Graphical representation of the solution to the heat equation for a "slab" of width ${\displaystyle \pi }$ given by:

${\displaystyle \ u_{t}=ku_{xx}}$

where k=1, subject to the boundary conditions:

${\displaystyle u_{x}(0,t)=0,\ \ u(\pi ,t)=70^{\circ }}$

and with the initial heat distribution given by:

${\displaystyle \ u(x,0)=70\cos ^{2}(x)}$

${\displaystyle \pi }$