Analytic Solution to Steady Heat Conduction with Transverse Radiation Heat Transfer

A unique analytic solution to the problem of steady heat conduction with radiative heat transfer normal to the conduction heat flow is presented. The solution is unique, as it does not assume zero temperature of the surroundings and addresses all possible tip boundary conditions for in-space applications. The temperature profiles in the direction of heat conduction are produced for a constant-temperature boundary condition at the base and three different boundary conditions at the tip: adiabatic, constant temperature, and radiative heat transfer. Approximate solutions to the implicit exact solution are also developed. An extended solution that includes convection for the adiabatic-tip boundary condition is also presented and compares very well to experimental data.