A $0\mathrm{.}12$ m thick wall, well$-$insulated on one side, is initially at a uniform temperature of $99\mathrm{.}0$C$.$ Suddenly, the temperature of the uninsulated surface changes to $19\mathrm{.}0$C$.$ Given the wall's thermal diffusivity of $1\mathrm{.}5106$m$2/$s$1\mathrm{.}5\backslash$times $10^\{-6\}\backslash ,\backslash$text$\{$m$\}^2/\backslash$text$\{$s$\}1\mathrm{.}5106$m$2/$s$,$ use the explicit method with time step $$t$=240$s$\backslash$Delta t $=240\backslash ,\backslash$text$\{$s$\}$t$=240$s and spatial step $$x$=30\mathrm{.}0$mm$\backslash$Delta x $=30\mathrm{.}0\backslash ,\backslash$text$\{$mm$\}$x$=30\mathrm{.}0$mm to solve for the temperature distribution in the wall after $16$ minutes.

Determine:

The temperature T$0$T$\_0$T$0$ at the insulated surface:

$$C $($to $1$ decimal place$)$

The temperature T$1$T$\_1$T$1$ at the first point adjacent to the insulated surface:

$$C $($to $1$ decimal place$)$

The temperature T$2$T$\_2$T$2$ at the next adjacent point:

$$C $($to $1$ decimal place$)$

The temperature T$3$T$\_3$T$3$ at the point adjacent to the uninsulated surface:

$$C $($to $1$ decimal place$)$

The temperature T$4$T$\_4$T$4$ at the uninsulated surface:

$$C $($to $1$ decimal place$)$