This page calculates the heat transfer coefficient for fully developed flow in a smooth circular tube. The convection calculation automatically switches between laminar and turbulent convection correlations based on Reynolds number.

The calculation is based on Nusselt number correlations.

The tube wall temperature *(T _{w})* is calculated as:

T_{w} = T_{b} + q / (h*A)

Where *h* is the average heat transfer coefficient, *A* is the
surface area of the tube, *q* is the heat load uniformly distributed on the
tube surface and *T _{b}*
is the fluid bulk temperature.

h = Nu k / D

Where *Nu* is the Nusselt Number, *k* the conductivity of the
fluid and *D* the diameter of the tube. The Nusselt number is calculated as:

For Laminar Flow - Re < 2300

Nu = 4.36 for uniform surface heat flux conditions

friction f = 64 / Re

For Turbulent Flow - 2300 < Re < 5 x 10^{6}

Nu = ( f / 8) ( Re - 1000 ) Pr / { 1 + 12.7( f / 8 )^{1/2} ( Pr^{2/3}
- 1 ) }

where f = ( 0.79ln Re - 1.64 ) ^{-2}

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

Re = fluid density x fluid velocity x diameter / dynamic viscosity

Pr = Specific heat x dynamic viscosity / thermal conductivity

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

T_{f} = (T_{w} + T_{b}) / 2

The above correlations are valid for Prandlt numbers in the range of 0.5 and 2000.

**References**

Gnielinski, V., *Int. Chem. Eng.*, 16, 359, 1976

Incropera, De Witt., *Fundamentals of Heat and Mass Transfer*,
3rd ed., John Wiley & Sons, eq.8.53, 8.63a & 8.63b, 1990.