WOLFRAM SYSTEM MODELER

# Convection

Lumped thermal element for heat convection (Q_flow = Gc*dT) # Wolfram Language

In:= `SystemModel["Modelica.Thermal.HeatTransfer.Components.Convection"]`
Out:= # Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

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. 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 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
```

# Connectors (3)

Gc solid Type: RealInput Description: Signal representing the convective thermal conductance in [W/K] Type: HeatPort_a Type: HeatPort_b

# Used in Examples (10) HeatLosses Modelica.Mechanics.MultiBody.Examples.Elementary Demonstrate the modeling of heat losses HeatLosses Modelica.Mechanics.Rotational.Examples Demonstrate the modeling of heat losses HeatLosses Modelica.Mechanics.Translational.Examples Demonstrate the modeling of heat losses SimpleCooling Modelica.Thermal.FluidHeatFlow.Examples Simple cooling circuit ParallelCooling Modelica.Thermal.FluidHeatFlow.Examples Cooling circuit with parallel branches IndirectCooling Modelica.Thermal.FluidHeatFlow.Examples Indirect cooling circuit PumpAndValve Modelica.Thermal.FluidHeatFlow.Examples Cooling circuit with pump and valve PumpDropOut Modelica.Thermal.FluidHeatFlow.Examples Cooling circuit with drop out of pump ParallelPumpDropOut Modelica.Thermal.FluidHeatFlow.Examples Cooling circuit with parallel branches and drop out of pump Motor Modelica.Thermal.HeatTransfer.Examples Second order thermal model of a motor