### 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 | where
α =
individual heat transfer coefficient [W/m^{2}·K]d = characteristic length [m] ( e.g. tube diameter)λ = thermal conductivity [W/m·K] c _{p} =
specific heat [J/kg·K]μ = dynamic viscosity [Pas] v = velocity [m/s] ρ = density [kg/m ^{3}] | |

The Prandtl number, Pr | ||

The Reynolds number, Re | ||

For natural convection one dimensionless number is added: | ||

The Grashof number, Gr | where
g = gravitational acceleration [m/s^{2}]β = volumetric expansion coefficient [K ^{-1}]ΔT = temperature difference [K] | |

At natural convection the following generalized equation applies: | ||

At forced convection the following generalized equation applies: | ||

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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