14 – Energy fluxes evaluation

The evaluation of the energy flux is done summing diffusive and convective flux, and it is given by the following equations:

1. Flux through a line x:


2. Flux through a line h:


And

q = energy flux;

ki = thermal condition at the interface, see chapter (6);

Ji = Jacobian of the coordinate transformation at the interface, equation (3.7);

a, g e b = coordinate transformation metrics at the interface, equations (3.4) to (3.6);

r = fluid density;

Cp = specific heat;

U e V = contravariant velocities at the interface, equations (3.2) and (3.3);

T = temperature at the interface;

Tref = reference temperature.

The convective flux, given by the second term on the right side of equations (14.1) and (14.2), uses as reference temperature Tref = 0.

Below is shown how energy fluxes are evaluated, q, at following faces of the elemental volumes:

East face:
 
(14.3)
North face:
    
 
(14.4)
 
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