WOLFRAM SYSTEMMODELER

Convection

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

Wolfram Language

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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

Description:

fluid

Type: HeatPort_b

Description:

Used in Examples (10)

HeatLosses

Demonstrate the modeling of heat losses

HeatLosses

Demonstrate the modeling of heat losses

HeatLosses

Demonstrate the modeling of heat losses

SimpleCooling

Example: simple cooling circuit

ParallelCooling

Example: cooling circuit with parallel branches

IndirectCooling

Example: indirect cooling circuit

PumpAndValve

Example: cooling circuit with pump and valve

PumpDropOut

Example: cooling circuit with drop out of pump

ParallelPumpDropOut

Example: cooling circuit with parallel branches and drop out of pump

Motor

Second order thermal model of a motor