WOLFRAM SYSTEMMODELER

# kc_evenGapTurbulent # Wolfram Language

In:= `SystemModel["Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.Channel.kc_evenGapTurbulent"]`
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 developed turbulent fluid flow through an even gap at heat transfer from both sides.

#### Functions kc_evenGapTurbulent and kc_evenGapTurbulent_KC

There are basically three differences:

• The function kc_evenGapTurbulent is using kc_evenGapTurbulent_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_evenGapTurbulent_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_evenGapTurbulent_KC, where an unknown mass flow rate is calculated out of a given mean convective heat transfer coefficient kc

#### Restriction

• identical and constant wall temperatures
• hydraulic diameter per gap length (d_hyd / L) ≤ 1
• 0.5 ≤ Prandtl number Pr ≤ 100)
• turbulent regime (3e4 ≤ Reynolds number ≤ 1e6)
• developed fluid flow
• heat transfer from both sides of the gap (target = Modelica.Fluid.Dissipation.Utilities.Types.kc_evenGap.DevBoth)

#### Geometry #### Calculation

The mean convective heat transfer coefficient kc for an even gap is calculated through the corresponding Nusselt number Nu_turb according to Gnielinski in [VDI 2002, p. Gb 7, sec. 2.4]

```    Nu_turb =(zeta/8)*Re*Pr/{1+12.7*[zeta/8]^(0.5)*[Pr^(2/3) -1]}*{1+[d_hyd/L]^(2/3)}
```

where the pressure loss coefficient zeta according to Konakov in [VDI 2002, p. Ga 5, eq. 27] is determined by

```    zeta =  1/[1.8*log10(Re) - 1.5]^2
```

resulting to the corresponding mean convective heat transfer coefficient kc

```    kc =  Nu_turb * lambda / d_hyd
```

with

 cp as specific heat capacity at constant pressure [J/(kg.K)], d_hyd = 2*s as hydraulic diameter of gap [m], eta as dynamic viscosity of fluid [Pa.s], h as height of cross sectional area in gap [m], kc as mean convective heat transfer coefficient [W/(m2.K)], lambda as heat conductivity of fluid [W/(m.K)], L as overflowed length of gap (normal to cross sectional area) [m] , Nu_turb as mean Nusselt number for turbulent regime [-], Pr = eta*cp/lambda as Prandtl number [-], rho as fluid density [kg/m3], s as distance between parallel plates of cross sectional area [m], Re = rho*v*d_hyd/eta as Reynolds number [-], v as mean velocity in gap [m/s], zeta as pressure loss coefficient [-].

Note that the fluid flow properties shall be calculated with an arithmetic mean temperature out of the fluid flow temperatures at the entrance and the exit of the gap.

#### Verification

The mean Nusselt number Nu_turb representing the mean convective heat transfer coefficient kc in dependence of the chosen fluid flow and heat transfer situations (targets) is shown in the figure below.

• Target 2: Developed fluid flow and heat transfer from both sides of the gap #### References

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