Thermal Analysis Equations

The heat transfer equation is a parabolic partial differential equation that describes the distribution of temperature in a particular region over given time:

$ρ c \frac{\partial T}{\partial t} - \nabla \cdot (k \nabla T) = Q$

Boundary conditions include temperatures on the boundaries or heat fluxes through the boundaries.

For convective heat flux through the boundary $h t c (T - T_{\infty})$ , specify the ambient temperature $T_{\infty}$ and the convective heat transfer coefficient htc.
For radiative heat flux $ε σ (T^{4} - T_{\infty}^{4})$ , specify the ambient temperature $T_{\infty}$ , emissivity ε, and Stefan-Boltzmann constant σ.