Question

An endurance testing process for some special-purpose long metallic hollow shells requires the outer surface temperature to be kept at 100^?C and inner surface temperature be kept at 50^?C over an extended period of time. During the testing, the inner surface temperature is maintained by supplying cooling fluid through the shells and the outer surface temperature is maintained by crossflow of hot air at 150^?C flowing at 2 m/s. There are two types of shells – one is a cylindrical pipe and with an outer diameter of 0.55 m, and the other is of square cross-section with 0.55 m (outer) sides. The cost of the testing is primarily affected by the flowrate of cooling fluid inside the hollow shells. The higher the flowrate the higher the cost. The flowrate of the cooling fluid at steady state is proportional to the rate of heat transfer between hot air and the outer surface. Which shells cost more to perform the tests? The square shells can be kept either the diagonals facing the flow or the sides facing the flow. Neglect radiation.

Answer 1

T_0 = 100 degree c T_hot air = 150 degree c v = 2 m/s D_pipe = 0.55 side of square = 0.55 m cost proportionalto How rate of cooling fluid Flow rate of cooling fluid proportionalto Rate of heat transfer between hot air & outer surface. Q = hA(Delta T) Delta T = 150 - 100 = 50 R For cylindrical pipe Re = V D/y = 2 times 0.55/2.86 times 10^- 5 = 38461.538 Air properties at 150 degree c v = 2.86 times 10^- 5 m^2/s k = 0.034425 w/m k p_r = 0.70275 R_e > 2300 N_u = 0.023(R_e_D)^0.8 (P_r)^n [n = 0.4 for fluid heated n = 0.3 for fluid cooled Here n = 0.3 as air is cooled Nu = 0.023 (38461.538)^0.8 (0.70275)^0.3 Nu = 96.336 hD/k = 96.336 h = 96.336k/D = 6.02975 \r\n Q = h A Delta T Let