Polar Station Heat Balance

What is modelled

A 12 by 6 by 3 metre habitat is kept at the thermostat setting by a heater that switches on and off. Heat leaves through the wall, which is a thin lining, a layer of insulation and a steel skin, and also with the air that leaks out and is replaced by cold air. People inside give off heat. The page integrates the indoor temperature and the fuel burned.

Equations

• Wall resistance R = 1/hi + Lp/kp + Lins/kins + 1/ho, U = 1/R, outside film ho = 5.7 + 3.8 v for wind v in m/s.
• Loss (U A + ρ cp V n / 3600)(Tin − Tout), heater need minus the crew heat of 100 W each.
• Lumped room C dT/dt = Pheater + Qcrew − (UA + H)(T − Tout) with time constant τ = C / (UA + H).
• Fuel E / (10 kWh/L × 0.85) litres and wind chill from the Canadian formula for skin exposure.

Checks run in the page

• A finite-difference conduction solution across the wall against the series-resistance flux.
• Cooling with the heater off after one time constant, against the 1/e value.
• Three days of thermostat control against the steady heater-power balance.
• Stepping the fuel tank to empty against tank divided by daily use.

Honest simplifications

All surfaces share the same U-value, the floor and thermal bridges are ignored, the air leakage is a fixed rate that does not rise with wind, the thermal capacity is one lumped number, the sun is absent and the burner is an ideal on-off device. The aurora and snow are decoration. It is a demonstration, not a design calculation for a real station.

• Press Thin insulation and see how much power the same room needs with 4 cm of insulation.
• Press Blizzard and note how little the wind adds once the wall is well insulated.
• Press Leaky hut, big crew and compare the air leakage loss with the wall loss.