Consider $1-$D$,$ transient, constant properties problem.

$2L=0\mathrm{.}1m$

$k_{\text{w}\text{a}\text{l}\text{l}}=10\frac{W}{mC},c_p=500\frac{f}{kgC},=1000k\frac{g}{m^2}$

$T_i=100C,T_{}=20C,h=60\frac{W}{m^{2}C}$

a$)$ Derive formulations via energy balance method. You may choose explicit or implicit approach.

b$)$ Solve the equations with a suitable method and obtain the time$-$dependent temperature distribution. Use a minimum of $6$ grids for $L.$ Move forward in time by $45$ seconds.

Could you please solve each premise step by step? It is very important for me to be transaction oriented rather than answer oriented. Thanks in advance.