.TransiEnt.Components.Heat.ThermalInsulation.Basics.Convection_L4

Information

1. Purpose of model

This is a model of linear heat convection, e.g., the heat transfer between a plate and the surrounding air; see also: ConvectiveResistor. It may be used for complicated solid geometries and fluid flow over the solid by determining the convective thermal conductance Gc by measurements.

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

The basic constitutive equation for convection is

Q_flow = Gc*(solid.T - fluid.T);

Q_flow: Heat flow rate from connector 'solid' (e.g., a plate)

to connector 'fluid' (e.g., the surrounding air)

Gc = G.signal[1] is an input signal to the component, since Gc is nearly never constant in practice. For example, Gc may be a function of the speed of a cooling fan. For simple situations, Gc may be calculated according to

Gc = A*h

A: Convection area (e.g., perimeter*length of a box)

h: Heat transfer coefficient

where the heat transfer coefficient h is calculated from properties of the fluid flowing over the solid. Examples:

Machines cooled by air (empirical, very rough approximation according to R. Fischer: Elektrische Maschinen, 10th edition, Hanser-Verlag 1999, p. 378):

h = 7.8*v^0.78 [W/(m2.K)] (forced convection)

= 12 [W/(m2.K)] (free convection)

where

v: Air velocity in [m/s]

Laminar flow with constant velocity of a fluid along a flat plate where the heat flow rate from the plate to the fluid (= solid.Q_flow) is kept constant (according to J.P.Holman: Heat Transfer, 8th edition, McGraw-Hill, 1997, p.270):

h = Nu*k/x;

Nu = 0.453*Re^(1/2)*Pr^(1/3);

where

h : Heat transfer coefficient

Nu : = h*x/k (Nusselt number)

Re : = v*x*rho/mue (Reynolds number)

Pr : = cp*mue/k (Prandtl number)

v : Absolute velocity of fluid

x : distance from leading edge of flat plate

rho: density of fluid (material constant

mue: dynamic viscosity of fluid (material constant)

cp : specific heat capacity of fluid (material constant)

k : thermal conductivity of fluid (material constant)

and the equation for h holds, provided

Re < 5e5 and 0.6 < Pr < 50

3. Limits of validity

(none)

4. Interfaces

(none)

5. Nomenclature

(no elements)

6. Governing Equations

(no equations)

7. Remarks for Usage

(none)

8. Validation

(no validation or testing necessary)

9. References

(none)

10. Version History

Model created by Michael von der Heyde (heyde@tuhh.de) for the Research Project "Future Energy Solution" (FES), 2020