A plane wall (left(k=20 mathrm{~W} / mathrm{m}{ }^{circ} mathrm{C} ight)) of thickness (40 mathrm{~cm}) has its outer

A plane wall \(\left(k=20 \mathrm{~W} / \mathrm{m}{ }^{\circ} \mathrm{C}\right)\) of thickness \(40 \mathrm{~cm}\) has its outer surfaces maintained at \(30^{\circ} \mathrm{C}\). If there is uniform internal heat generation of \(0.2 \mathrm{MW} / \mathrm{m}^{3}\) in the plane wall, determine the temperature distribution in the plane wall. Solve this problem using

(a) Four linear elements;

(b) One quadratic element;

(c) One modified quadratic element with only two nodes. Compare the results with analytical solutions.