Register to reply

Heat transfer problem - conduction in a cylinder

Share this thread:
ana111790
#1
Feb15-11, 03:34 PM
P: 43
1. The problem statement, all variables and given/known data
The following cylinder has a temperature inside Ti and temperature outside To. Using the general equation for heat conduction in a cylinder, write the temperature distribution equation as a function of the radius T(r). What is the temperature midway at r=a? (Take the heat conductivity = k, and length of cylinder is L).
Assume no convection and constant temperature across the length of the cylinder.



2. Relevant equations

Fourier's Law in cylindrical coordinates: q''= -k (dT/dr)

3. The attempt at a solution
Boundary conditions:
r=ri, T=Ti
r=ro, T=To

So integrating Fourier's equation with these boundary points I get:
To-Ti= -roq'' ln(ro/ri)

I think this gives the temperature difference though, not the distribution and I also have the q'' (flux term) still in the equation as an unknown. How would I find the temperature distribution and T(r=a)?
Phys.Org News Partner Science news on Phys.org
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
RTW69
#2
Feb16-11, 01:59 PM
P: 374
Steady-state, no heat generation for cylinder: d/dr(r*dT/dr)=0

integrate twice with respect to r: T(r)=C_1*ln(r)+C_2


Register to reply

Related Discussions
Heat transfer mechanisms problem; Conduction Introductory Physics Homework 4
Heat Transfer Problem Conduction and Convection Engineering, Comp Sci, & Technology Homework 12
Heat transfer via conduction. Advanced Physics Homework 1
Heat Transfer (Conduction) problem Introductory Physics Homework 1
Heat Transfer - Conduction Engineering, Comp Sci, & Technology Homework 0