How to Modify Fourier's Heat Conduction Equation for a Finite Body?

[debjit625]

Homework Statement

This is the question as it was given...no other data was given.
Obtain Fourier's heat conduction equation in three dimensions in an infinite medium in steady state.What modifications will be required in case of a finite body?

2. The attempt at a solution
Well I can derive 3D Fourier's heat conduction equation not a problem,
∂u/∂t = h ∇²u (without radiation losses )
and at steady state it will be ∇²u = 0
here u(x,y,z,t) is temperature and h is thermal diffusivity.

But what I don't get is infinite medium and the finite body , will the finite body will have radiation losses ?,it has to do something with boundary conditions may be.I don't get the question properly ,please help me understanding it.

Thanks

 

[soarce]

Indeed, for finite body one has to include boundary conditions, e.g. no heat flow through the boundary or constant temperature at the boundary.

 

[Chestermiller]

Even though, for a finite body, the boundary conditions need to be included in solving the steady state heat conduction equation, the equation itself does not change.