# Homework Help: Research project on heat transfer

1. May 8, 2017

### chrismdn

1. The problem statement, all variables and given/known data
have you ever encountered this equation? it is the energy differential equation through a rectangular tube

2. Relevant equations
uρ(∂i/∂x)+vρ(∂i/∂y)+wρ(∂i/∂x)-[∂/∂x(k∂t/∂x)+∂/∂y(k∂t/∂y)+∂/∂z(k∂t/∂x)]=0
heat transfer coeff is k

3. The attempt at a solution
have you any idea how to derive this equation? I am reviewing a paper for a project and this equation derivation might be helpful for me. any help would be appreciated.

chris

2. May 8, 2017

### Staff: Mentor

I guess that t is temperature, but what is i? This looks like a conservation equation. You probably need to check out a book on fluid mechanics.

3. May 8, 2017

### Staff: Mentor

If i were the same thing as t, this would look like the steady state differential heat balance equation for a fluid experiencing both heat advection (u,v,w) and conduction. If that were the case, then the rho in your equation would be the product of heat capacity and density, and the parameter k, rather than being the heat transfer coefficient, would be the thermal conductivity.