A cubic block, each side a$=1$cm$,$ made of fused silica $($SiO$\_(2)),$ is heated to

$150\backslash$deg C and suddenly immersed to an oil bath at $20\backslash$deg C with a convection heat transfer

coefficient of h$=200($W$)/($m$^(2))*$K$.$ Assume the properties of the cube are constant: density

$\backslash$rho $=2200$k$($g$)/($m$^(3)),$ specific heat C$\_($p$)=800($J$)/($k$)$g$*$K$,$ thermal conductivity k$=1\mathrm{.}4($W$)/($m$)*$K$.$

Derive an analytical solution for the temperature of the block using separation of

variables approach.