If you arc standing in a room that is held at a constant 75degreeF and your body

Question

If you arc standing in a room that is held at a constant 75degreeF and your body temperature remains at a constant 98.6degreeF, compare the magnitudes of the different modes of heat transfer (convection, conduction, and radiation). Assume that the surface arc of an average human is 1.7 m2, the thermal conductivity for still air is k = 0.024 W/m-K, the air reaches the ambient temperature in 5 cm, the surroundings arc at the same temperature as the air, the emissivity of a person is 0.95, and the heat transfer coefficient for a person is 20 W/m2-K. After doing this analysis, which, if any, modes could be considered negligible?

Explanation / Answer

convert temperature from fahrenheit to kelvin scale Room temperature (Tr)= 75 F =297 K Body temperature (Tb) =98.6 F =310.15 K Area of the body (A)=1.7 m^2 conductivity of air (k)=0.024 W/m-K air reaches surrounding temperature in (dx)= 5cm=0.05m emissivity of person (e)=0.95 heat transfer coefficient (h)=20 W/m^2-K a) heat transfer due to convection = h*A*(Tb-Tr) =20*1.7*(310.15-297) =447.1 J/s b) heat transfer due to conduction =-k*A*(Tr-Tb)/dx =0.024*1.7*(310.15-297)/0.05 =10.73 J/s c) heat transfer due to radiation = e*A*sigma*(Tb^4-Tr^4) sigma = stephen's constant =5.67*10^-8 W/(m^2.K^4) heat transfer due to radiation =0.95*1.7*5.67*10^-8*(310.15^4-297^4) =134.81 J/s therefore heat transfer due to conduction is very small as compared to two other. Hence it can be neglected.

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