- #1

pm272

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I have been trying to solve this problem that has been keeping me up at night for a coupe weeks at least. If anyone can help me, I would be greatly appreciated.

Hot air enters a cylindrical duct. The duct has some R-value and radiation and convection is being accounted for on the outside surface of the duct. What is the bulk temperature of the air and the duct surface after some length, L?

I approached this problem as follows:

1) I sectioned out the duct into n dx lengths each with their own energy balances.

2) The first dx will see air entering at T_entering. This is T_i. The air is leaving at T_i+1. Air properties are dictated by this entering air temperature. Internal convection coefficient can be found as an empirical calculation - same with outside convection coeff.

3) Now I analyze the conduction problem of the duct itself with an external boundary condition accounting for convection and radiation. The internal boundary condition would be a temperature. I am using a Newton-raphson iterative method to solve the non-linear equation.

The problem I am running into is that I can find an external wall temperature based upon whatever internal bulk air temp I am using but I am unsure how to account for the fact that T_i+1 will change from T_i, and therefore continue through the entire length. I believe that I require another equation.

It seems similar to solving a 1-D conduction problem with radiation except that the internal temperature is changing along the length of the duct (as is wall temp).

This problem must be possible since I can essentially solve this using any CFD package.

Thank you