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6.3 Thermal Management 41 Sky temperatures are found to be 75 K colder than air temperatures during sunlit hours and 40 K colder at night, at least near the Phoenix lander site (68◦N; Gendron et al., 2010). Although temperatures that far north are colder on average than in the mid-latitudes, we retained these rough temperature differences in calculating our overall profiles. Ground temperatures are found to track air temperatures very closely on Mars. Gendron et al. (2010) also report a ground emissivity coefficient of 98% (this compares with terrestrial emissivity of sand at 75%). Martian sky emissivity was unknown; while on Earth it is 75%, there is tremendous water vapor in the Earth’s atmosphere. We assume that the thin Martian sky has an emissivity close to 1, and use 98% for consistency with the ground emissivity coefficient. As a result, the sky radiates 52 W/m2 (sunlit) and 36 W/m2 (night), while the ground radiates 217 W/m2 (sunlit) and 89 W/m2 (night). Following Kirchhoff’s Law, absorption coefficients of the PEC system are equal to their emissivities at 10 μm, so these are also 5%, and overall thermal gain of the panel is 27 W/m2 (sunlit) and 13 W/m2 (night). Due to the low absorption coefficients, the sky and ground emissivities are in fact not very important; if we lowered these to 75%, the thermal gain of the PEC would be lower by only 6 W/m2 (sunlit) or 3 W/m2 (night). Additional convective losses due to wind can be many times the radiative losses; we estimate this ranges from 0–2 W/m2-K based on calculations in Gendron et al. (2010). Using 1 W/m2-K as representing average conditions (wind speed 4 m/s) for the top and bottom surfaces, total losses from both surfaces are 80 W/m2 (sunlit) and 180 W/m2 (night). As will be seen below, while these losses can be compensated for under normal thermal operating conditions, higher wind speeds will result in significant temperature drops that must be addressed. Sunlit Night Incident radiation on PEC panel 400.3 0.0 W/m2 Converted to chemical energy –50.0 0.0 W/m2 Remaining thermal energy 450.4 0.0 W/m2 Radiative losses (top surface) –20.1 –20.1 W/m2 Radiative losses (bottom surface) –20.1 –20.1 W/m2 Radiative gain from sky (top) 2.6 1.8 W/m2 Radiative gain from ground (bottom) 10.9 4.4 W/m2 Convective losses (top surface) –40.0 –90.0 W/m2 Convective losses (bottom surface) –40.0 –90.0 W/m2 Total thermal losses –106.6 –213.8 W/m2 Net thermal energy balance 343.7 –213.8 W/m2 Table 6.3: Energy balance of PEC Panel Total losses from the PEC system are therefore approximately 107 W/m2 (sunlit) or 214 W/m2 (night). During sunlit hours, this still results in a significant net gain of 344 W/m2 to be stored for release during nighttime. Assuming 10 h of full sunlight (somewhat less than half a Martian sol), there is 12.4 MJ/m2 or 1980 MJ of gross thermal energy to be released over the 14.7 h ofPDF Image | ISRU Challenge Production of O2 and Fuel from CO2
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