Heat Transfer Coefficient Calculation

1

I am trying to simulate the laminar flow with heat transfer problem in a square duct with fixed wall temperature. The flow is hydrodynamically developped (fully developped velocity profile imposed at inlet) and thermally developping. The script and mesh are here https://github.com/bragostin/Fenics
I use two methods to calculate the average heat transfer coefficient:

  1. Integration of local values:
    Area = assemble(T/T*ds_bc(association_table["noslip"]))
    LMDT = ((Tw - T_out_avg) - (Tw - T_in_avg)) / ln((Tw - T_out_avg) / (Tw - T_in_avg))   
    htc_avg = assemble(dot(k*grad(T), n)*ds_bc(association_table["noslip"])) / Area / LMDT

yielding 34 W/m2 K
2. Global value:

    ds_bc = ds(subdomain_data=boundaries)    
    U = sqrt(dot(u,u))
    u_in_avg = assemble(U*ds_bc(association_table["inlet"])) / (We * He)
    u_out_avg = assemble(U*ds_bc(association_table["outlet"])) / (We * He)
    T_in_avg = assemble(U*T*ds_bc(association_table["inlet"])) / (u_in_avg * We * He)
    T_out_avg = assemble(U*T*ds_bc(association_table["outlet"])) / (u_out_avg * We * He)
    DT_avg = T_out_avg - T_in_avg
    Heat_Load = u_in_avg * We * He * rho * cp * DT_avg
    htc_avg = Heat_Load / (Area * LMDT)

yielding 234 W/m2 K.
I think the second value is wrong, but I still cannot understand why this difference, they should be equal.

1 Like
2

My bad: it was a meshing issue, nothing to do with Fenics. As I refine the mesh the two values converge.