Chapter 1 Radiation Heat ranfer Special opic: Heat ranfer from the Human Body 1-7C Ye, roughly one-third of the metabolic heat generated by a peron who i reting or doing light work i diipated to the environment by convection, one-third by evaporation, and the remaining one-third by radiation. 1-75C Senible heat i the energy aociated with a temperature change. he enible heat lo from a human body increae a (a the kin temperature increae, (b the environment temperature decreae, and (c the air motion (and thu the convection heat tranfer coefficient increae. 1-76C Latent heat i the energy releaed a water vapor condene on cold urface, or the energy aborbed from a warm urface a liquid water evaporate. he latent heat lo from a human body increae a (a the kin wettedne increae and (b the relative humidity of the environment decreae. he rate of evaporation from the body i related to the rate of latent heat lo by latent m vapor h fg where h fg i the latent heat of vaporization of water at the kin temperature. 1-77C he inulating effect of clothing i expreed in the unit clo with 1 clo = 0.155 m.c/w = 0.880 ft.f.h/btu. Clothing erve a inulation, and thu reduce heat lo from the body by convection, radiation, and evaporation by erving a a reitance againt heat flow and vapor flow. Clothing decreae heat gain from the un by erving a a radiation hield. 1-78C (a Heat i lot through the kin by convection, radiation, and evaporation. (b he body loe both enible heat by convection and latent heat by evaporation from the lung, but there i no heat tranfer in the lung by radiation. 1-79C he operative temperature operative i the average of the mean radiant and ambient temperature weighed by their repective convection and radiation heat tranfer coefficient, and i expreed a operative hconv ambient h h h conv rad rad urr ambient When the convection and radiation heat tranfer coefficient are equal to each other, the operative temperature become the arithmetic average of the ambient and urrounding urface temperature. urr 1-60
Chapter 1 Radiation Heat ranfer 1-80 he convection heat tranfer coefficient for a clothed peron while walking in till air at a velocity of 0.5 to m/ i given by h = 8.6V 0.53 where V i in m/ and h i in W/m.C. he convection coefficient in that range vary from 5.96 W/m.C at 0.5 m/ to 1. W/m.C at m/. herefore, at low velocitie, the radiation and convection heat tranfer coefficient are comparable in magnitude. But at high velocitie, the convection coefficient i much larger than the radiation heat tranfer coefficient. Velocity, m/ 0.50 0.75 1.00 1.5 1.50 1.75.00 h = 8.6V 0.53 W/m.C 5.96 7.38 8.60 9.68 10.66 11.57 1.0 h 13.0 1.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 0. 0.6 0.8 1.0 1. V 1. 1.6 1.8.0 1-61
Chapter 1 Radiation Heat ranfer 1-81 A man wearing ummer clothe feel comfortable in a room at C. he room temperature at which thi man would feel thermally comfortable when unclothed i to be determined. Aumption 1 Steady condition exit. he latent heat lo from the peron remain the ame. 3 he heat tranfer coefficient remain the ame. he air in the room i till (there are no wind or running fan. 5 he urface area of the clothed and unclothed peron are the ame. Analyi At low air velocitie, the convection heat tranfer coefficient for a tanding man i given in able 1-3 to be.0 W/m.C. he radiation heat tranfer coefficient at typical indoor condition i.7 W/m.C. herefore, the heat tranfer coefficient for a tanding peron for combined convection and radiation i room= 0 C kin= 33 C h h h. 0. 7 8. 7 W / m. C combined conv rad he thermal reitance of the clothing i given to be R cloth 0. 7 clo 0. 