Pipe Insulation Thickness for a Target Heat Loss
The inverse of the pipe-heat-loss-radial tile: the insulation thickness that caps radial heat loss at a target rate per foot, thickness = (od/2) x (exp(2*pi*(k/12)*(hot - amb)/q) - 1). A 2 in pipe at 200 F in 70 F air with k 0.25 held to 40 BTU/hr/ft needs about 0.53 in of insulation. Targets a heat-loss (energy-code / process) budget, not a surface temperature (the insulation-thickness tile does that). Round up to a stocked wall; conduction only (conservative). ASHRAE / ASTM C335 and the manufacturer govern.
Formula and source
thickness = (OD/2) x (exp(2*pi*k'*(T_hot - T_amb)/q) - 1), the inverse of q = 2*pi*k'*(T_hot - T_amb)/ln(r2/r1), where r1 = OD/2, k' = k_value/12 (BTU/(hr.ft.F)), and q is the target heat loss per foot.
Fourier conduction through a cylindrical shell (public heat-transfer formula), solved for the thickness; insulation k-values per ASHRAE Fundamentals / ASTM C335, by name.
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