A 20-mm-diameter, 1-m-long, thin-walled copper tube contains a material that generates thermal energy at a volumetric rate of \(\dot{q}=0.2 \mathrm{MW} / \mathrm{m}^{3}\). The rod is cooled by air at atmospheric pressure in cross flow at a velocity of \(2 \mathrm{~m} / \mathrm{s}\). It is proposed to decrease the temperature of the material by spraying a thin, porous coating of thickness \(t=2 \mathrm{~mm}\) onto the exterior of the copper tube. The coating is then saturated with liquid water, leading to evaporative cooling at the exposed surface of the coating. The thermal conductivity of the water-saturated coating is \(k_{c}=3.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Determine the temperature of the copper tube with and without the coating. The ambient conditions are characterized by a temperature of \(25^{\circ} \mathrm{C}\) and a relative humidity of 45 percent.