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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 10⁶
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/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 = Heat transfer coefficient (W/m² - °C)
A = Area of the Tube/Pipe (m²)
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.