Chapter 4, Problem 4.33P

An igloo is built in the shape of a hemisphere, with aninner radius of 1.8 m and walls ofcompacted snow thatare 0.5 m thick. On the inside of the igloo, the surfaceheat transfercoefficient is $6{\text{W/m}}^2\cdot \text{K;}$ on the outside,under normal wind conditions, it is $\text{15}{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ Thethermal conductivity of compacted snow is $\text{0}\text{.15}\text{W/m}\cdot \text{K}\text{.}$ The temperature of the ice cap onwhich the igloo sits is $-20°\text{C}$ and has the same thermal conductivity as thecompacted snow.

1. Assuming that the occupants’ body heat provides acontinuous source of 320 W within the igloo, calculatethe inside air temperature when the outsideair temperature is $T_{\infty }=-40°\text{C}\text{.}$ Be sure to considerheat losses through the floor of the igloo.
2. Using the thermal circuit of part (a), perform aparameter sensitivity analysis to determine whichvariables have a significant effect on the inside airtemperature. For instance, for very high wind conditions,the outside convection coefficient coulddouble or even triple. Does it make sense to constructthe igloo with walls half or twice as thick?