To defrost ice accumulated on the outer surface of an automobile windshield,
warm air is blown over the inner surface of the windshield. Consider an
automobile windshield \(\left(k_{w}=1.4 \mathrm{~W} / \mathrm{m} \cdot
\mathrm{K}\right)\) with an overall height of \(0.5 \mathrm{~m}\) and thickness
of \(5 \mathrm{~mm}\). The outside air ( \(1 \mathrm{~atm}\) ) ambient temperature
is \(-20^{\circ} \mathrm{C}\) and the average airflow velocity over the outer
windshield surface is \(80 \mathrm{~km} / \mathrm{h}\), while the ambient
temperature inside the automobile is \(25^{\circ} \mathrm{C}\). Determine the
value of the convection heat transfer coefficient, for the warm air blowing
over the inner surface of the windshield, necessary to cause the accumulated
ice to begin melting. Assume the windshield surface can be treated as a flat
plate surface.