# Heat transfer coefficient in forced convection and its dependence of temperature

I'm working on a Ansys Fluent of an Aluminium coil annealing furnace with the goal of estimating the heat transfer coefficients at different temperatures and ventilator/fan speed conditions. The furnace transfers heat coils by blowing hot air through round nozzles at high speeds, i.e. similar to a impinging jet. I have simulated cases with different inlet air temperatures and velocities and then calculated the HTC from the average temperature and heat flux of the coil at each surface as well as the inlet air temperature. An ideal gas law was used for the material properties of air. Velocity inlets and pressure outlets were used for the inflow and outflow of air.

The results show higher HTC for higher fan speeds, which is expected. But it also shows a considerable lowering of HTCs with increasing temperature. On closer investigation, it seems to be that the HTCs have a dependence on the mass flow rate of the jets, which decreases with increasing temperature. Is this expected in theory?

Are you holding the mass flow constant?

If not, if it is based on the velocity & temperature then the higher temperatures cause gases, and most fluids, to expand.

• No, the mass flow is not constant as I'm using the ideal gas formulation. But why should the HTC decrease, if the fluid expands, i.e. density decreases? I thought the HTC is mostly dependent on Reynolds number, i.e. fluid velocity.
– Ash
Apr 21, 2022 at 8:46
• @Ash if the gas expands, then there are fewer molecules in the same volume to transfer the heat. Feynman has a set of 6 lectures you can find on the web... Apr 21, 2022 at 9:01
• Thanks for the tip! Yes, I can understand that in terms of molecules. I was instead thinking about the empirical equations for HTC under different flow conditions. It has a strong dependence on the Reynolds number. But I was wondering where the density term was. Finally remembered that the Reynolds number has an indirect density dependence in terms of kinematic viscosity.
– Ash
Apr 21, 2022 at 16:23

Found the answer. The heat transfer coefficient has a dependence on Reynolds number which also has the kinematic viscosity term, which in turn depends on the gas density. So naturally when the density decreases at higher temperatures, so does Re and correspondingly the HTC. Refer here for more information on impinging jets.

• So, like I put in my answer: the gas expands… Apr 21, 2022 at 17:44