Bare Pipe Heat Loss (Convection and Radiation)
What an uninsulated steam or hot-water line gives up to the room, from its outside diameter, surface temperature.
Example
You enter
- Pipe outside diameter (in; 2-in pipe is 2.375) 2.375
- Pipe surface temperature (°F) 280
- Air temperature (°F) 80
- Surface emissivity (0.8 oxidized steel, 0.1 aluminum jacket) 0.8
- Pipe length (ft) 1
You get
- Heat loss per linear foot 350
Checked against published worked examples from: Engineers Edge.
Details, formula, and sources
ScopeWhat an uninsulated steam or hot-water line gives up to the room, from its outside diameter, surface temperature, and the air temperature. Natural convection off a horizontal pipe plus radiation, and on bare steel the radiation is close to half. A 2 in steel pipe at 280 F in 80 F still air loses about 345 BTU/hr per foot, the figure a published bare-pipe table gives within 1.5%. Bright aluminum jacketing (emissivity 0.1) cuts the radiation by eight. Still air; a draft raises it. A screen; the engineer governs.
Formula or tableAir at the film temperature Tf = (Ts + Ta)/2: mu = 1.716e-5 (Tf/273.15)^1.5 (383.55)/(Tf + 110.4), k = 0.0241 (Tf/273.15)^1.5 (467.15)/(Tf + 194), rho = 101325/(287.05 Tf), Pr = 1006 mu/k; Ra = g (1/Tf) |Ts - Ta| D^3/(nu alpha); Nu = {0.60 + 0.387 Ra^(1/6)/[1 + (0.559/Pr)^(9/16)]^(8/27)}^2 (Ra <= 1e12); hc = Nu k/D; hr = eps sigma (Ts^4 - Ta^4)/(Ts - Ta), sigma = 0.1714e-8 BTU/hr ft2 R4; q/L = pi D (hc + hr)(Ts - Ta).
Source and editionNatural convection from a long horizontal cylinder (Churchill and Chu, Int. J. Heat Mass Transfer 18, 1975) and gray-body radiation to large surroundings, standard heat transfer as in Incropera and ASHRAE Fundamentals, by name.
Free accessChecked against the free Engineers Edge table 'Heat Loss from Bare Steel Pipe to Still Air at 80 F' (1, 2, and 4 in pipe at 180, 280, and 380 F): with emissivity 0.8 all nine values agree within 1.5%.
What governsEstimate. AHJ and licensed professional govern.
API field namesod_in, surface_f, amb_f, emissivity, length_ft, q_per_ft_btuh
- Convection Churchill-Chu horizontal-cylinder correlation, air properties at the film temperature, 1 atmChurchill and Chu (1975)
- Radiation gray surface to large surroundings at the air temperatureStefan-Boltzmann
- Wind optional (added 2026-10-09): forced cross-flow convection by Churchill-Bernstein (1977), Nu = 0.3 + 0.62 Re^(1/2) Pr^(1/3)/[1 + (0.4/Pr)^(2/3)]^(1/4) [1 + (Re/282000)^(5/8)]^(4/5), combined with natural convection as (Nu_F^3 + Nu_N^3)^(1/3); reproduces Incropera Example 7.4 (Re 6,071, Pr 0.700, Nu 40.6)Churchill and Bernstein (1977); Incropera
- Surface temperature taken as the fluid temperature (thin metal wall)scope of this tile