This page calculates the average heat transfer coefficient and plate temperature for an isothermal (constant temperature) heated horizontal flat plate's upper surface or a cooled plate's lower surface in a natural convection environment. The convection calculation automatically switches between calculation methods based on Rayleigh 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 / cl

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 Ra values between 2x10^{4} and 10^{6}

Nu = 0.54 (Gr* Pr)^{0.25}

For Ra values between 10^{6} and 10^{11}

Nu = 0.15 (Gr* Pr)^{0.33}

For the above equations *Ra* is the Rayleigh number, *Gr* is
the Grashof number, and *Pr* is the Prandtl number and are calculated using fluid
properties as follows:

Ra = (Gr * Pr)

Pr = kinematic viscosity / thermal diffusivity

Gr = gravity x (coefficient of expansion) x (T_{p} - T_{a}) x cl^{3}
/ (kinematic viscosity)^{2}

Where *cl* is the characteristic dimension which is calculated
using:

cl = area / perimeter

In addition, you must define the fluid properties at the film
temperature *T _{f}* defined as follows, except for the density
which is defined at the reference temperature of 20 C.

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

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

Rho = Rho_{ref} (T_{ref} +273) / (T_{f}
+ 273)

**References**

Lloyd, J. R. and W. R. Moran, *Natural Convection Adjacent to
Horizontal surface of Various Planforms*, ASME Pap. 74-WA/HT-66.

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.

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