modelMonoLayerAir

Heat transfer correlations (convection and radiation) for air cavities

Information

Model for computing convective/radiative heat transfer inside air cavities.

Optional error which can be enabled/disabled with parameter checkLowPerformanceGlazing checks if the user unintentionally is simulating low performance glazing with default emissivities.

Assumption and limitations

Only valid for horizontal or vertical surfaces.

References

Horizontal:
K.G.T. Hollands, G.D. Raithby, L. Konicek, Correlation equations for free convection heat transfer in horizontal layers of air and water, International Journal of Heat and Mass Transfer, Volume 18, Issues 7–8, July–August 1975, Pages 879-884, ISSN 0017-9310, http://dx.doi.org/10.1016/0017-9310(75)90179-9.
(http://www.sciencedirect.com/science/article/pii/0017931075901799)

Vertical:
Wright, J. 1996. A correlation to quantify convective heat transfer between vertical window glazings, ASHRAE Transactions, 102(1): 940-946.

Parameters

Type	Name	Default	Description
Modelica.Units.SI.Area	A		Surface area
Modelica.Units.SI.Angle	inc		Inclination of surface at port a
Modelica.Units.SI.Length	d		Cavity width
Modelica.Units.SI.Emissivity	epsLw_a		Longwave emissivity of material connected at port_a
Modelica.Units.SI.Emissivity	epsLw_b		Longwave emissivity on material connected at port_b
Modelica.Units.SI.TemperatureDifference	dT_nominal	1	Nominal temperature difference, used for linearising Rayleigh number
Modelica.Units.SI.ThermalConductivity	k	0.026	Thermal conductivity of medium, default for air, T=20C
Boolean	linearise	true	Linearise Grashoff number around expected nominal temperature difference
Boolean	checkCoating	true	Throws an error if the cavity does not have a coating
Advanced
Modelica.Media.Interfaces.Types.IsobaricExpansionCoefficient	beta	3.43e-3	Thermal expansion coefficient of medium, default for air, T=20C
Modelica.Units.SI.KinematicViscosity	nu	15e-6	Kinematic viscosity of medium, default for air, T=20C
Modelica.Units.SI.ThermalDiffusivity	alpha	22e-6	Thermal diffusivity of medium, default for air, T=300K

Components

Type	Name	Default	Description
Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a	port_a
Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_b	port_b
Modelica.Units.SI.ThermalConductance	G	hA + A5.86*(1/((1/epsLw_a) + (1/epsLw_b) - 1))
Real	Nu	if ceiling or floor then (if linearise then (1 + (1.44(1 - 1708/Ra) + ((Ra/5830)^(1/3) - 1)))/2 else if ceiling then IDEAS.Utilities.Math.Functions.spliceFunction(pos = 1 + (1.44max(1 - 1708/Ra, 0) + max((Ra/5830)^(1/3) - 1, 0)), neg = 1, x = sign(port_a.T - port_b.T)Ra - 500, deltax = 100) else IDEAS.Utilities.Math.Functions.spliceFunction(pos = 1 + (1.44max(1 - 1708/Ra, 0) + max((Ra/5830)^(1/3) - 1, 0)), neg = 1, x = sign(port_b.T - port_a.T)Ra - 500, deltax = 100)) elseif vertical then (if Ra > 5e4 then 0.0673838Ra^(1/3) elseif Ra > 1e4 then 0.028154Ra^0.41399 else 1 + 1.75967e-10Ra^2.2984755) else 1	Correlations from Hollands et al. and Wright et al.
Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a	port_emb		Internal port

Revisions

September 9, 2019, by Kristoff Six:
Updated with checkCoating for issue #1038.
November 10, 2016, by Filip Jorissen:
Revised implementation for horizontal surfaces such that less state events are generated.
November 15, 2016, by Filip Jorissen:
Revised documentation for IDEAS 1.0.
February 10, 2016, by Filip Jorissen and Damien Picard:
Revised implementation.
November 15, 2015, by Filip Jorissen:
First implementation.