Question

4. You have been hired by "The Dr. Oz Show" to compare the rate of heat loss from a human body by free convection heat transfer with the typical energy intake from the consumption of food (2,500 Kilocalories/day). Model the body as a vertical cylinder with a 12" diameter and 6' tall in still air at 75°F. Assume the skin temperature is 95°F and neglect radiation, transpiration cooling (sweating), and the effects of clothing. Assume air properties are: v= 1.725 x 104 ft2/s, k = 0.01493 Btu/h.ft."R, and Pr 0.707. Show and reference all work. (10 points) Ra.-GrL.Pr= Note: gas film R-F+460 1cal = 4.1868 J 1 Btu-1.055056 kJ

Answer 1

Calculate the film temperature 75 +95 -85°F - 545 °R Properties at film temperature. 0.01493 Btuh ft-R y 1.725x10* ft /s Pr 0.707 545 -1.834x 103 R- Rayleigh Number Pr 32.2x1.834x10 x(95-75)x I' x 0.707 (1.725x10-) - 2.806 x10 Nusselt number constant for vertical cylinder with the Rayleigh number c 0.59,m -1/4 Nusselt number 025 0.59x(2.806x10') -42.94 Free convection coefficient 42.94 x 0.01493 Btuh ft R 0.641 Btuh ft2oR Free convection heat loss from the body in a day 0.641x(xlx6)x(95-75) 24 1.69 Btu hr 241.69B24 hr 1055 kJ h day 1Btu I 19.677 kJ/day Energy intake to the body in a day 2500x10 cal 4.1868 J day cal -10467 kJ/day Therefore, the cncrgy intake in a day is 10467 kJ and the rate of hcat loss is, 6119.677 kJ which is around 58%