[Than]

Currently, I am trying to implement explicit algebraic heat flux models based on Manservisi2014 (https://doi.org/10.1016/j.ijheatmass...er.2013.10.017)
and Youssef1992 (https://doi.org/10.1016/0017-9310(92)90329-Q) in OpenFOAM.

I would like to use constant heat flux boundary conditions, which leads, according to these papers, to the following boundary condition for the dissipation of temperature variance:

here refers to the positon of the wall.
Using a zero-gradient for half of the temperature variance () leads, under approximating the boundary condition with first order finite differences, to:

which is definitely incorrect.
So my question is:
Does anyone know how the boundary condition for dissipation of temperature variance at constant wall heat flux can be implemented numerically in OpenFOAM?

Many thanks in advance.

Greetings
Than