.Buildings.ThermalZones.Detailed.BaseClasses.InfraredRadiationExchange

Information

This model computes the infrared radiative heat transfer between the interior surfaces of a room. Each opaque surface emits radiation according to

Eⁱ = σ   Aⁱ   εⁱ   (Tⁱ)⁴,

where σ is the Stefan-Boltzmann constant, Aⁱ is the surface area, εⁱ is the absorptivity in the infrared spectrum, and Tⁱ is the surface temperature. If the parameter linearizeRadidation is set to true, then the term (Tⁱ)⁴ is replaced with T₀³ Tⁱ, where T₀ = 20°C is a parameter.

The incoming radiation at surface i is

Gⁱ = -∑_j   F^j,i   J^j

where F^j,i is the view factor from surface j to surface i, J^j is the radiosity leaving surface j and the sum is over all surfaces. For opaque surfaces, it follows from the first law that the radiosity Jⁱ is

Jⁱ = -Eⁱ - (1-εⁱ)   Gⁱ.

For windows, the outgoing radiosity is an input into this model because the window model computes this quantity directly.

For each surface i, the heat balance is

0 = Qⁱ + Jⁱ + Gⁱ.

For opaque surfaces, the heat flow rate Qⁱ is set to be equal to the heat flow rate at the heat port. For the glass of the windows, the radiosity outflow at the connector is set to the radiosity Gⁱ that is leaving the surface.

The view factor from surface i to j is approximated as

F^i,j = A^j ⁄ ∑_k A^k.

Revisions

• November 30, 2021, by Michael Wetter:
  Removed test on radiation balance that was added for debugging purposes.
• April 14, 2020, by Michael Wetter:
  Changed homotopyInitialization to a constant.
  This is for IBPSA, #1341.
• January 23, 2017, by Michael Wetter:
  Corrected wrong start value for J. The start value was positive, but J(each max =0).
  This is for issue 627.
• May 21, 2015, by Michael Wetter:
  Reformulated to reduce use of the division macro in Dymola. This is for issue 417.
• May 30, 2014, by Michael Wetter:
  Removed undesirable annotation Evaluate=true.
• June 27, 2013, by Michael Wetter:
  Changed model because the outflowing radiosity has been changed to be a non-negative quantity. See track issue #158.
• April 18, 2013, by Michael Wetter:
  Removed cardinality function as this is deprecated in the MSL specification and not correctly implemented in omc.
• February 10, 2012 by Wangda Zuo:
  Fixed a bug for linearization of T4.
• April 21, 2011 by Michael Wetter:
  Fixed a bug in the view factor calculation, and rewrote the model to reduce simulation time. The bug caused too much radiosity to flow from large to small surfaces because the law of reciprocity for view factors was not satisfied. This led to low surface temperatures if a surface had a large area compared to other surfaces.
• April 2, 2011 by Michael Wetter:
  Added homotopy operator.
• Feb. 3, 2011, by Michael Wetter:
  Corrected bug in start value of radiosity, reformulated equations to get smaller system of coupled equations.
• Dec. 1, 2010, by Michael Wetter:
  First implementation.