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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.