# Governing equations

OpenTerrace solves partial differential equations for both phases.

$\epsilon_f \rho_f c_{p,f} \frac{\partial T}{\partial t} = - \rho_f c_{p,f} u \frac{\partial T}{\partial x} + \frac{\partial}{\partial x}\left( k_f\frac{\partial T}{\partial x}\right) + S$
$\epsilon_b \rho_b c_{p,b} \frac{\partial T}{\partial t} = \frac{\partial}{\partial x}\left( k_b\frac{\partial T}{\partial x}\right) + S$

The source term S contains effects such as coupling between the phases or heat loss to surroundings.