A plane wall (left(k=10 mathrm{~W} / mathrm{m}^{circ} mathrm{C} ight)) of thickness (50 mathrm{~cm}) has its exterior surface

A plane wall \(\left(k=10 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}\right)\) of thickness \(50 \mathrm{~cm}\) has its exterior surface subjected to convection environment of \(30^{\circ} \mathrm{C}\) with a surface heat transfer coefficient of \(600 \mathrm{~W} / \mathrm{m}^{2}{ }^{\circ} \mathrm{C}\). Determine the temperature distribution in the plane wall using

(a) Four linear elements;

(b) One quadratic element;

(c) One modified quadratic element with only two nodes. Compare the results with analytical solution. If the heat transfer coefficient increases to \(10,000 \mathrm{~W} / \mathrm{m}^{2}{ }^{\circ} \mathrm{C}\), what happens to the temperature of the exterior surface?