7 0155. m. C / W = 0.109 m. C / W Noting that the urface area of an average man i 1.8 m, the enible heat lo from thi peron when clothed i determined to be enible, clothed A ( R cloth kin 1 h ambient combined (1.8 m (33 0 C 1 0.109m. C/W + 8.7 W/m. C From heat tranfer point of view, taking the clothe off i equivalent to removing the clothing inulation or etting R cloth = 0. he heat tranfer in thi cae can be expreed a enible,unclothed A ( kin h 1 combined ambient (1.8 m (33 1 ambient 8.7 W/m. C C o maintain thermal comfort after taking the clothe off, the kin temperature of the peron and the rate of heat tranfer from him mut remain the ame. hen etting the equation above equal to 10 W give ambient 6. C 10W room Clothed peron kin= 33 C Unclothed peron herefore, the air temperature need to be raied from to 6.C to enure that the peron will feel comfortable in the room after he take hi clothe off. Note that the effect of clothing on latent heat i aumed to be negligible in the olution above. We alo aumed the urface area of the clothed and unclothed peron to be the ame for implicity, and thee two effect hould counteract each other. 1-6
Chapter 1 Radiation Heat ranfer 1-8E An average peron produce 0.50 lbm of moiture while taking a hower. he contribution of hower of a family of four to the latent heat load of the air-conditioner per day i to be determined. Moiture 0.5 lbm Aumption All the water vapor from the hower i condened by the air-conditioning ytem. Propertie he latent heat of vaporization of water i given to be 1050 Btu/lbm. Analyi he amount of moiture produced per day i m vapor = (Moiture produced per peron(no. of peron = (0.5 lbm/peron( peron/day = lbm/day hen the latent heat load due to hower become Q latent = m vaporh fg = ( lbm/day(1050 Btu/lbm = 100 Btu/day 1-83 here are 100 chicken in a breeding room. he rate of total heat generation and the rate of moiture production in the room are to be determined. Aumption All the moiture from the chicken i condened by the air-conditioning ytem. Propertie he latent heat of vaporization of water i given to be 30 kj/kg. he average metabolic rate of chicken during normal activity i 10. W (3.78 W enible and 6. W latent. Analyi he total rate of heat generation of the chicken in the breeding room i gen,total q gen,total (No.of chicken (10. W/chicken(100chicken = 100 W he latent heat generated by the chicken and the rate of moiture production are 100 Chicken 10. W gen,latent q gen,latent (No.of chicken (6. W/chicken(100chicken = 6W = 0.6kW m moiture h gen,latent fg 0.6kJ/ 30kJ/kg 0.0006kg/ 0.6 g/ 1-63
Chapter 1 Radiation Heat ranfer 1-8 Chilled air i to cool a room by removing the heat generated in a large inulated claroom by light and tudent. he required flow rate of air that need to be upplied to the room i to be determined. Aumption 1 he moiture produced by the bodie leave the room a vapor without any condening, and thu the claroom ha no latent heat load. Heat gain through the wall and the roof i negligible. Propertie he pecific heat of air at room temperature i 1.00 kj/kgc (able A-15. he average rate of metabolic heat generation by a peron itting or doing light work i 115 W (70 W enible, and 5 W latent. Analyi he rate of enible heat generation by the people in the room and the total rate of enible internal heat generation are gen,enible total, enible q gen,enible (No.of people (70W/peron(150 peron = 10,500W gen,enible lighting 10,500 000 1,500W hen the required ma flow rate of chilled air become m air C total, enible p 1.5 kj/ 1.5kg/ (1.0 kj/kg C(5 15 C 15 C Chilled air Light kw 150 Student Dicuion he latent heat will be removed by the air-conditioning ytem a the moiture condene outide the cooling coil. 5 C Return air 1-6
