Question

You are one of five astronauts in a spacecraft that is traveling in deep space. Your spacecraft can be thermally modeled as a cylindrical shell made of polished aluminum with uniform thickness that is capped at the ends, being 20m long and having an inner and outer radius of 2.9 m and 3 m with the cap at each end being 10 cm thick. Aluminum has a constant thermal conductivity of 237 W/m K over a wide temperature range, from -70oC to 120oC. The convective heat transfer coefficient in space is always 0 W/m2 K. That means that all losses from the spacecraft will be from radiative losses into space which will be purely a function of the outer wall temperature.
1. 10pt – Radiation
a. 2.5pt – If the outer wall of the spacecraft were at 5oC and had an emissivity of 1, what would the rate of heat loss be for the spacecraft into space? Assume the incoming solar radiation is negligible 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 losses and temperature from part 1.b, calculate the temperature of the inner wall of the spacecraft. Assume the temperatures are all at steady state since the electronics in the spacecraft produce exactly the correct amount of heat to prevent the craft from cooling off. Also assume the inner wall is a uniform temperature and that the cap and cylindrical shell of the spacecraft conduct heat in parallel to one another.
3. 10pt – Convection
A burst of high energy cosmic rays knocks out all electronics in the spacecraft. The spacecraft cools down to an uninhabitable level. As you succumb to the freezing temperatures, you realize that there is an emergency heat fan in the spacecraft. You turn it on before losing consciousness. If the fan heats the air inside to 30oC, what must be the convective heat transfer coefficient inside the spacecraft in order to deliver enough heat to the walls to bring the inside of the walls up to 10oC and keep them there so that the electronics can restart? Since most of the astronauts are already dead, assume all of the heat must come from the heat fan and the losses are still only from radiation into space. How much power must the heat fan output in order to do this?

Answer 1