|MadSci Network: Engineering|
In metals and other materials that use electrons to conduct heat, thermal gradients do produce small but measurable voltages and currents. Carbon thermal conduction is dominated by phonons though it is a semiconductor and does have some commonality with metals in that electrons do contribute some to the conduction of thermal energy. However carbon is orders of magnitude higher in electrical resistance, so any current would be correspondingly orders of magnitude lower. Even if a gradient of several thousand degrees Celsius is present the amount of current and voltage available will not be sufficient to power say a thermoelectric cooling device.
If the carbon-carbon is doped to increase its conductivity the heat flux through the material and into the structure of the spacecraft will increase as well. Any improvement in heat rejection will have to be greater than the additional heat flux or else the new effect will be an increase in the temperature of the spacecraft.
There are also at least three practical engineering considerations with any active cooling method such as you propose.
First, you would have to have an electrode on the hot side of the shield to provide a full electrical circuit. The electrode will have to have good electrical conduction and be able to withstand the high temperatures. Tungsten might be a suitable choice, but it is a very good thermal conductor. That means that a thermal short circuit through the heat shield will be introduced wherever there is an electrode.
A major problem facing an electrical based system is the loss of efficeincy when the materials operate at very high temperatures and the generally low efficiency of thermoelectrics. Only a few percent of the potential electrical power may be realized from this method of electricity production.
The third practical consideration is once you extract the heat from the heat shield you still have to get rid of it. Radiation cooling is used for the Shuttle. Ablative cooling was used for Apollo and will be used for the Crew Exploration Vehicle. If you bring the heat into the spacecraft, you will have to move it through the vehicle to the colder regions and reject the heat to the surrounding environment. Depending on the portion of the descent in which the vehicle is, that surrounding environment could well be very hot plasma. Unless your radiator surfaces are warmer or you have an alternative method for dumping the heat overboard you will actually gain additional heat from your radiators ratehr than reject it. This would lead to overheatig of th spacecraft.
This quick analysis does not address the weight and risk penalties associated with a complex heat rejection system for active cooling. Both are likely very considerable.
The idea is a good one, and it does have scientific merit. However, given current efficiencies and the additional weight of an active heat rejection system. the engineering of the vehicle will almost certainly dictate that active cooling of this nature will result in the loss of performance and reduced payloads. If advances are made in thermoelectrics and efficiencies approaching that of a typical steam generator are realized, then your idea may work.
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