The compartment heater of an automobile exchanges heat between warm radiator fluid and cooler outside air. The flow rate of water is large compared to the air, and the effectiveness, \(\varepsilon\), of the heater is known to depend on the flow rate of air according to the relation, \(\varepsilon \sim \dot{m}_{\text {air }}^{-0.25}\).

(a) If the fan is switched from low to high and \(\dot{m}_{\text {air }}\) is doubled, determine the percentage increase in the heat added to the car, if fluid inlet temperatures remain the same.

(b) For the low-speed fan condition, the heater warms outdoor air from -10 to \(30^{\circ} \mathrm{C}\). When the fan is turned to medium, the airflow rate increases \(50 \%\). Find the new outlet temperature.