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Flat Plate Heat Transfer Convected Equation and Calculator

Heat Transfer Engineering
Thermodynamics
Engineering Physics

Flat Plate heat transfer coefficient and heat convected equation and calculator

Average convection heat transfer coefficient and heat convected from an isothermal (constant temperature) flat plate at a specified temperature in free stream flow.

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Preview: Convection heat transfer flat plate calculator

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

q = h · A · (T_p - T_a )

h = Nu · k / L

The Nusselt number is calculated as:

For Laminar Flow - Re < 500,000
Nu = 0.664 Re^0.5 Pr^0.33

For Turbulent Flow - Re > 500,000
Nu = Pr^0.33 ( 0.037 Re^0.8 -871)

Re = u _m · L / v
Pr = K_v / T_d

K_v = v / ρ

T_d = k / ( ρ · c_p )

Fluid properties at the film temperature T_f defined as follows:

T_f = (T_p + T_a ) / 2

Where:

q = Heat Dissipated (W)
k = Thermal Conductivity of Fluid (W/m - °C)
h = Heat transfer coefficient (W/m² - °C)
A = Area of the plate (m²)
W = Plate width (m)
L = Plate length (m)
T_p = Plate temperature °C
T_a = Ambient fluid temperature °C
T_f = Fluid properties at the film temperature °C
h = Average heat transfer coefficient (W/m² - °C)
Nu = Nusselt Number
L = length of the plate (m)
Re = Reynolds number
Pr = Prandtl number
Re = Fluid velocity x Length / kinematic viscosity
K _v = Kinematic viscosity (kg/m-s) = Dynamic Viscosity / Density
ρ = Density (kg/m³)
c_p = Specific Heat capacity (J/(kg·K))
v = Dynamic Viscosity (kg/m-s)
u _m = Fluid/Flow Velocity (m/s)
T_d = Thermal Diffusivity (m²/s)

The above correlations are valid for Prandlt numbers in the range of 0.6 and 50 and are not suitable for low Prandtl fluids like liquid metals and high Prandtl fluids like heavy oils or silicons.

References

Schlichting, H., Boundary Layer Theory , 7th ed., McGraw Hill Book Company, New York, 1979.

Schultz-Grunow, F., Nues Widerstandsgesetz fur glatte Platten Luftfartforschung , vol. 17, p. 239, 1940.

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