$!$could you explain how to non$-$dimentionallize? i cant understand why thermal diffusivity$($c$)$ becomes $1$ in no $-$dimension. and solve this problem A solid slab occupying the space between $y=-b$ and $y=+b$ is initially at temperature $u_0.$ At

time $t=0$ the surfaces at $y=+-b_{?}$ are suddenly raised to $u_1$ and maintained there. Find $u(y,t{)}_{?}.$

Hint$)$ For this problem it is helpful to introduce the following dimensionless variables:

Dimensionless temperature :${}_{?}=\frac{u_1-u}{u_1-u_0}$

Dimensionless $y$ coordinate $\frac{\text{:}}{b}ar()=\frac{y}{b}$

Dimensionless time $,\frac{\text{:}}{b}ar(=\frac{c^{2}t}{b^2}),$ where $c^2$ is the thermal diffusivity.

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{t}}=c^2\frac{de{l}^{2}u}{del{y}^2}$

With these dimensionless variables you can derive the appropriate governing heat equation, initial $u(y,0)=u_0$

and homogeneous boundary conditions to get the solution by the variable$-$separation method.