Fourier Equation:
q′′=-k∇T
Conduction Equation:
ρcP ∂T/∂t=∇∙(k∇T)+qgen
Boundary Conditions-
Constant Surface Temperature- T(0,t) = Ts (Dirichlet Condition)
Constant applied flux- -k d/dx T(0,t) = q'' (Neumann Condition)
Heat Equation:
∂T/∂x=α (∂2T)/(∂x2)
α=k/(ρCP) (thermal diffusivity)
Video on Fourier's Law