# temperature problem

• Aug 24th 2011, 06:06 PM
wik_chick88
temperature problem
slab of material $-1 \leq x \leq 1$ is initally at a temperature given by
$T = T_{0}(1 + x) \ for \ -1 \leq x \leq 0$
$= T_{0}(1 - x) \ for \ 0 < x \leq 1$,
and the surfaces $x = \pm 1$ are maintained at zero temperature.
Show that the temperature is
$T=\frac{8T_{0}}{\pi^{2}} \sum^{\infty}_{n=0} \frac{1}{(2n+1)^2} cos \frac{(2n+1) \pi x}{2} exp[-k(n+ \frac{1}{2})^2 \pi^2 t]$
• Aug 25th 2011, 06:24 AM
Jester
Re: temperature problem
Have you tried separation of variables?

Note: For those that are reading this post, I'm sure the OP meant to include the governing PDE

$T_t = kT_{xx}$
• Sep 5th 2011, 03:29 AM
wik_chick88
Re: temperature problem
how would i do that?