Need some help, i think I missed a constant for one of the equations for radiati

Question

Need some help, i think I missed a constant for one of the equations for radiation.

Under conditions for which the same room temperature is maintained by a heating or cooling system, it is not uncommon for a person to feel chilled in the winter but comfortable in the summer Consider a room whose air temperature is maintained at 20°C throughout the year, while the walls of the room are nominally at 27°C and 14°C in the summer and winter, respectively, The exposed surface of a person in the room may be assumed to be at a temperature of 32°C throughout the year and to have an emissivity of 0.90·The coefficient associated with heat transfer by natural convection between the person and the room air is approximately 2 W/m2-K Calculate the following Heat flux due to convection 24 wim2 Heat flux due to radiation in the summer: 5.3 W/m Heat flux due to radiation in the winter: W/m2

Explanation / Answer

To = 20 C

Ts = 27 C

Tw = 14 C

Tp = 32 C

e = 0.9

k = 2 W/m^2K

a. heat flux due to convection = q'c

q'c = k*dT = k(Tp - To) = 2(32 - 20) = 24 W/m^2

b. heat flux due to radiation in summer = q'r

q'r = e*sigma*(Ts^4

Ts = 32+273.16K

sigma = 5.67*10^-8

q'r = 442.52314 W/m^2

c. in winters

q'r = e*sigma(Tp)^2 = 0.9*sigma*(32 + 273.16)^2 = 442.52314 W/m^2

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