Seperation of variables - Product solutions for unsteady heat conduction

[Chard3000]

Hey guys,

I was wondering about problem 12C.1 in Transport phenomena by Bird, Stewart and lightfoot.

The problem states that a block of material initially at uniform T0 is suddenely exposed to T1 at all surfaces.

Assume a solution of T=X(x,t)Y(y,t)Z(z,t)

any help with separation of variables of this type (3D)

thanks

 

[fzero]

Have you tried substituting that expression into the heat equation?

 

[Chard3000]

I have tried to to... but I do not understand how to do a separation of variables for 3 dimensions.

 

[fzero]

Did T = X(x,t)Y(y,t)Z(z,t) come from a suggestion in the problem or did you come up with that? T = X(x) Y(z) Z(z) W(t) is a better choice.

Either way, unless you start writing down some equations and explain what's confusing you, you won't get too far.