Radiation

Radiative exchange: Q = Gr·σ·(T_a⁴ − T_b⁴).

  • thermal
  • Modelica Standard Library
  • 2 ports
  • 1 parameter
BlockRadiationKindradiationLibraryThermal

Description

Radiative heat exchange between two surfaces, following the Stefan–Boltzmann law. The heat flow grows with the difference of the fourth powers of the absolute temperatures.

Example

Cooling a hot part A 10 W part cools through a thermal resistance into a heatsink that convects and radiates to 20 °C.

10 WPart 100 J/KHeat flowR 2 K/WHeatsink 500 J/Kh·A 5 W/KConvectionAir 20 °CRadiationRoom 20 °CPart temperatureAcross R350 KHeld at 350 KG 1 W/KBody 100 J/K20 W at 1500 sHeaterBody temperature
In Gradara, select a Radiation block and press F1, then choose Open example. It opens as a new model in My models, ready to run.

Also in this example:ConstantStepHeat capacitorThermal conductorThermal resistorConvectionFixed temperatureTemperature sourceFixed heat flowHeat flow sourceTemperature sensorHeat flow sensorTemperature difference sensor

Ports

Conserving terminals 2

  • aport_athermal

    Heat port of surface a. Heat flow Q from a to b enters here.

  • bport_bthermal

    Heat port of surface b. Q leaves here.

Parameters

  • Net radiation conductanceGr0.01 m²

    ≥ 0

    Net radiation conductance, in m²: an area weighted by emissivities and view factor. For a small body in large surroundings, Gr = ε · A.

Equations

Modelica
Q = Gr · σ · (port_a.T⁴ − port_b.T⁴), σ = 5.67 × 10⁻⁸ W/(m²·K⁴)
port_a.Q_flow = Q, port_b.Q_flow = −Q

Implementation

Modelica Standard Library 4.1.0Modelica.Thermal.HeatTransfer.Components.BodyRadiation
MSL documentation

Assumptions and limitations

  • Gray, diffuse surfaces with a fixed Gr. No heat storage.

Tips

  • Temperatures are absolute; the ports must be in kelvin, as all thermal ports are.

See also

Select a block in Gradara and press F1 to open its page offline.