How to Solve the Inhomogeneous Heat Equation for a Cylindrical Rod?

[mumaga]

inhomogeneuos heat equation!

Homework Statement

∂θ/∂t= D∇2θ + K, the mensioned equation is the heat equation for a cylindrical rod , and the requaired is to find the ordinary differential equation for θ(r) .where the radius of the rod is R , and K is constant ( correspond to a constant rate pf heat production)

Homework Equations

The Attempt at a Solution

i use separation of variables to obtain the required for a homogeneous heat equation , but with the constant the method didn't work out.
thanks for your time.

 

[tiny-tim]

Welcome to PF!

∂θ/∂t= D∇2θ + K, the mensioned equation is the heat equation for a cylindrical rod , and the requaired is to find the ordinary differential equation for θ(r) .where the radius of the rod is R , and K is constant ( correspond to a constant rate pf heat production)

Hi mumaga! Welcome to PF!

(I assume you mean ∂θ/∂t= C∇²θ + K, where C and K are constants, and θ depends only on t and r.)

See http://en.wikipedia.org/wiki/Heat_equation#Homogeneous_heat_equation