Semi$-$infinite solid $($constant Ts$)$

A highway made of asphalt $(=2115k\frac{g}{m^3},c_p=920\frac{J}{k}g*K,$ and $k=0\mathrm{.}062\frac{W}{m}*K)$ is initially at a uniform temperature of $55C.$ Suddenly the highway surface temperature is r to $25C$ by rain. Determine the temperature at the depth of $3$ cm from the highway surface the heat flux transferred from the highway after $60$ minutes. Assume the highway surface temperature is maintained at $25C.$

Assumptions $1$ The highway is treated as semi$-$infinite solid. $2$ Thermal properties are con Heat transfer by radiation is negligible.

$(25$ points$)$ A large plane wall with a constant thermal conductivity $k$ and uniform heat generation $e_{\text{g}\text{e}\text{n}}^{}$ as shown in the figure is subjected to convection on the right side. The temperature on the left side is maintained at a temperature $T_0.$ We solve this problem numerically using the finite difference formulation. Below is the linear system that represents the problem when $x=0\mathrm{.}1m,k=4\mathrm{.}5\frac{W}{m}-K,e_{\text{g}\text{e}\text{n}}^{}=2000\frac{W}{m^3},T_0=10C,T_{}=2C,$ and $h=125\frac{W}{m^2}-K.$ Please fill in blanks $($a$)$ through $($e$)$ and show your work.

$\{[T_0],[T_1],[T_2],[T_3],[T_4],[T_5],[T_6]$