Related Resources: heat transfer

### Forced Convection Entry Region Circular Pipe Heat Transfer Equation and Calculator

Forced Convection Entry Region Circular Pipe / Tube Equation and Calculator

Equation and calculator to determine the mean heat transfer coefficient for simultaneously developing velocity and temperature fields in a circular smooth tube. ALL calculators require a Premium Membership

Tube wall temperature (Tw ) is calculated as:

Tw = Tb + q / (hm A)

hm = Num · k / D

hmult = Num / Nuf-dev

The Nusselt number is calculated as:

For Laminar Flow - Re < 2300
If (Re Pr / L / D)(1/3) ( v/ vw ) 0.14 >= 2.0 ; flow is developing.
Num = 1.86 (Re Pr / (L/D) )(1/3) (v / vw ) 0.14
valid for 0.48 < Pr < 16,700 and 0.0044 < ( v/ vw )0.14 < 9.75
Else; flow is fully developed
Num = 3.66 ; uniform temperature

For Turbulent Developing Flow - 2300 < Re < 5 x 106
Nu = Nudev ( 1 + 2.4254 / ( L / D )0.676 ) ; valid for Pr = 0.7, i.e. air
Where:    Nudev = ( f / 8) ( Re - 1000 ) Pr / { 1 + 12.7( f / 8 )1/2 (  Pr2/3 - 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 = ρ um D / v
Pr = Cp v / k

Film temperature Tf defined as follows:

Tf = (Tw + Tb ) / 2

Where:

C p = Specific Heat capacity (J/(kg·K))
k = Thermal Conductivity of Fluid (W/m - °C)
v = Dynamic Viscosity (kg/m-s)
vw = Dynamic Viscosity (kg/m-s)
ρ = Density (kg/m3)
D = Diameter of Tube/Pipe (m)
L = Tube/Pipe Length (m)
Tb = Bulk Fluid Temperature °C
u m = Fluid/Flow Velocity (m/s)
Re = Reynolds number
Pr = Prandtl number
f = Friction
Nu = Nusselt Number
hm = Heat transfer coefficient (W/m2 - °C)
hmult = Heat Transfer Muliplier
A = Area of the Tube/Pipe (m2)
Tw = Average Wall Temperature °C

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.