A Passive Solar Heating Wall for Cold-Climate Low-Income Housing: A Computed Sizing Rule, Temperature-Lift Budget, and Cost per Degree

A thermal-mass passive solar heating wall (glazing, cavity, 0.25 m dense concrete mass, vents) for a 20.0 m2 room in a poorly insulated house is computed with a two-layer lumped thermal simulation run to periodic steady state against a matched no-wall baseline. The reference assembly (8.0 m2 glazing, 4,400 kg mass, 2,534 USD on stated unit rates) delivers a mean indoor temperature lift on 15 January from 7.95 K (35 N, clear) to 0.64 K (55 N, overcast); at 45 N partly cloudy the lift is 3.45 K, night lift 3.71 K, night delivery 3.368 kWh, stored-heat delivery of at least 100 W for the full 15.03 h night, and cost per degree of lift 734.49 USD. A sizing sweep gives the rule: area drives lift at 0.37 K per m2, night delivery is greatest at 0.25 m thickness, and cost per degree rises from 611.83 USD at 0.15 m to 1,002.88 USD at 0.45 m. In a warm clear early-autumn spell the closed wall peaks at 31.24 C and a free vent area of 0.10 m2 holds the peak to 26.20 C. All results are simulated, not measured; nothing was built or hardware-tested. Computations are reproducible from the deposited compute.py and results.json.