Heat transfer -- one-dimensional energy balance for the heating of a fluid...

1. Oct 25, 2015

Ian Limjap

1. The problem statement, all variables and given/known data
1. Perform a one-dimensional energy balance for the heating of a fluid through a hot pipe in order to develop a differential equation that governs the variation of the mean temperature of the fluid along the length pipe. The pipe has an inner diameter D and length L; its walls are kept at a constant temperature Tw. The fluid has a mean velocity v. The heat transfer coefficient h between the pipe wall and the fluid is constant, and the radial convective heat flux q is:

q = hA(Tw − T ) where T is the mean temperature of the fluid.

If the fluid has a mean inlet temperature To, solve the above differential equation to obtain an expression for the variation of the temperature with the distance x along the pipe. For this part of the problem, you can neglect the influence of conduction (i.e. assume k ≈ 0) and assume heat transfer along the pipe only occurs through convection.

2. Relevant equations
Accumulation=in-out+generation
Generation=0
3. The attempt at a solution
0=q(x)A(x)-q(x+deltax)A(x+deltax)+h(Tw-T)A+p(x)A(x)v1-p(x)A(x+deltax)v2
=>d/dx[rho*v*U(x)A(x)]+d/dx[p(x)A(x)v]=h(Tw-T)A/deltax
Any help will be greatly appreciated.
Thanks.

2. Oct 30, 2015

Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?