I have a gas flowing down a tube which has walls at constant temperature, and I am wondering what the temperature profile of this gas is along the tube. I know that temperature will vary with radius of the tube, however I am mainly concerned with the the temperature profile along the tube. I have seen this video (https://www.youtube.com/watch?v=bYvPtxhO70s&ab_channel=KodyPowell) which was helpful, however I cannot find values for the heat transfer coefficient of my gas of interest. I have found thermal conductivities here for my gases of interest (https://www.engineersedge.com/heat_transfer/thermal-conductivity-gases.htm). Any information to help solve this question is much appreciated!
Sean Okonsky, You probably know the mass flow rate (Fm) and gas inlet temperature (To), so you only need to formulate the energy balance. Here it will take a simplified form: FmcdT=β(Tw-T)dS ==> dT/dl=(πdβ/Fmc)(Tw-T), T(0)=To, β - mass transfer coefficient from wall to gas (an appropriate criteria equation is needed), d - tube diameter, l - current length, c - specific heat.
The temperature distrubution depends greatly on the flow regime (turbulent, laminar), flow structure (developed or developing) and the heat transfer mode (forced convection, mixed convection, radiation). You should check Richardson number (Ri=Gr/Re2) to determine if you are dealing with forced or mixed convection problem. If you're solving a mixed convection problem, the flow may be weakly compressible if the Mach number Ma
The asymptotic value of Nusselt number for a fully developped laminar flow (i.e. far from the tube's entrance region) is:
4.36 for a constant heat flux boundary condition as provided by M. habchi.
3.66 for a constant temperature boundary condition.
In the developing region the Nu number is much high and decreases as the flow develops to reach the constant values above.
Hope this information is helpful
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