Diffusion term

For turbulent flow $ \lambda$ in the energy equation has to be replaced by $ \lambda + \lambda_t$ where

$\displaystyle \lambda_t = \frac{c_p \mu_t}{Pr_t},$ (703)

where $ Pr_t \approx 0.9$ is the turbulent Prandl number. Therefore, one now arrives at:

$\displaystyle \int_{A}^{} \lambda^T \frac{\partial T}{\partial n} da \approx \s...
...F}} + \nabla T_f ^{(m-1)} \cdot (\boldsymbol{n}_f - \boldsymbol{j}_f) \right ],$ (704)

where $ \lambda^T := \lambda + \lambda_t$ and

$\displaystyle (\lambda_t)_f ^{(m-1)} = \frac{c_p ^{(m-1)} \rho ^{(m-1)} k ^{(m-1)} }{Pr_t \; \omega ^{(m-1)} }.$ (705)

$ \omega$ is the turbulence frequency. The dynamic turbulent viscosity $ \mu_t$ can be written as $ \mu_t = \rho k / \omega$.

The boundary conditions for the diffusion term amount to: