Question 2.9: A man stands in a freezer room of a local fast food restaura...
A man stands in a freezer room of a local fast food restaurant, with clothes having a surface temperature of 5°C and emissivity of 0.3. What is the rate of heat loss from the surface of his clothes if the temperature of the freezer walls is –20°C? Assume that the situation can be modelled as a small sphere of surface area 1 m^{2} representing the man, inside a larger sphere, and that black body surfaces are assumed.
Use \dot{q}_{b,1} = \sigma A_{1}F_{1-2} (T_{2}^{4} – T_{2}^{4}) with F_{1-2} = 1 and A_{1} = 1 m^{2}
\dot{q}_{b,1-2} = 5.67 \times 10^{-8} \times 1 \times 1 \times (253^{4} – 278^{4}) = -106 WIt is interesting to note that 100 W is a reasonably maintainable heat generation rate from a healthy standing person, and that the thickness of cloth, γ, of conductivity 0.08 W/mK, say, required to maintain the surface temperature of 5°C if the skin temperature beneath is maintained at 22°C is from the Fourier Law:
106 = 0.08 \times 1 \times (22 – 5)/\gammaand
γ = 0.013 m or 13 mm
the thickness of a thick fleece.