kc_turbulent

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Calculation of the mean convective heat transfer coefficient kc for a hydrodynamically developed turbulent fluid flow over an even surface.

Functions kc_turbulent and kc_turbulent_KC

There are basically three differences:

  • The function kc_turbulent is using kc_turbulent_KC but offers additional output variables like e.g. Reynolds number or Nusselt number and failure status (an output of 1 means that the function is not valid for the inputs).
  • Generally the function kc_turbulent_KC is numerically best used for the calculation of the mean convective heat transfer coefficient kc at known mass flow rate.
  • You can perform an inverse calculation from kc_turbulent_KC, where an unknown mass flow rate is calculated out of a given mean convective heat transfer coefficient kc

Restriction

  • constant wall temperature
  • turbulent regime (Reynolds number 5e5 < Re < 1e7)
  • Prandtl number 0.6 ≤ Pr ≤ 2000

Geometry

plate

Calculation

The mean convective heat transfer coefficient kc for flat plate is calculated through the corresponding Nusselt number Nu_turb according to [VDI 2002, p. Gd 1, eq. 2]:

Nu_turb = (0.037 * Re^0.8 * Pr) / (1 + 2.443/Re^0.1 * (Pr^(2/3)-1))

and the corresponding mean convective heat transfer coefficient kc:

kc =  Nu_turb * lambda / L

with

cp as specific heat capacity at constant pressure [J/(kg.K)],
eta as dynamic viscosity of fluid [Pa.s],
kc as mean convective heat transfer coefficient [W/(m2.K)],
lambda as heat conductivity of fluid [W/(m.K)],
L as length of plate [m],
Nu_turb as mean Nusselt number for turbulent regime [-],
Pr = eta*cp/lambda as Prandtl number [-],
rho as fluid density [kg/m3],
Re = v*rho*L/eta as Reynolds number [-].

Verification

The mean Nusselt number in turbulent regime Nu representing the mean convective heat transfer coefficient kc for Prandtl numbers of different fluids is shown in the figure below.

kc_turbulent

References

VDI:
VDI - Wärmeatlas: Berechnungsblätter für den Wärmeübergang. Springer Verlag, 9th edition, 2002.