The inner pipe of a double-pipe heat exchanger has an OD of 1.9 in. and contains 36 rectangular fins of the type shown in the sketch below. The fins are made of steel (k = 34.9 Btu/h *ft *F) and are 0.5 in. high and 0.035 in. thick. The pipe wall temperature is 250 F and the fluid in the annulus surrounding the fins is at 150 F with a heat-transfer coefficient of 30 Btu/h * ft2 * F. Calculate:
(a) The fin efficiency.
(b) The rate of heat transfer from one fin per foot of pipe length.
(c) The prime surface area per foot of pipe length.
(d) The rate of heat transfer from the prime surface per foot of pipe length.
(e) The weighted efficiency of the finned surface.
(f) The total rate of heat transfer (from fins and prime surface) per foot of pipe length.
(g) The thermal duty for the exchanger is 390,000 Btu/h. What length of pipe is required to satisfy this duty?