The Thick Mattress Problem: Heat-Soak Time Scales With the Square of Thickness in Bed Bug Room Treatments

Whole-room heat treatment is widely used against bed bugs, and treatment failures are widely reported in thick bedding. This study models a mattress as a slab of foam with thermal diffusivity 1.4e-7 m2/s, heated from both faces by 60 C air, starting at 22 C, with a core criterion of 50 C at the centre plane. Time to criterion follows the first-term conduction solution and grows with the square of thickness: 3.17 hours for a 10 cm mattress, 12.68 hours for 20 cm, and 28.52 hours for 30 cm. With a 25 percent margin, the corresponding treatment holds are 3.96, 15.85 and 35.66 hours, costing USD 1.43, USD 5.70 and USD 12.84 in heater electricity at 2 kW. A treatment day sized for thin bedding therefore cannot clear a thick mattress, whatever the air temperature gauge reads, because the limit is conduction inside the mattress rather than heat supply to the room. The originated rule is to size the hold time from the thickest item in the room using the square law, or to split, stand or open thick items so that no conduction path exceeds about 10 cm. This study is simulated, not measured. SIMULATED, NOT MEASURED.