This page calculates the average heat transfer coefficient and plate temperature for an isothermal (constant temperature) flat plate in free stream flow. The convection calculation automatically switches between laminar and turbulent convection correlations based on Reynolds number.

The calculation is based on Nusselt number correlations.

The heat flow *(q)* from the plate is calculated as:

q = h A x (T_{p} - T_{a})

Where *h* is the average heat transfer coefficient, *A* is the
area of the plate, *T _{p}* is the plate temperature and

h = Nu k / L

Where *Nu* is the Nusselt Number, *k* the conductivity of the
fluid and *L* the length of the plate. 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)

Where *Re* is the Reynolds number and *Pr* is the Prandtl
number are calculated using fluid properties as follows:

Re = fluid velocity x Length / kinematic viscosity

Pr = kinematic viscosity / thermal diffusivity

In addition, you must define the fluid properties at the film
temperature *T _{f}* defined as follows:

T_{f} = (T_{p} + T_{a}) / 2

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.