Annular aluminum fins of rectangular profile are attached to a circular tube having an outside diameter of 50 mm and an outer surface temperature of 250 °C. The fins are 4 mm thick and 15 mm long. There are 120 fins per meter of tube length. The system is in ambient air at a temperature of 25 °C, and the surface convection coefficient is 50 W/(m²·K). a) What is the efficiency of a single fin? (10 pts) b) What is the effectiveness of a single fin? (10 pts) c) What is the overall surface efficiency? (15 pts) d) What is the rate of heat transfer per unit length of the tube? (15 pts)

Acommercial grade cubical freezer, 4 m on a side, has a composite wall consisting of an exterior sheet of 5.0-mm thick plain carbon steel (kst= 60.5 w/m k), an intermediate layer of 100-mm thick polyurethane insulation (kins 0.02 w/m k), and an inner sheet of 5.0- mm thick aluminium alloy (kal polyurethane insulation and both metallic sheets are each characterized by a thermal contact resistance of r 2.5 x 104 m2 k/w. (a) what is the steady-state cooling load that must be maintained by the refrigerator under conditions for which the outer and inner surface temperatures are 25°c and -5°c, respectively? (b) for power saving purpose, which wall material should be increased/reduced in. thickness in order to reduce 50% of the cooling load found in part (a)? redesign the thickness of the proposed material. 177 w/m-k). adhesive interfaces between the q=575.93 w