I am working on modeling of air-heater component. A simplified representation of system is as follows:
Cold air flow enters steel duct at one end. Inside duct is Calrod heating element shaped as ellipse. Follwing heat transfer occur simulteneously:-
- Air gains heat from surface of heated calord.
- Air also exchanges heat with duct inner surface.
- Calrod element radiates heat to duct inner surface.
- Duct loses heat by radiation to surroundings as well as convection.
System is solved by taking energy balance equations on Air mass, Duct mass and Heater element mass.
My question is in regards to convection between air and duct. In model, I have considered whole assembly to be made of 5 parts along duct length. In each part respective thermal balance on air, duct and heated element mass is taken. In each part, I consider air to be lump-sum mass. Entering air gains heat from calrod and gains some temperature ( which would in real world be average temperature). Problem occurs when that temperature is used for convection transfer with duct. In actual process, air flow is fast enough (0.013 $\frac{m^3}{sec}$) so that air that actually is in contact with heater element doesn't reach duct surface. So air that exchanges heat with duct inner surface is at lower temperature than average air's temperature. This gives incorrect duct temperature predictions. How can I properly set $\Delta T$ for convection heat exchange with duct?