What is the physical significance of the number of transfer units $\mathrm{NTU}=h A_{s} / \dot{m} c_{p} ?$ What do small and large NTU values tell about a heat transfer system?

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at $− 20^\circ C.$ Air approaches the tube bank in the normal direction at $0^\circ C$ and 1 atm with a mean velocity of 4 m/s. The tubes are arranged in-line with longitudinal and transverse pitches of $S_L = S_T = 1.5 cm.$ There are 30 rows in the flow direction with 15 tubes in each row. Determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. Evaluate the air properties at an assumed mean temperature of $—5^\circ C$ and 1 atm. Is this a good assumption?

Consider a 50-cm-diameter and 95-cm-long hot water tank. The tank is placed on the roof of a house. The water inside the tank is heated to $80^\circ C$ by a flat-plate solar collector during the day. The tank is then exposed to windy air at $18^\circ C$ with an average velocity of 40 km/h during the night. Estimate the temperature of the tank after a 45-min period. Assume the tank surface to be at the same temperature as the water inside, and the heat transfer coefficient on the top and bottom surfaces to be the same as that on the side surface. Evaluate the air properties at $50^\circ C.$

The upper surface of a metal plate is being cooled with parallel air flow while its lower surface is subjected to a uniform heat flux of $810 W/m^2.$ The air has a free stream velocity and temperature of 2.5 m/s and $15^\circ C,$ respectively. Determine the surface temperature of the plate at x = 1.5 m from the leading edge.

The top surface of the passenger car of a train moving at a velocity of 70 km/h is 2.8 m wide and 8 m long. The top surface is absorbing solar radiation at a rate of $200 W/m^2,$ and the temperature of the ambient air is $30^\circ C.$ Assuming the roof of the car to be perfectly insulated and the radiation heat exchange with the surroundings to be small relative to convection, determine the equilibrium temperature of the top surface of the car.

The top surface of the passenger car of a train moving at a velocity of $70 \mathrm{~km} / \mathrm{h}$ is $3.2 \mathrm{~m}$ wide and $8 \mathrm{~m}$ long. If the outdoor air is at 1 atm and $25^{\circ} \mathrm{C}$, find the drag force working on the top surface of the car.