Chapter 1 Radiation Heat ranfer 1-85 he average mean radiation temperature during a cold day drop to 18C. he required rie in the indoor air temperature to maintain the ame level of comfort in the ame clothing i to be determined. Aumption 1 Air motion in the room i negligible. he average clothing and expoed kin temperature remain the ame. 3 he latent heat lo from the body remain contant. Heat tranfer through the lung remain contant. Propertie he emiivity of the peron i 0.95 (from Appendix table. he convection heat tranfer coefficient from the body in till air or air moving with a velocity under 0. m/ i h conv = 3.1 W/m C (able 1-3. Analyi he total rate of heat tranfer from the body i the um of the rate of heat lo by convection, radiation, and evaporation, ( Q Q body, total enible latent lung conv rad latent lung Noting that heat tranfer from the kin by evaporation and from the lung remain contant, the um of the convection and radiation heat tranfer from the peron mut remain contant. enible,old enible,new ha ( ha ( ha ( ha ( air,old A ( 0.95A [( A ( 73 0.95A [( urr,old urr,new ( 73 73 Setting the two relation above equal to each other, canceling the urface area A, and implifying give ] (18 73 ] air, new h 0. 95 ( 73 h 0. 95 ( 18 73 8 31. ( 0. 95 5. 67 10 ( 91 95 0 air, new Solving for the new air temperature give air, new = 9.0C herefore, the air temperature mut be raied to 9C to counteract the increae in heat tranfer by radiation. C C 1-65
Chapter 1 Radiation Heat ranfer 1-86 he average mean radiation temperature during a cold day drop to 1C. he required rie in the indoor air temperature to maintain the ame level of comfort in the ame clothing i to be determined. Aumption 1 Air motion in the room i negligible. he average clothing and expoed kin temperature remain the ame. 3 he latent heat lo from the body remain contant. Heat tranfer through the lung remain contant. Propertie he emiivity of the peron i 0.95 (from Appendix table. he convection heat tranfer coefficient from the body in till air or air moving with a velocity under 0. m/ i h conv = 3.1 W/m C (able 1-3. Analyi he total rate of heat tranfer from the body i the um of the rate of heat lo by convection, radiation, and evaporation, ( Q Q body, total enible latent lung conv rad latent lung Noting that heat tranfer from the kin by evaporation and from the lung remain contant, the um of the convection and radiation heat tranfer from the peron mut remain contant. enible,old enible,new ha ( ha ( ha ( ha ( air,old A ( 0.95A [( A ( 73 0.95A [( urr,old urr,new ( 73 73 Setting the two relation above equal to each other, canceling the urface area A, and implifying give ] (1 73 ] h 0.95 ( 73 3.1( 0.955.6710 h 8 Solving for the new air temperature give air, new = 39.0C 0.95 (1 73 (85 95 0 herefore, the air temperature mut be raied to 39C to counteract the increae in heat tranfer by radiation. C C 1-66
Chapter 1 Radiation Heat ranfer 1-87 A car mechanic i working in a hop heated by radiant heater in winter. he lowet ambient temperature the worker can work in comfortably i to be determined. Aumption 1 he air motion in the room i negligible, and the mechanic i tanding. he average clothing and expoed kin temperature of the mechanic i 33C. Propertie he emiivity and aborptivity of the peron i given to be 0.95. he convection heat tranfer coefficient from a tanding body in till air or air moving with a velocity under 0. m/ i h conv =.0 W/m C (able 1-3. Analyi he equivalent thermal reitance of clothing i R cloth 0. 7 0. 7 0155. clo m. C / W = 0.1085 m. C / W Radiation from the heater incident on the peron and the rate of enible heat generation by the peron are Radiant heater 0. 05 0. 05( 10 kw 0. 5 kw = 500 W rad, incident rad, total 0. 5 0. 5( 350 W 175 W gen, enible gen, total Under teady condition, and energy balance on the body can be expreed a E E E 0 in out gen 0 rad from heater conv+rad from body gen, enible or rad,incident h conv A ( 0.95(500W (.0 W/m A ( K(1.8m (306 0.95(1.8 m (5.6710 urr -8 W/m urr K urr [(306K gen,enible 0 urr 175W 0 Solving the equation above give urr 66. K = -7.0 C herefore, the mechanic can work comfortably at temperature a low a -7C. 1-67