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Using finite element method, determine the temperature distribution in the wall in given figure and calculate heat flow through the wall.

A - Steel

B - Insulation

$K_A = 55 \times 10^{-3} \space \space w/mm^{\circ} c $

$K_B = 0.1 \times 10^{-3} \space \space w/mm^{\circ} c $

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(i) To find nodes and elements

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(ii) Element matrix equation

$$ \frac{KA}{h_e} \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} \begin{Bmatrix} \theta_1 \\ \theta_2 \end{Bmatrix} = \begin{Bmatrix} Q_1 \\ Q_2 \end{Bmatrix} $$

For element 1

K = 55 x 10$^{-3}$ W/mm$^\circ$ C; A = 1mm$^2$; h$_e$ = 2mm

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