Thermal Physics problem: Heat transfer coefficient?

[rune]

I'm having a bit of trouble with a Thermal Physics exercise. I was wondering if anyone knew what the definition of the heat transfer coefficient was? I can't find anything about it in my textbook (Thermal Physics, 2nd ed., C.B.P. Finn).

More specifically, the assignment at hand says to find the temperature T(r) in a hollow cyllinder with length L (where r is the distance from the axis of the cyllinder, so that the cyllinder is symmetric about this axis), inner radius r_1, outer radius r_2, inner wall is kept at temperature T_1 and outer wall temperature is kept at T_2 (temperature of the surroundings), after equilibrium has been reached. The material of the cyllinder has heat transfer coefficient H. Also, T_2<T_1. (It also asks explicitly if the result depends on H.)

Any tips or hints to get me started?

 

[Nenad]

Thermal Conductivity coefficient is what you're looking for. The equation to use is:
q = -(kA)\frac{dt}{dx}

where

q is heat flow rate is watts.

k is thermal conductivity in \frac{W}{m \Dot K}

A is cross sectional area normal to flow in m^2

\frac{dt}{dx} is the temperature gradient in \frac{K}{m}

Regards,

Nenad

 

[rune]

First of all, thanks for the help Nenad.
I guess I should've mentioned the text was in Norwegian, and heat transfer coefficient seemed like the most direct translation of the wording in the text. Another thing I think i mis-translated was that it said stationary conditions, not equillibrium.

I think I got it right thanks to your help though:
First setting A=2 \pi rL, and then using your equation: \frac{dQ}{dt}=-(HA)\frac{dT}{dr}=C , where I set the heat flow rate to a constant since there are stationary conditions (but not zero since that would be absurd as long as we are using energy to maintain T_1 on the inner wall, right?).
For simplicity, I then set C'=-\frac{C}{H2 \pi L}, and the resulting differential equation is:
dT=\frac{C'}{r}dr
which gives:
T(r)=C'\ln(r)+T_0
solving for C' and T_0 using given initial conditions (T(r_1)=T_1 and T(r_2)=T_2) gives:
T(r)=\frac{T_2-T_1}{\ln(\frac{r_2}{r_1})}\ln(\frac{r}{r_1})+T_1
Thus T(r) doesn't depend on H.