.
This is because it is common for these types of modules and packages to use a
single layer heat spreader in copper-tungsten (CuW) or copper-molybde-num
(CuMo) connected to a cold plate. An important benefit of this method is that
it allows microwave hybrid designers and high power amplifier packaging
engineers a method to quickly perform trade studies to determine the maximum
mounting temperature for integrated circuits.