Bare Flat Surface Heat Loss (Convection + Radiation)
Heat lost from a bare tank wall, equipment panel or duct face to still air.
Example
You enter
- Surface orientation vertical
- Height of a vertical surface, or one side of a horizontal one (ft) 8
- Width, or the other side (ft) 10
- Surface temperature (°F) 180
- Air temperature (°F) 70
- Surface emissivity (0.9 painted, 0.1 bright aluminum) 0.9
You get
- Q total (Btu/h) 18810
- Conv coefficient 0.8934
- Rad coefficient 1.2441
Checked against published worked examples from: Incropera, DeWitt, Bergman and Lavine, Fundamentals of Heat and Mass Transfer.
Details, formula, and sources
ScopeNatural convection for a vertical surface or a horizontal one facing up or down, plus radiation at the surface emissivity. An 8 by 10 ft painted wall at 180 F in 70 F air loses about 18,800 BTU/hr, 235 BTU/hr per sq ft, more than half of it by radiation. A hot surface facing up loses far more by convection than one facing down. Gives the combined surface coefficient the insulation calculators ask for. A screen.
Formula or tableAir at the film temperature (Sutherland mu and k, ideal-gas density, cp 1,006 J/kg K); Ra = g (1/Tf) |Ts - Ta| L^3/(nu alpha). Vertical (L = height): Nu = 0.68 + 0.670 Ra^(1/4)/[1 + (0.492/Pr)^(9/16)]^(4/9) to Ra 1e8 and [0.825 + 0.387 Ra^(1/6)/(1 + (0.492/Pr)^(9/16))^(8/27)]^2 from Ra 1e9; between them the two are blended on log10(Ra), because they differ by a third at Ra 1e9 and a hard switch made the loss jump with a small change in height (the blend is this tile's, not a published correlation). Horizontal (L = area/perimeter): hot side up or cold side down Nu = 0.54 Ra^(1/4) to Ra 1e7, else 0.15 Ra^(1/3); hot side down or cold side up Nu = 0.27 Ra^(1/4). h_rad = eps sigma (Ts^4 - Ta^4)/(Ts - Ta), sigma = 0.1714e-8 BTU/hr ft2 R4; q = (h_conv + h_rad) A (Ts - Ta).
Source and editionFree convection from flat plates as given in Incropera, DeWitt, Bergman and Lavine, Fundamentals of Heat and Mass Transfer, Ch. 9 (Churchill and Chu 1975 for the vertical plate; McAdams for the horizontal plate), and gray-body radiation to large surroundings, by name.
Free accessStandard heat-transfer correlations; checked against the textbook's Example 9.3 (a 0.75 by 0.3 m duct at 45 C in 15 C air: sides 4.23, top 5.47, bottom 2.07 W/m2 K), reproduced within 1%.
What governsEstimate. AHJ and licensed professional govern.
API field namesorientation, side_a_ft, side_b_ft, surface_f, amb_f, emissivity, q_total_btuh, conv_coefficient, rad_coefficient
- Characteristic length height for a vertical plate; area over perimeter for a horizontal oneIncropera Ch. 9
- Radiation gray surface to large surroundings at the air temperatureStefan-Boltzmann
- Still air no wind or forced convection; the surface temperature is uniformscope of this tile