Related Resources: heat transfer

Isothermal Vertical Plate Natural Convection Equation and Calculator

Isothermal Vertical Plate Natural Convection Equation and Calculator

Radiative and Convective heat transfer from an isothermal vertical plate. The average convective heat transfer coefficient is calculated assuming natural convection conditions. The convection calculation automatically switches between laminar and turbulent convection correlations based on Rayleigh number. The plate transfers heat from only one of its sides. It is assumed to be insulated on the other. equation and calculator.

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Fluid Properties at Film Temperature , Except for Density. (Defaults are for Air at 20 °C).

To account for convection only, make the emissivity equal to 0. Similarly, to account for radiation only, make the thermal conductivity = 0.

Calculations is based on Nusselt number correlations. The heat flow (q) from the Circular Rod is calculated as:

q = h · A · (Tp - Ta )

h = Nu · k / H

The Nusselt number is calculated as:

For Laminar Flow - Ra < 109
Nu = 0.68 + (0.670Ra1/4 )/[1+(0.492/Pr)9/16 ]4/9

For Turbulent Flow - Ra is between > 109
Nu = {0.825 + (0.387Ra1/6 )/[1+(0.492/Pr)9/16 ]8/27 }2

Ra = Gr · Pr
Pr = v / a
a = k / ( ρ Cp)
Gr = g ·cte ( Tp - Ta) · H3 / v2

Film temperature at the reference temperature of 20 °C.

Tf = (Tp + Ta ) / 2

Fluid density at at film temperature using perfect gas law:

ρ = ρref ( Tref+ 273) / ( Tf + 273)

Qrad = σ · A · e · (Tp4 - Ta4 )

Where:

q = Heat Dissipated (W)
h = Average heat transfer coefficient (W/m2 - °C)
A = Area of plate (m2)
Tp = Plate temperature °C
Ta = Ambient fluid temperature °C
Tf = Film temperature °C
Nu = Nusselt Number
k = Thermal Conductivity of Fluid (W/m - °C)
H = Height of plate (m)
W = Width of plate (m)
Ra = Raleigh number - for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or natural convection.
Pr = Prandtl number
Gr = Grashof number
v = Kinematic viscosity (m2/s)
a = Thermal Diffusivity (m2/s)
g = Gravity (9.80665 m/s2 )
cte = Coefficient of thermal expansion (1/K)
ρ = Density calculated at film temperature Tf (kg/m3)
ρref = Density at reference temperature Tref of 20 °C (kg/m3)
Tref = 20 °C
e = Emissivity of surface
σ = Stefan-Boltzman constant = 5.670367 × 10-8 kg- s-3 K-4

References

Churchill, S. W. and H. H. S. Chu, Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate , Int. J. Heat and Mass Transfer , 18, 1323, 1975

Incropera, De Witt., Fundamentals of Heat and Mass Transfer , 3rd ed., John Wiley & Sons, p543, eq.9.26 & 9.27, 1990.

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