Hours to Danger: A Lumped Thermal Model of Passive Survivability in a Mid-Rise Apartment Block During a Blackout Heatwave, and a Priced Retrofit Bound

SIMULATED, NOT MEASURED. When a blackout coincides with a heatwave, how long does each flat in a mid-rise apartment block stay below a danger threshold, and what does more safe time cost? A lumped single-node thermal model of a 60 m2 flat, resolved by floor (ground, middle, top) and orientation (north, east, south, west), includes fabric conduction, solar gain through glazing, roof solar load, internal gains, thermal mass, and night ventilation. Under a repeating heatwave day of 38 C maximum and 26 C minimum, initial indoor temperature 26 C, and a danger threshold of 32 C indoor air temperature, every unretrofitted flat crosses the threshold: fastest is the top-floor east-facing flat at 32.9 hours, the top-floor west-facing flat crosses at 36.3 hours, and the slowest (ground floor, north-facing) lasts 62.25 hours. The top floor fails first as a class, and flats without night cooling accumulate heat day on day. A retrofit package of external shading, cool-roof and roof-insulation treatment, added thermal mass, and secure night ventilation, priced at $1540 per flat, prevents any modelled flat from crossing within the 120-hour simulation window: at least 87.1 additional safe hours for the worst flat at no more than $17.68 per additional safe hour per flat. The governing planning bound is the worst flat, not the building average.