### 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.

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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 10^{6}

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/m^{3})

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/m^{2} - °C)

h_{mult} = Heat Transfer Muliplier

A = Area of the Tube/Pipe (m^{2})

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.

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