Transform the problem
PDE: $\quad u_{t} = 9 u_{xx} , \qquad 0 < x < 1 , \quad t > 6$
BC: $\quad u(0,t) = 0 \quad u(1,t) = 0$
IC: $\quad u(x,6) = f(x)$
into a dimensionless problem. Assume $x$ and $u$ already do not have units, so you only change time. You wish to arrive at
PDE: $\quad u_{\tau} = u_{xx} , \qquad 0 < x < 1 , \quad \tau > 0$
BC: $\quad u(0,\tau) = 0 \quad u(1,\tau) = 0$
IC: $\quad u(x,0) = f(x)$

Transform $t$ to $\tau$.
$\tau = {}$

help (formulas)