WOLFRAM SYSTEM MODELER

# kc_laminar # Wolfram Language

In:= `SystemModel["Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_laminar"]`
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 for a helical pipe in the laminar flow regime.

#### Functions kc_laminar and kc_laminar_KC

There are basically three differences:

• The function kc_laminar is using kc_laminar_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_laminar_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_laminar_KC, where an unknown mass flow rate is calculated out of a given mean convective heat transfer coefficient kc

#### Restriction

• laminar regime (Reynolds number ≤ critical Reynolds number Re_crit)
• neglect influence of heat transfer direction (heating/cooling) according to Sieder and Tate

The critical Reynolds number Re_crit in a helical pipe depends on its mean curvature diameter d_coil . The smaller the mean curvature diameter of the helical pipe, 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. Gc 2, eq. 5] :

`    Nu = 3.66 + 0.08*[1 + 0.8*(d_hyd/d_coil)^0.9]*Re^m*Pr^(1/3)`

with the exponent m for the Reynolds number

`    m = 0.5 + 0.2903*(d_hyd/d_coil)^0.194`

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.