Related Resources: heat transfer

Forced Convection Entry Region Circular Pipe Heat Transfer Equation and Calculator

Heat Transfer Engineering
Thermodynamics
Engineering Physics

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

Preview: Forced Convection Entry Region Circular Pipe / Tube Calculator

Tube wall temperature (T_w ) is calculated as:

T_w = T_b + q / (h_m A)

h_m = Nu_m · k / D

h_mult = Nu_m / Nu_f-dev

The Nusselt number is calculated as:

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

For Turbulent Developing Flow - 2300 < Re < 5 x 10⁶
Nu = 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 = ρ u_m D / v
Pr = C_p v / k

Film temperature T_f defined as follows:

T_f = (T_w + T_b ) / 2

Where:

C _p = Specific Heat capacity (J/(kg·K))
k = Thermal Conductivity of Fluid (W/m - °C)
v = Dynamic Viscosity (kg/m-s)
v_w = Dynamic Viscosity (kg/m-s)
ρ = Density (kg/m³)
D = Diameter of Tube/Pipe (m)
L = Tube/Pipe Length (m)
q = Heat Load (W)
T_b = Bulk Fluid Temperature °C
u _m = Fluid/Flow Velocity (m/s)
Re = Reynolds number
Pr = Prandtl number
f = Friction
Nu = Nusselt Number
h_m = Heat transfer coefficient (W/m² - °C)
h_mult = Heat Transfer Muliplier
A = Area of the Tube/Pipe (m²)
T_w = 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.