You are one of five astronauts in a spacecraft that is travelingin deep space. Your spacecraft can be thermally modeled as acylindrical shell made of polished aluminum with uniform thicknessthat is capped at the ends, being 20m long and having an inner andouter radius of 2.9 m and 3 m with the cap at each end being 10 cmthick. Aluminum has a constant thermal conductivity of 237 W/m Kover a wide temperature range, from -70oC to 120oC. The convectiveheat transfer coefficient in space is always 0 W/m2 K. That meansthat all losses from the spacecraft will be from radiative lossesinto space which will be purely a function of the outer walltemperature.
1. 10pt – Radiation
a. 2.5pt – If the outer wall of the spacecraft were at 5oC and hadan emissivity of 1, what would the rate of heat loss be for thespacecraft into space? Assume the incoming solar radiation isnegligible since the spacecraft is so far away from the sun.
b. 7.5pt – The emissivity of polished aluminum is actually 0.05.Using this fact and the fact that the measured heat loss is 7151 W,calculate the temperature of the outside of the spacecraft.
2. 10pt – Steady Conduction
Create a thermal circuit model of the spacecraft. Using the lossesand temperature from part 1.b, calculate the temperature of theinner wall of the spacecraft. Assume the temperatures are all atsteady state since the electronics in the spacecraft produceexactly the correct amount of heat to prevent the craft fromcooling off. Also assume the inner wall is a uniform temperatureand that the cap and cylindrical shell of the spacecraft conductheat in parallel to one another.
3. 10pt – Convection
A burst of high energy cosmic rays knocks out all electronics inthe spacecraft. The spacecraft cools down to an uninhabitablelevel. As you succumb to the freezing temperatures, you realizethat there is an emergency heat fan in the spacecraft. You turn iton before losing consciousness. If the fan heats the air inside to30oC, what must be the convective heat transfer coefficient insidethe spacecraft in order to deliver enough heat to the walls tobring the inside of the walls up to 10oC and keep them there sothat the electronics can restart? Since most of the astronauts arealready dead, assume all of the heat must come from the heat fanand the losses are still only from radiation into space. How muchpower must the heat fan output in order to do this?