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[UTchemE09]

Hi,

I'm a Undergrade ChemE student at UT, and was wondering if anyone can help me out with doing energy balances on elemental shell volumes using Fourier's law? I have a couple very general, basic questions about setting up the differential equations. My teacher barely speaks english and no one knows what's going on in the class right now- I kind of have an idea from the book and his typed lecture notes, but I'm a little hazy on some of the details. We are assuming steady state, and unidirectional heat flow. Can anyone set up and solve the differential equation to get the temperature profile for heat flowing through a cylinder? I'll start it off, and see if anyone can pick up where I'm having confusion.

I am doing an energy balance through a cylinder whose orientation is laying down sideways. The r direction is in the radial direction of the circle of the cylinder, the z direction runs the length, and we'll call theta "b" I'm assuming heat is only flowing in the z direction- down the length of the cylinder.

q = heat flux = heat flow/area
Total energy (heat) = q*area where area is perpendicular to the flow. The balance will be on an elemental volume from z to (z + deltaz) where delta simply means change in z.

A = I - O = - (O - I)
= (qz*A(z + delta z) - (qz*Az) Az = A(z + delta z) = (pi*r^2)

Now I'm stuck on how to set up the derivative...I think you're supposed to divide by volume at this point, and chance the delta's to differentials?