How Does Radial Temperature Vary in a Thermally Conductive Hollow Cylinder?

AI Thread Summary
The discussion focuses on determining the radial temperature variation, T(r), in a thermally conductive hollow cylinder with inner radius r1 and outer radius r2, in dynamic thermal equilibrium. The heat current equation, which relates thermal conductivity, area, and temperature difference, is central to the analysis. Participants emphasize the need to account for the changing area when calculating heat currents, suggesting the use of calculus. A thin shell approach is recommended to simplify the calculations, as the area difference between the inner and outer surfaces can be negligible for small thicknesses. The conversation highlights the importance of applying the heat conduction equation correctly to derive the temperature profile within the cylinder.
Domisterwoozy
Messages
6
Reaction score
0

Homework Statement


A hollow cylinder of length L has inner radius, r1, outer radius, r2 , and
thermal conductivity, k. It is in dynamic thermal equilibrium, with its interior
held at temperature T1 and its exterior at a different temperature, T2. What is the
radial temperature dependence, T(r), within the cylinder, r1 ≤ r ≤ r2 ?

Homework Equations


Heat Current = KA(T-T)/L

The Attempt at a Solution


I know heat current out equals heat current in and than you solve for T. However, I cannot figure out how to calculate the heat currents since the area is changing.
 
Physics news on Phys.org
You need to use calculus. Consider a very thin shell surrounding the center of the cylinder, of thickness dr. The area of one side isn't very different from the area of the other, so you can use that heat conduction equation.
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

How Is the Equilibrium Temperature Derived in a Coaxial Cylinder Configuration?
Replies
4
Views
2K
Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
Replies
8
Views
2K
Velocity of a hollow cylinder at the bottom of an incline
Replies
9
Views
4K
Radial Heat Conduction through a Cylindrical Pipe
Replies
3
Views
2K
How does the rise in temperature of fuse wire depend upon its radius?
Replies
12
Views
1K
I Warm-up time for a hollow cylinder
Replies
5
Views
2K
Temperature dependent heat-conductivity
Replies
3
Views
1K
Calculating Heat Transfer in a Cylinder with CO2 Gas at Different Temperatures
Replies
3
Views
1K
Radial current in a hollow metal cylinder
Replies
24
Views
23K
How to Calculate Heat Current in a Spherical Shell?
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top