Cooling
Because industrial, residential, or agricultural activities use energy, they will produce heat. Every human produces an average of 100 Watts of heat as well. This heat eventually needs to be dissipated into the environment, or the temperature will rise and the settlement will become too hot. Heat can be transported away from the settlement via convection, conduction, and radiation, or by mass transfer and phase change.
Agriculture in particular requires large amounts of light, typically between 400 and 600 W/m2 to be productive. This light turns into heat, that must be removed from the greenhouse or grow room. A large part of the heat is transferred to water vapor by the plants by evapo-transpiration. This water must be removed from the air by condensation (phase change) using cooling. The cooling fluid removes the heat through mass transfer, and eventually heat transfer to the environment. When designing a Martian settlement, a heat balance must be established between the heat gains from the processes in the settlement and solar loads during the day, and the losses to the environment.
Convection
Convection on Mars is minimal due to its very thin atmosphere, with even fan-assisted convection appearing to be less mass efficient than radiative cooling[1].
The convection equation is Q=h*A*dT, where:
- Q is the convective heat transfer (Watts)
- A is the area(m2)
- h is the experimental coefficient for convective heat transfer (J/m2*°K)
- dT is the temperature difference (°K) between the surface and the convective fluid.
A typical forced convection system on Mars for 100 kW of cooling might mass 300 kg, use a 4 kW fan and measure about 12m square(ref 3).
The temperatures of the coolant (CO2) would vary from 400 to 350 °K, for an environment at 260 K. This might be used to cool a nuclear reactor, or a Sterling engine using a Brayton cycle.
Conduction
Conduction into Mars regolith or megaregolith (soil or bedrock) may be feasible, since the ground's average temperature is around -60C. On Earth ground-source heat pumps are feasible for cooling. On Mars, depending on the ground conditions, sufficient cooling may be available via the building's foundation alone, or this could be augmented with cooling channels, which could be combined with existing utility trenches used for power or materials.
Challenges include the low temperature of the ground requiring a careful choice of working fluid, and interior humidity may deposit frost, and will certainly condensate, on cooling panels.
Most regolith will have poor thermal conductivity, requiring either additional conduction area such as drilled cooling pipes or channels, or a soil treatment such as water injection to increase thermal conductivity by filling the soil pore voids with ice. The Insight mission has measured conductivity in the order of 0,04 W/m°K. This is close to the thermal conductivity of polystyrene at 0,038 W/m°K. So Martian regolith can be considered as an effective thermal insulator.
The conduction equation is: Q=U*A*dt or Q=k/t*A*dt where:
- Q is the conduction heat transfer (Watts)
- A is the area (m2)
- dt is the temperature difference
- U is the heat transfer coefficient (Watts/m2). U=k/t where:
- k is the thermal conductivity of a material in Watts/m°K
- t is the material thickness (m)
Radiation
Radiative cooling is a standard solution for spacecraft, since the large temperature difference between outer space (around 3K) and human habitable areas (around 300K) gives substantial radiative cooling from high emissivity surfaces. However, near the terrestrial planets and closer to the sun the actual 'space temperature' is usually set at 200K.
The Stefan-Boltzmann law describes the thermal emission of a black body radiator as Q=A*e*σ*dT4, where:
- Q is the radiative heat transfer (Watts)
- A is the area of the radiating surface (m2)
- e is the surface emissivity, a dimensionless value between 0 and 1 that indicates how well a surface emits radiation
- σ is the Stephen Boltzman constant 5,67 e-8 W/m2°K)
- dt is the temperature difference between the radiating surface and the environment (°K)
On Mars, for a surface of 293K (about 20C) with emissivity 0.8, the black body radiative cooling can reach 334 W/m2 when facing the cold dark of space, but is closer to 260 W/m2 when the average temperature of the environment is taken into account.
During the nighttime a structure's roof could be used for radiative cooling, which could be as simple as a high-emissivity coating applied to the existing roof. However, the thermal resistance of the roof construction will reduce conduction considerably, and the actual surface temperature may be much lower than the interior temperature. In particular, the thick radiation shielding required for the settlement usually has a low coefficient of conduction. So some form of mass transfer of energy will probably be required between the interior of the settlement and the radiators at the surface.
One challenge with radiative cooling is keeping sunlight from warming the radiator panels. A possible mitigation is a careful arrangement of mirrors[2] to reflect sunlight away, or a paint with high visible reflectance and high thermal emittance. This allows the radiative surface to reflect light while still emitting heat. The sun has most of its light in higher frequencies (visible light), while radiative heat is at a much lower frequency (infra red light). So a paint can reflect the light from the sun (reflectance) and absorb little heat, while having a high thermal emittance.
Mass transfer and phase change
Heat can be transporter by moving a mass from one point, where it gains heat, to another, where it loses heat, through one or more of the heat transfer mechanisms mentioned above. The mass transfer equation is Q=ṁ*Cp*dT where:
- Q is the power (Watts)
- ṁ is the mass flow (kg/s)
- Cp is the specific heat (Joules/kg/°K). The amount of heat a given material can store. Water, for example, store 4,18 kJ/kg/°K.
- dT is the temperature difference of the mass flow between the source and the heat sink (°K).
A material can also either gain or lose energy through phase change. It can melt (solid to liquid), evaporate (liquid do gas) or sublimate (solid to gas) and gain energy, or it can lose energy by condensing (gas to liquid) or solidifying (liquid to solid). The phase change equation is Q=ṁ*Phe where: Q = The phase change power (Watts)
- m is the mass flow (kg/s)
- Phe is the phase change energy (J*/kg)
Mass transfer usually requires compressors (for gasses) or pumps (for liquids). The equation for pump power is P=(Q*dp)/ɳ where:
- P is the Pump power (Watts)
- dp is the pressure change (Pa)
- Q is the Volume flow (m3/s)
- ɳ is the pump efficiency (usually between 0.6 and 0.8)
References
- ↑ von Arx and Delgado, "Convective heat transfer on Mars", AIP Conference 1991 https://aip.scitation.org/doi/abs/10.1063/1.40133?journalCode=apc
- ↑ Lunarpedia Lunar Radiator https://lunarpedia.org/w/Lunar_Radiator
3- Colgan, N., Nellis, G., & Anderson, M. (2021). Forced Convection Heat Rejection System for Mars Surface Applications. In Proceedings of the Wisconsin Space Conference (Vol. 1, No. 1).
