WOLFRAM SYSTEM MODELER

# Wolfram Language

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`SystemModel["Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Plate.kc_turbulent"]`
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# 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

#### 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.

#### References

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