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Horizontal Plate, Heated Up — Isothermal

Average h and heat rate from an isothermal horizontal plate with its hot face up.

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Orientation alone can halve your cooling: the same plate at the same ΔT convects about twice as well with its hot face up as with its hot face down.

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Figures assume typical conditions and the stated method. For measured, guaranteed numbers on your plant, our engineers run site surveys, heat loss audits, and full process models.

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Horizontal Plate, Heated Face Up — Isothermal

Calculates the average convective heat transfer coefficient and total heat rate for a horizontal plate whose heated surface faces upward (equivalently, a cooled surface facing downward). Buoyant fluid rises freely away from the surface, so this orientation convects more strongly than the heated-down case.

Characteristic Length

For a horizontal plate the characteristic length is the area-to-perimeter ratio:

Lc=PA=2(L+W)LW

Rayleigh Number

Properties are evaluated at the film temperature Tf=(Ts+T)/2:

Ra=ν2gβ(TsT)Lc3Pr

Nusselt Number

Nu=0.54Ra1/4(104Ra107) Nu=0.15Ra1/3(107<Ra1011)

Heat Transfer Coefficient and Heat Rate

h=LcNuk,Q=hA(TsT),A=LW

References

  • Lloyd, J. R. and Moran, W. R., Natural Convection Adjacent to Horizontal Surfaces of Various Planforms, ASME Pap. 74-WA/HT-66.
  • Fujii, T. and Imura, H., Int. J. Heat Mass Transfer, vol. 15, p. 755, 1972.
  • Incropera, F. P. and DeWitt, D. P., Fundamentals of Heat and Mass Transfer.
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Frequently asked questions

Average h and heat rate from an isothermal horizontal plate with its hot face up. Enter your inputs and press Calculate — the worked solution shows every step of the method with your numbers substituted in.

When there is no fan, pump or significant draught — enclosures, outdoor surfaces on still days, passive heat sinks. If there is any imposed flow, compare the two mechanisms: when Gr/Re² is well below one, forced convection dominates and the forced-convection calculators are the right tools.

No — it computes the convective part only. At typical natural-convection coefficients of 2–10 W/m²·K, radiation from a painted or oxidised surface is often the same order of magnitude, so total heat loss should add a radiative term from the Radiation calculators.