An igloo is built in the shape of a hemisphere, with an inner radius of 1.8 m and walls of compacted snow that are 0.5 m thick. On the inside of the igloo, the surface heat transfer coefficient is 6 W/m2  K; on the outside, under normal wind conditions, it is 15 W/m² ∙ K. The thermal conductivity of compacted snow is 0.15 W/m∙ K. The temperature of the ice cap on which the igloo sits is -20°C and has the same thermal conductivity as the compacted snow.

 

(a) Assuming that the occupants’ body heat provides a continuous source of 320 W within the igloo, calculate the inside air temperature when the outside air temperature is T_∞ = -40°C. Be sure to consider heat losses through the floor of the igloo.

(b) Using the thermal circuit of part (a), perform a parameter sensitivity analysis to determine which variables have a significant effect on the inside air temperature. For instance, for very high wind conditions, the outside convection coefficient could double or even triple. Does it make sense to construct the igloo with walls half or twice as thick?