.TransiEnt.Producer.Gas.BiogasPlant.HeatTransfer.FreeConvection.NusseltFreeConvection_horizontalSurface

Information

1. Purpose of model

Evaluates the Nusselt Correlation for Natural Convection Heat Transfer at horizontall surfaces.

2. Level of detail, physical effects considered, and physical insight

(Description)

3. Limits of validity

L (characteristic length) must be chosen according to geometry

4. Interfaces

(none)

5. Nomenclature

Ra := Rayleigh number,

Pr := Prandtl number

Nu := Nusselt number

6. Governing Equations

Heat flow from surface to fluid on upper surface

for Ra * f_2(Pr) <=7e4 (laminar)

Nu := 0.766 [Ra *f_2(Pr)]^{1/5}

for Ra * f_2(Pr) > 7e4 (turbulent)

Nu := 0.15 [Ra * f_2(Pr)]^{1/3}

f_2(Pr) := [1+(0.322/Pr)^{11/20}]^{-20/11}

Heat flow from surface to fluid on lower surface

Nu := 0.6 [Ra * f_1(Pr)]^{1/5}

f_1(Pr) := [1+(0.492/Pr)^{9/16}]^{-16/9}

7. Remarks for Usage

important to determine whether geometry helping (case 1) or hindering (case2) the flow driven by buoancy.

use together with functions calculating correct Rayleigh and Prandtl numbers

8. Validation

(no validation or testing necessary)

9. References

[1] Klan, H., & Thess, A. (2013). F2 Wärmeübertragung durch freie Konvektion: Außenströmung. In VDI-Wärmeatlas (pp. 757-764). Springer Vieweg, Berlin, Heidelberg.

10. Version History

Created by Philipp Jahneke (philipp.koziol@tuhh.de), Aug 2018

Interface

function NusseltFreeConvection_horizontalSurface
  extends TransiEnt.Basics.Icons.Function;
  input Modelica.Units.SI.RayleighNumber Ra "Rayleight number calculated with properties of medium";
  input Modelica.Units.SI.PrandtlNumber Pr "Prandtl number (property of medium)";
  input Boolean upside = true "true if convection takes place on the upper side of the surface";
  input Boolean hotSurface = true "true if the surface is warmer then the fluid";
  output Modelica.Units.SI.NusseltNumber Nu;
  final parameter Real f1 = (1 + (0.492/Pr)^(9/16))^(-16/9);
  final parameter Real f2 = (1 + (0.322/Pr)^(11/20))^(-20/11);
end NusseltFreeConvection_horizontalSurface;