The homotopy analysis method (HAM) has been used to develop an analytical solution for the
thermal performance of a circular-thin-foil heat flux gage with temperature dependent thermal conductivity
and thermal contact resistance between the edge of the foil and the heat sink. Temperature
distributions in the foil are presented illustrating the effect of incident heat flux, radiation emission
from the foil, variable thermal conductivity, and contact resistance between the foil and the heat sink.
The HAM results agree up to four places of decimal with the numerical solutions generated using the
symbolic algebra package Maple. This close comparison vouches for the high accuracy and stability
of the analytic solution.
