This page calculates the mean heat transfer coefficient for simultaneously developing velocity and temperature fields in a circular smooth tube assuming a square abrupt entry. The convection calculation automatically switches between laminar and turbulent convection correlations based on Reynolds number. The correlations used apply for both uniform heat flux and temperature in the turbulent regime. In the laminar regime a correlation based on constant temperature is assumed.

The calculation is based on a mean Nusselt.

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

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

Where *h _{m}* is the average heat transfer
coefficient between the entry and distance

h_{m} = Nu_{m} k / D

Where *Nu _{m}* is the mean Nusselt Number,

For Laminar Flow - Re < 2300

If (Re Pr / L / D)^{(1/3)} ( µ/ µ_{w} )^{0.14} >=
2.0 ; flow is developing.

Nu_{m} = 1.86 (Re Pr / (L/D) )^{(1/3)} (µ /
µ_{w})^{0.14 }

valid for 0.48 < Pr < 16,700 and
0.0044 < (µ / µ_{w})^{0.14} < 9.75 ^{
}Else ; flow is fully developed

Nu_{m} = 3.66 ; uniform temperature

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

Nu_{m} = Nu_{dev }( 1 + 2.4254 / ( L / D )^{0.676}) ;
valid for Pr = 0.7, i.e. air

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

valid for 0.5 < Pr < 2,000

and f = ( 0.79ln Re - 1.64 ) ^{-2}
are the Nusselt and friction values for fully developed flow

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

µ = dynamic viscosity of the fluid

µ_{w} = dynamic viscosity evaluated at the temperature of the wall

In addition, you must define all fluid properties at the film
temperature *T _{f}* defined as shown below except for µ

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

**References**

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

Incropera, De Witt., *Fundamentals of Heat and Mass Transfer*,
3rd ed., John Wiley & Sons, eq.8.57, 8.63a & 8.63b, 1990.

Rohsenow, W. R., J. P. Hartnett and Y. I. Cho, *Handbook
of Heat Transfer*, 3rd ed., McGraw Hill, 1998, p. 5.29.