The metallic sheet shown in Figure P 3.25 is 75 cm long and is floating at the surface of a stagnant oil pool. Air with atmospheric pressure and T ∞ ,G = 300 K temperature flows parallel to the plate....

The metallic sheet shown in Figure P 3.25 is 75 cm long and is floating at the surface of a stagnant oil pool. Air with atmospheric pressure and T_∞,G = 300 K temperature flows parallel to the plate. The mass and thermal resistance across the metallic sheet are negligibly small. The temperature of the oil bulk is T_∞,L = 278 K. Assume that the oil has a density of 890 kg/m³
, a specific heat of 1.9 kJ/kg·K, a viscosity of 0.1 kg/m·s, and a thermal conductivity of 0.15 W/m·K. The air velocity is adjusted so that the metallic sheet moves with a velocity U₀
= 4 cm/s.

a. Prove that the air velocity is U_∞
= 6.4 m/s.

b. Calculate the maximum thicknesses of the velocity and temperature boundary layers on both sides of the metallic sheet.

c. Neglecting heat conduction along the metallic sheet, calculate the temperature of the sheet at its center.