Heat Convection through a Vertical Pipe

AstroWave

Hello everyone,

I am trying to model the flow of steam through a vertical cylinder. Ultimately I would like to find the surface temperature as a function of the length of the pipe. I am assuming the steam cools as it moves upward along the length of the pipe and it is a steady-state process, so T only varies with position (1-dimensional).

Doing a shell balance around a small portion of the pipe I am confused about the convection term entering in from the base and leaving through the top of the shell. I understand the cross sectional area concerning this convection term is the area of a circle. However, I am uncertain about how to determine the gradient for the surface temperature when all of the terms in the energy balance are due to convection.

I have seen the similar process done for a solid pipe (long fin) where there was conduction through the shell and convection out of the side. But I am confused by fluid motion inside the shell.

Any advice on this conceptually, or if you could recommend another approach, would be appreciated.

256bits

You have to determine whether you are dealing with laminar or turbulent flow to begin with. The analysis is not a plug into an equation and get the answer,

Consider this article:
http://people.msoe.edu/~kumpaty/cour...18/Week6_7.pdf