WOLFRAM SYSTEMMODELER

kc_laminar

Wolfram Language

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SystemModel["Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_laminar"]
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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 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

pic_helicalPipe

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.

fig_helicalPipe_kc_laminar

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.