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  • $\begingroup$ What actually energy conservation means in your case? $\endgroup$ Commented Oct 4, 2021 at 4:45
  • $\begingroup$ In the section CONSTANTS, I am calculating the heat required to heat the fluid up 10K. From that I am calculating the heat flux (heat per area) to set as Neumann BC on the solid. In the section Energy balance analysis I am calculating the enthalpy difference of the fluid, as well as integrating the heat flux on the wall and comparing these. When using the single line as you proposed in the old threat, energy conservation is not given, as you are using the fluid temperature for each boundary cell of the solid but not using the average temperature as function of z coordinate vice versa. $\endgroup$ Commented Oct 4, 2021 at 7:30
  • $\begingroup$ Simply put: With energy conservation I am meaning, the energy input of the system equals the energy output of the system. Heat input is from the heat flux at the wall and heat output is through the 1D region outlet at z=l $\endgroup$ Commented Oct 4, 2021 at 7:34
  • $\begingroup$ If you are curious to compare the energy conservation of your old approach and mine you can run the code from my old question (link at the top) and change the wall temperature function in the "SOLVE CHANNEL" section from " tempIntegrateInterpFun[z]" to "Tw[i, z]". Tw[i,z] is basically just your approach put into a function. $\endgroup$ Commented Oct 4, 2021 at 7:43
  • $\begingroup$ @Tobias One could try to use structured mesh in $z$ direction by means of function ExtrudeMesh from MeshTools. Than in each slice $z_i$ average wall temperature is calculated by $T_w(z_i)=\int_{-\pi/2}^{\pi/2}T(r_a\cos\varphi,H_a+r_a\sin\varphi,z_i)d \varphi/\pi$. By avoiding surface integration we can diminish (I hope) calculation time $\endgroup$ Commented Oct 11, 2021 at 7:41