WOLFRAM SYSTEMMODELER

Convection

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

Wolfram Language

In[1]:=
SystemModel["Modelica.Thermal.HeatTransfer.Components.Convection"]
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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[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

Connectors (3)

Gc

Type: RealInput

Description: Signal representing the convective thermal conductance in [W/K]

solid

Type: HeatPort_a

fluid

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