WOLFRAM SYSTEMMODELER

# kc_turbulent # Wolfram Language

In:= `SystemModel["Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_turbulent"]`
Out:= # Information

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

Calculation of the mean convective heat transfer coefficient kc of a helical pipe for turbulent flow regime.

#### 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

The critical Reynolds number Re_crit in a helical pipe depends on its mean curvature diameter. The smaller the mean curvature diameter of the helical pipe d_mean , the earlier the turbulent regime will start due to vortexes out of higher centrifugal forces.

#### Geometry #### Calculation

The mean convective heat transfer coefficient kc for helical pipes is calculated through the corresponding Nusselt number Nu according to [VDI 2002, p. Ga 2, eq. 6]:

```    Nu = (zeta_TOT/8)*Re*Pr/{1 + 12.7*(zeta_TOT/8)^0.5*[Pr^(2/3)-1]},
```

where the influence of the pressure loss on the heat transfer calculation is considered through

```    zeta_TOT = 0.3164*Re^(-0.25) + 0.03*(d_hyd/d_coil)^(0.5) and
```

and the resulting mean convective heat transfer coefficient kc

```    kc =  Nu * lambda / d_hyd
```

with

 d_mean as mean diameter of helical pipe [m], d_coil = f(geometry) as mean curvature diameter of helical pipe [m], d_hyd as hydraulic diameter of the helical pipe [m], h as slope of helical pipe [m], kc as mean convective heat transfer coefficient [W/(m2K)], lambda as heat conductivity of fluid [W/(mK)], L as total length of helical pipe [m], Nu = kc*d_hyd/lambda as mean Nusselt number [-], Pr = eta*cp/lambda as Prandtl number [-], Re = rho*v*d_hyd/eta as Reynolds number [-], Re_crit = f(geometry) as critical Reynolds number [-].

#### Verification

The mean Nusselt number Nu representing the mean convective heat transfer coefficient kc is shown below for different numbers of turns n_nt at constant total length of the helical pipe. The convective heat transfer of a helical pipe is enhanced compared to a straight pipe due to occurring turbulences resulting out of centrifugal forces. The higher the number of turns, the better is the convective heat transfer for the same length of a pipe.

Note that the ratio of hydraulic diameter to total length of helical pipe d_hyd/L has no remarkable influence on the coefficient of heat transfer kc .

#### References

GNIELINSKI, V.:
Heat transfer and pressure drop in helically coiled tubes.. In 8th International Heat Transfer Conference, volume 6, pages 2847?2854, Washington,1986. Hemisphere.