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
Outlet: default zero gradient
Cylinder wall: Temperature fixed value 100 deg, nut Spalding Wall-function
My y+ values are between 20 and 40.
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.