Fully Developed Flow between two parallel plates

[JasonB_VT]

Hey you all,

I have a practice exam problem which is causing some difficulty for me.

Basically I have a fully developed flow through two parallel plates. One plate has a constant heat flux and the other plate is heavily insulated.

I have found the velocity profile: U=2*Uinf*(1-r^2/h^2)
where h is the radius.

Now I have set up the boundary condition to solve the differential equation but I'm confused on which equation to use. There is a general equation (I would post it here but its too messy) that will solve temperature distributions in a tube. With these equations, however, there is either a constant temperature or constant flux around the whole boundary.

I am confused on how to go about solving this problem, any advice will help! Thank you.

 

[minger]

You can basically start with governing equations. Start canceling out terms until you're left with a differential equation that you can solve.

For example, you can show that radial velocity = 0; you know that d/dz = 0 as well.

 

[RandomGuy88]

Like minger mentioned start with the governing equation and then apply the boundary conditions. Which in your case would be constant heat flux at both boundaries. Heavily insulated means no heat flux which is a constant heat flux of 0.

If the flow is fully developed for both velocity and temperature between two plates you should only be left with the diffusion term perpendicular to the plates because there is no temperature gradient in the flow direction and no velocity component perpendicular to the plates. The only other thing to consider would be viscous dissipation but I guess it depends on the situation whether or not you want to keep that term.