[universez]

In compressible flow solvers, eEqu and hEqu share the same parameter "thermal diffusivity", or turbulence->alphaEff() in the following equations. However, my understanding of the meaning of thermal diffusivity should be different in these equaitons, i.e. , (for a laminar flow),

In eEqu, alpha = K / (Cv rho), where Cv, k and rho are heat capacity at constant volume, theremal conductivity and density, respectively.

while, in hEqu, alpha = k / ( Cp rho), where Cp, k and rho are heat capacity at constant pressure, theremal conductivity and density, respectively.

My questions are:

1, my understanding about alpha is right or wrong?
2, if i am right, is openFoam wrong ?, or there is specific application inside openfoam dealing with this issue?

========================================
In sonicFoam eEqu is

solve
(
fvm::ddt(rho, e)
+ fvm::div(phi, e)
- fvm::laplacian(turbulence->alphaEff(), e)
==
- p*fvc::div(phi/fvc::interpolate(rho))
);

========================================
In rhoPisoFoam hEqu is

fvScalarMatrix hEqn
(
fvm::ddt(rho, h)
+ fvm::div(phi, h)
- fvm::laplacian(turbulence->alphaEff(), h)
==
DpDt
);