Radiant Floor Heat Output
q = 2 x (T_surface - T_room)^1.1 Btu/hr-ft^2, with the ~85 F surface comfort cap (~39 Btu/hr-ft^2 in a 70 F room). An 85 F floor over a 70 F room gives 39.3; solving inverse, a 30 Btu/hr-ft^2 load needs an 81.7 F surface. Solves either direction. The panel manufacturer's ratings and radiant-loop-sizing govern.
Formula and source
q = 2 x (T_surface - T_room)^1.1 Btu/hr-ft^2; inverse T_surface = T_room + (q/2)^(1/1.1); comfort cap ~85 F surface.
The radiant-floor heat-output relation q = 2 (Tsurface - Troom)^1.1 with the ~85 F surface comfort limit, from ASHRAE / radiant-panel practice, by name.
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