Research project on heat transfer

[chrismdn]

Homework Statement

have you ever encountered this equation? it is the energy differential equation through a rectangular tube

Homework 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

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

 

[DrClaude]

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.

 

[Chestermiller]

Homework Statement

have you ever encountered this equation? it is the energy differential equation through a rectangular tube

Homework 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

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

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.