Horizontal Plate Natural Convection Equations and Calculator

Heat Transfer Engineering
Thermodynamics
Engineering Physics

Horizontal Plate Isothermal Heated Natural Convection Equation and Calculator

Average heat transfer coefficient and plate temperature for an isothermal (constant temperature) heated horizontal flat plate's lower surface or a cooled plate's upper surface in a natural convection environment.

Horizontal Plate Isothermal Heated Natural Convection Equation and Calculator

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Preview: Horizontal Plate Isothermal Heated Natural Convection Calculator

Calculations is based on Nusselt number correlations.
q = h · A · ( Tp - Ta )

Film Temperature
Tf = ( Tp - Ta )

Fluid density at the film temperature is automatically calculated from the following relationship based on the perfect gas law:

ρ = ρref (Tref + 273) / (Tf + 273)

Prandtl Number
Pr = v / α

α = k / (ρ · Cp)

v = μ / ρ

Grashof Number
Gr = g · cte · ( Tp - Ta ) · ( A / (2W + 2L) )3 / v2

Rayleigh Number
Ra = Gr · Pr

The Nusselt number is calculated as:

For Ra values between 105 and 1011
Nu = 0.27 (Gr · Pr) 0.25

h is Average heat transfer coefficient
h = Nu · k / ( A / (2W + 2L) )

Convective Heat Transfer
qconv = h ·A · ( Tp - Ta )

Radiative heat transfer
qrad = σ · A e · ( Tp4 - Ta4 )

Total Heat Transfer
qtot = qconv + qrad

Where:

Tf = Film temperature °C
Tp = Plate temperature °C
Ta = Ambient Temperature °C
Tref = Reference Temperature °C
Cp = Specific Heat J/kg- °C
cte = Coefficient of thermal expansion (1/K)
k = Thermal Conductivity (W/m - °C)
μ = Dynamic Viscosity ( kg/m-s )
ρ = Density (kg/m3)
ρref = Density (kg/m3)
Nu = Nusselt Number
W = Width of Plate (m)
L = Length of Plate (m)
a = Area of plate (m2 )
e = Emissivity
Pr = Prandtl number
Ra = Raleigh number - for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or natural convection.
h = Average heat transfer coefficient (W/m2 - °C)
g = 9.81 (m/s2)
h = Average Heat Transfer (W/m2 - °C )
σ = .00000005678 0r 5.678 x 10-8
qconv = Convective Heat Transfer (W)
qrad = Radiative Heat Transfer (W)
qtot = Total uniform heat load on plates (W)

References

Hatfield, D. W. and D. K. Edwards, Edge and Aspect Ratio Effects on Natural Convection from the Horizontal Heated Plate Facing Downwards , Int. J. Heat Transfer, vol. 24, p. 1019, 1981.

Fujii, T. and H. Imura, Natural Convection Heat Transfer from a Plate with Arbitrary Inclination , Int. J. Heat Mass Transfer, vol. 15, p. 755, 1972.

Clifton, J. V. and A. J. Chapman, Natural Convection on a Finite-Size Horizontal Plate , Int. J. Heat Mass Transfer, vol. 12, p. 1573, 1969.

Holman, J.P., Heat Transfer , 7th ed., McGraw Hill Book Company, New York, 1990. p. 333 - 352

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