# Heat flux

Hi!

I am trying to calculate the heat transfer coefficients in a circular pipe but i have had some problems with the energy balance. My case is this:

Circular pipe 10 m long and 1 m diameter.
Inlet: velocity 0.01 m/s, Temperature 150 deg
Cylinder wall: Temperature fixed value 100 deg, nut Spalding Wall-function

My y+ values are between 20 and 40.

Energy balance:

In: (Inlet velocity)*(Inlet temperature)*(Inlet area)*(specific heat*density)
Out: (heat flux at wall)*(wall area) + (Outlet velocity)*(Outlet temperature)*(Outlet area)*(specific heat*density)

This does not add up to zero unless the heat flux at the wall is multiplied with the density.
Also if I use a heat flux boundary condition on the wall face instead of a fixed temperature there is no difference in outlet temperature when i change the density.

### Heat Flux definition bug for incompressible flow

Thanks for your explanation of the problem.

I can confirm your findings. This is a bug, where the Heat Flux boundary specification and the Heat Flux scalar field result are represented as 'Heat Flux / rho' for incompressible flow. This will be fixed in the next version of Caedium. As a workaround you will need to:

• Specify the Heat Flux boundary condition as 'Heat Flux / rho'
• Create a new Scalar Field result 'Heat Flux * rho', where rho is a constant set to your density

### Heat Flux definition fixed in Caedium v5

This Heat Flux definition bug for incompressible flow is fixed in Caedium v5.