A composite wall consist of three materials, as shown in fig. Convection heat transfer takes place on inner surface of the wall with $T_\infty=800^0c$ and $h = 30W/{m^2}^0c$. The outer surface temperature $T_0= 20^0c$. Determine temperature distribution in the wall.

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(i) Number of nodes and elements

(ii) Element matrix equation

$$\begin{Bmatrix} \begin{bmatrix} h_cA & 0 \\ 0 & 0 \end{bmatrix} + \frac{kA}{h_e} \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} \end{Bmatrix} \begin{Bmatrix} \theta_1 \\ \theta_2 \end{Bmatrix} = \begin{Bmatrix} Q_1 \\ Q_2 \end{Bmatrix}$$

For element 1

h$_c$ = …