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OpenFOAM's Energy Equation 'h' Form: Replacing 'Fourie' with Gradient of 'hk/cp'

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Old   January 27, 2024, 20:01
Default OpenFOAM's Energy Equation 'h' Form: Replacing 'Fourie' with Gradient of 'hk/cp'
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In the "h" form of the energy equation, OpenFOAM has replaced the "Fourier Law" with the gradient of "h" multiplied with "k/cp". I want to know what kind of assumptions should be satisfied to validate this. I think Cp must be a constant value, but in reality , most fluids don't satisfy this condition.

fvm::laplacian(turbulence->alphaEff(), he)

\frac{\partial h}{\partial x} = \frac{\partial h}{\partial T} \frac{\partial T}{\partial x} =  C_p \frac{\partial T}{\partial x}
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Old   January 29, 2024, 09:09
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No - I don't believe so. You have written out the chain rule which demonstrates that grad T can be replaced with grad h divided by Cp ... there is no need for Cp to be constant. However, note that:

C_p \equiv (\frac{\partial h}{\partial T})_p

and this provides you your assumption ... the equivalence holds for constant pressure, which is generally acceptable for many flows but may prove problematic for strongly compressible flows.
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