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23.4.4 Energy Equation

The energy equation for the mixture takes the following form:

 \frac{\partial}{\partial t}\sum_{k=1}^{n} (\alpha_k \rho_k E... ... + p)) = \nabla \cdot \left(k_{\rm eff} \nabla T \right) + S_E (23.4-7)

where $k_{\rm eff}$ is the effective conductivity ( $\sum \alpha_k (k_k+ k_t)$), where $k_t$ is the turbulent thermal conductivity, defined according to the turbulence model being used). The first term on the right-hand side of Equation  23.4-7 represents energy transfer due to conduction. $S_E$ includes any other volumetric heat sources.

In Equation  23.4-7,

 E_k = h_k - \frac{p}{\rho_k} + \frac{v_k^2}{2} (23.4-8)

for a compressible phase, and $E_k = h_k$ for an incompressible phase, where $h_k$ is the sensible enthalpy for phase $k$.

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