### Round Duct Heat Transfer Coefficient Wall Temperature Heat Transfer Equation and Calculator

**Heat Transfer Engineering**

**Thermodynamics**

**Engineering Physics **

Round Duct Heat Transfer Coefficient and Wall Temperature Equation and Calculator

Equation and calculator 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.

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Preview: Round Duct Heat Transfer Coefficient and Wall Temperature Calculator

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

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

h = Nu · k / D

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

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

valid for Prandlt numbers in the range of 0.5 and 2000.

Where:

C _{p} = Specific Heat capacity (J/(kg·K))

k = Thermal Conductivity of Fluid (W/m - °C)

v = 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 = Heat transfer coefficient (W/m^{2} - °C)

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

T_{w} = Average Wall Temperature °C

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.

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