Steel Convection

Steel Convection
Heat transfer from steel plate to air?

I'd like to know the BTU/hr or kW given off into the air by a steel plate of 1 square foot. Assume the air and the steel are maintained at constant temperatures of 80F and 140F respectively and that there is hardly any air movement (no forced convection).

FYI, I'm looking to determine the heat given off by an uninsulated hot water 3000 gallon reservoir (5 foot diameter by 20 feet high) into the space where it is located (mechanical room).

Thanks!
So as to be clear, this installation is not yet built and so I can't take any measurements.

The two modes of heat transfer are natural convection and radiation.

q = hAΔT + σAε(Tsurf - Tamb)^4

where, for the convective term, h is the convective heat transfer coefficient (given below), A is the area (ft²), and ΔT is the differential temperature (ºF), where ΔT = Tsurf - Tamb, Tsurf is the surface temperature (ºF), Tamb is the ambient temperature (ºF); for radiative heat transfer, σ is the Stefan-Boltzman Constant (1.714×10^-9 BTU/hr-ft²-R), A is the area (ft²), ε is the surface emmisivity, and Tsurf (R) and Tamb (R) are as defined earlier.

The convective heat transfer coefficient, h, is:

h = Nu(k/L)

where k is the conductivity of gas at film temperature (Btu/hr-in-ºF) and L is the effective length of the horizontal or vertical surface.

The Nusselt number, Nu, for horizontally heated surfaces facing upward is:

Nu = (0.54)(GrPr)^(1/4)for 10^5 < GrPr < 2×10^7

Nu = (0.14)(GrPr)^(1/3) for 2×10^7 < GrPr < 3×10^10

and, for horizontally heated surfaces facing downward:

Nu = (0.27)(GrPr)^(1/4) for 3×10^5 < GrPr < 3×10^10

The Nusselt number, Nu, for vertically heated surfaces is:

Nu = {0.825 + (0.387)(GrPr)^(1/6)/[1 + (0.492/Pr)^(9/16)]^(8/27)}²for 10^-1 < GrPr < 10^12

For both horizontally and vertically heated surfaces, the Grashof number, Gr, is:

Gr = gβ(ΔT)L³/ν²

where g is the gravitational acceleration constant (in/s²), β is the gas coefficient of thermal expansion (1/ºF), where β = 1/(Tabs) for an ideal gas, ΔT is the differential temperature (ºF), where ΔT = |Tsurf - Tamb|, Tsurf is the surface temperature (ºF), Tamb is the ambient temperature (ºF), L is the effective length of the horizontal or vertical surface, ν is the kinematic viscosity of gas at the film temperature (in²/s), and Pr is the Prandtl number. Note that k, Gr, and Pr are each a function of air temperature, and can be found in any "Properties of Air" table.

The rest is just "plug and chug." If you have trouble applying the above equations, contact me.