Calculation of the individual heat transfer coefficient


Dimensionless numbers and equations

Calculation of the individual heat transfer coefficients involves the following dimensionless numbers:

The Nusselt number, Nu Nusselt number            where α = individual heat transfer coefficient [W/m2·K]
d = characteristic length [m]  (e.g. tube diameter)
λ = thermal conductivity [W/m·K]
cp = specific heat [J/kg·K]
μ = dynamic viscosity [Pas]
v = velocity [m/s]
ρ = density [kg/m3]
The Prandtl number, Pr Prandtl number
The Reynolds number, Re Reynolds number

For natural convection one dimensionless number is added:
The Grashof number, Gr Grashof number where g    = gravitational acceleration [m/s2]
β    = volumetric expansion coefficient [K-1]
ΔT  = temperature difference [K]

At natural convection the following generalized equation applies:
Nu = f(Gr, Pr)

At forced convection the following generalized equation applies:
Nu = f(Re, Pr)

With dimensionless numbers and equations any consistent system of units can be applied.

The physical meaning of the different dimensionless numbers are as follows:
Nu = (characteristic length)/(theoretical film thickness)
Pr = (momentum diffusivity)/(thermal diffusivity)
Re = (momentum by eddy diffusion)/(momentum by molecular transport)
Gr = (inertia forces)/(viscous shear forces)·(buoyancy forces)/ (viscous shear forces)


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Forced convection, laminar flow
Forced convection, turbulent flow
Typical Nu - Pr - Re relationship
 

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