What is the analytical solution for unsteady heat conduction in a long cylinder?

Question

the boundry conditions are:
T(R,t)=T* &
the temprature gradient in r=0 would be zero

the initial condition is:
T(r,0)=Ti

Answer 1

EDIT: Corrections made 12/3; 12/5

It appears you are looking for a solution T(r,t); the cylinder is specified long to avoid end effects. The solution to the heat equation is ∂T/∂t = del^2(T).

In cylindrical coordinates (with no z-axis variation) this would be

∂T/∂t = K*(1/r)∂/∂r(r * ∂T∂r) + (1/r^2) ∂^2T/∂ø^2

K=cp*rho/kt cp = sp heat, rho = dens kt coeff of therm cond.

There may be published solutions to this eq. somewhere; Try plugging in T=K*e^-t/t0*e^-r/R with your boundary conditions.

Answer 2

Are you looking for radial or longitudinal conduction?

Answer 3

Look up answer on : http://www.engr.unl.edu/~glibcontent