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12-49 12-80E A fan is blowing air over the entire body of a person. The average temperature of the outer surface of the person is to be determined for two cases. Assumptions 1 Steady operating conditions exist. 2 Radiation effects are negligible. 3 Air is an ideal gas with constant properties. 4 The average human body can be treated as a 1-ft-diameter cylinder with an exposed surface area of 18 ft2. 5 The local atmospheric pressure is 1 atm. Properties We assume the film temperature to be 100qF. V = 6 ft/s The properties of air at this temperature are (Table A-22E) Person, Ts T f = 85qF k 0.01529 Btu/h.ft.qF 300 Btu/h Q 1.809 u 10 - 4 ft 2 /s Pr 0.7260 D = 1 ft Analysis The Reynolds number is (6 ft/s)(1 ft) VD 3.317 u 10 4 Re 4 2 Q 1.809 u 10 ft /s The proper relation for Nusselt number corresponding to this Reynolds number is Nu hD k 0.3 0.62 Re 0.5 Pr 1 / 3 >1 (0.4 / Pr) @ 2 / 3 1/ 4 ª § Re · 5 / 8 º «1 ¨¨ ¸¸ » «¬ © 282,000 ¹ »¼ 4/5 ª 0.62(3.317 u 10 4 ) 0.5 (0.7260)1 / 3 « §¨ 3.317 u 10 4 1 0.3 1/ 4 « ¨© 282,000 1 (0.4 / 0.7260) 2 / 3 ¬ > @ · ¸ ¸ ¹ 5/8 º 4/5 » » ¼ 107.8 The heat transfer coefficient is k 0.01529 Btu/h.ft.qF h Nu (107.8) 1.649 Btu/h.ft 2 .qF D 1 ft Then the average temperature of the outer surface of the person becomes Q 300 Btu/h Q hAs (Ts Tf ) o Ts Tf 85qF + hAs (1.649 Btu/h.ft 2 .qF)(18 ft 2 ) 95.1qF If the air velocity were doubled, the Reynolds number would be (12 ft/s)(1 ft) VD 6.633 u 10 4 Re 4 2 Q 1.809 u 10 ft /s The proper relation for Nusselt number corresponding to this Reynolds number is Nu hD k 0.3 0.62 Re 0.5 Pr 1 / 3 >1 (0.4 / Pr) @ 2 / 3 1/ 4 ª § Re · 5 / 8 º «1 ¨¨ ¸¸ » «¬ © 282,000 ¹ »¼ 4/5 ª 0.62(6.633 u 10 4 ) 0.5 (0.7260)1 / 3 « §¨ 6.633 u 10 4 0.3 1 1/ 4 « ¨© 282,000 1 (0.4 / 0.7260) 2 / 3 ¬ > @ · ¸ ¸ ¹ 5/8 º Heat transfer coefficient is k 0.01529 Btu/h.ft.qF h Nu (165.9) 2.537 Btu/h.ft 2 .qF D 1 ft Then the average temperature of the outer surface of the person becomes Q 300 Btu/h 85qF + Q hAs (Ts Tf ) o Ts Tf hAs (2.537 Btu/h.ft 2 .qF)(18 ft 2 ) » » ¼ 4/5 165.9 91.6qF PROPRIETARY MATERIAL. © 2008 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.