N 2. (a) State and explain the four rules governing view factor relations in radiation. (8 marks) (b) In a shell-and-tube heat exchanger, what factors should be taken into consideration when deciding whether a fluid should be allocated to the shell side or tube side? (5 marks) (c) A shell-and-tube heat exchanger with 2 shell passes and 4 tube passes is used to heat glycerine from 20 C to 50 C using hot water, which enters the thin-walled 20 mm diameter tubes at 80 C and leaves at 40 C. The total length of tubing in the heat exchanger is 460 m. The convective heat transfer coefficient on the shell side is 45 W m K- and that on the tube side 250 W m K-. The outer surface of the tubes has accumulated deposits causing a fouling resistance of 0.0008 m KW- Using the appropriate equations from Table Q2 and the chart in APPENDIX Q2, determine the rate of heat transfer from the water to the glycerine, stating any assumptions. (12 marks) TABLE Q2 Dittus-Boelter equation, turbulent pipe flow Colburn's equation, turbulent pipe flow Sieder-Tate expression, laminar pipe flow Nu = 0.023 Res Pr* (n = 0.3 cooling 0.4 heating) 10.14 Nu=0.023 Re8 Pro33 1 H 033 Pre Nu-1.86 Re Pr 2014 Correction factor F Correction factor F 1.0 Correction factor F 0.9 0.8 Correction factor F 0.7 0.6 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 P-7-1 (a) One-shell pass and 2, 4, 6, etc. (any multiple of 2), tube passes 1.0, 0.9 0.8 0.7 0.6 1.0 R= 051 7 0 01 02 03 04 05 06 07 08 09 10 P (b) Two-shell passes and 4, 8, 12, etc. (any multiple of 4), tube passes 0.9 0.8 0.7 0.6 1.0 0.9 0.8 R=4.0 3.0 20.15 10 08-06-04-02 0.7 0.6 T-T 4-4 R= 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 P (c) Single-pass cross-flow with both fluids unmized R APPENDIX Q2 R-4030 20 15 10 08 06 0402 1-1 -4 R-40-30 20 15 10.08.06.04 02 T R-40 30-20.15-1.008 0.6 04-02- 4-4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (d) Single-pass cross-flow with one fluid mixed and the other anmized