Question $2$

You need to study the temperature distribution in the following fin. Assuming $1-$D heat transfer in the $x-$direction, a uniform and constant convective coefficient of heat transfer $(h)$ and air temperature $(T_{}).$

a$.$ Write the explicit equation for the temperature of Node $2(T_2^{n+1})$ in the case of transient heat transfer.

b$.$ For Node $2,$ find the expression for $t_{\text{m}\text{a}\text{x}}$

c$.$ Write the energy balance for Node $7$ in the case where the fin has reached steady state

Use general properties $,C_P,k$ for your calculations. Consider the heat transfer only from the top and bottom surface of the fin, neglect the heat transfer on the sides of the fin