Buildings.HeatTransfer.Convection

Package with models for convective heat transfer

Information

This package provides component models to compute heat convection.

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name	Description
Exterior	Model for a exterior (outside) convective heat transfer
Interior	Model for a interior (room-side) convective heat transfer
Functions	Functions for convective heat transfer
Examples	Collection of models that illustrate model use and test models
Validation	Collection of validation models
BaseClasses	Package with base classes for Buildings.HeatTransfer.Convection

Buildings.HeatTransfer.Convection.Exterior

Model for a exterior (outside) convective heat transfer

Buildings.HeatTransfer.Convection.Exterior

Information

This is a model for a convective heat transfer for exterior, outside-facing surfaces. The parameter conMod determines the model that is used to compute the heat transfer coefficient:

If conMod= Buildings.HeatTransfer.Types.ExteriorConvection.Fixed, then the convective heat transfer coefficient is set to the value specified by the parameter hFixed.

If conMod= Buildings.HeatTransfer.Types.ExteriorConvection.TemperatureWind, then the convective heat transfer coefficient is computed based on wind speed, wind direction and temperature difference.

The total convection coefficient h_t is the sum of the temperature-driven free convection coefficient h_n and the wind-driven forced convection coefficient h_f,

h_t = h_n + h_f

The free convection coefficient h_n is computed in the same way as in Buildings.HeatTransfer.Convection.Interior. The forced convection coefficient h_f is computed based on a correlation by Sparrow, Ramsey, and Mass (1979), which is

h_f = 2.537 W R √( P v ⁄ A )

where W=1 for windward surfaces and W=0.5 for leeward surfaces, with leeward defined as greater than 100 degrees from normal incidence, R is a surface roughness multiplier, P is the perimeter of the surface and A is the area of the surface. This is the same equation as implemented in EnergyPlus 6.0.

We make the simplified assumption that the surface is square, and hence we set

h_f = 2.537 W R √( 4 v ⁄ √(A) )

The surface roughness is specified by the parameter surfaceRoughness which has to be set to a type of Buildings.HeatTransfer.Types.SurfaceRoughness.The coefficients for the surface roughness are

Roughness index	R	Example material
VeryRough	2.17	Stucco
Rough	1.67	Brick
MediumRough	1.52	Concrete
MediumSmooth	1.13	Clear pine
Smooth	1.11	Smooth plaster
VerySmooth	1.00	Glass

References

Sparrow, E. M., J. W. Ramsey, and E. A. Mass. 1979. Effect of Finite Width on Heat Transfer and Fluid Flow about an Inclined Rectangular Plate. Journal of Heat Transfer, Vol. 101, p. 204.

Walton, G. N. 1981. Passive Solar Extension of the Building Loads Analysis and System Thermodynamics (BLAST) Program, Technical Report, United States Army Construction Engineering Research Laboratory, Champaign, IL.

Extends from Buildings.HeatTransfer.Convection.BaseClasses.PartialConvection (Partial model for heat convection).

Parameters

Type	Name	Default	Description
Area	A		Heat transfer area [m2]
ExteriorConvection	conMod	Buildings.HeatTransfer.Types...	Convective heat transfer model
CoefficientOfHeatTransfer	hFixed	3	Constant convection coefficient [W/(m2.K)]
SurfaceRoughness	roughness	Buildings.HeatTransfer.Types...	Surface roughness
Angle	azi		Surface azimuth [rad]
Angle	til	til(displayUnit="deg")	Surface tilt [rad]
Initialization
TemperatureDifference	dT.start	0	= solid.T - fluid.T [K]

Connectors

Type	Name	Description
HeatPort_a	solid
HeatPort_b	fluid
input RealInput	v	Wind speed [m/s]
input RealInput	dir	Wind direction (0=wind from North) [rad]

Modelica definition

model Exterior "Model for a exterior (outside) convective heat transfer" extends Buildings.HeatTransfer.Convection.BaseClasses.PartialConvection; parameter Buildings.HeatTransfer.Types.ExteriorConvection conMod= Buildings.HeatTransfer.Types.ExteriorConvection.TemperatureWind "Convective heat transfer model"; parameter Modelica.SIunits.CoefficientOfHeatTransfer hFixed=3 "Constant convection coefficient"; parameter Buildings.HeatTransfer.Types.SurfaceRoughness roughness= Buildings.HeatTransfer.Types.SurfaceRoughness.Medium "Surface roughness"; parameter Modelica.SIunits.Angle azi "Surface azimuth"; parameter Modelica.SIunits.Angle til(displayUnit="deg") "Surface tilt"; Modelica.Blocks.Interfaces.RealInput v(unit="m/s") "Wind speed"; Modelica.Blocks.Interfaces.RealInput dir(unit="rad", displayUnit="deg", min=0, max=2*Modelica.Constants.pi) "Wind direction (0=wind from North)"; Modelica.SIunits.CoefficientOfHeatTransfer hF "Convective heat transfer coefficient due to forced convection"; Modelica.SIunits.HeatFlux qN_flow "Convective heat flux from solid -> fluid due to natural convection"; Modelica.SIunits.HeatFlux qF_flow "Convective heat flux from solid -> fluid due to forced convection"; protected constant Modelica.SIunits.Velocity v_small = 0.5 "Small value for wind velocity below which equations are regularized"; final parameter Real cosTil=Modelica.Math.cos(til) "Cosine of window tilt"; final parameter Real sinTil=Modelica.Math.sin(til) "Sine of window tilt"; final parameter Boolean isCeiling = abs(sinTil) < 10E-10 and cosTil > 0 "Flag, true if the surface is a ceiling"; final parameter Boolean isFloor = abs(sinTil) < 10E-10 and cosTil < 0 "Flag, true if the surface is a floor"; parameter Real R(fixed=false) "Surface roughness"; Real W(min=0.5, max=1) "Wind direction modifier"; initial equation if (roughness == Buildings.HeatTransfer.Types.SurfaceRoughness.VeryRough) then R=2.17; elseif (roughness == Buildings.HeatTransfer.Types.SurfaceRoughness.Rough) then R=1.67; elseif (roughness == Buildings.HeatTransfer.Types.SurfaceRoughness.Medium) then R=1.52; elseif (roughness == Buildings.HeatTransfer.Types.SurfaceRoughness.MediumSmooth) then R=1.13; elseif (roughness == Buildings.HeatTransfer.Types.SurfaceRoughness.Smooth) then R=1.11; elseif (roughness == Buildings.HeatTransfer.Types.SurfaceRoughness.VerySmooth) then R=1.00; else R=0; end if; equation if (conMod == Buildings.HeatTransfer.Types.ExteriorConvection.Fixed) then qN_flow = hFixed * dT; W = 1; hF = 0; qF_flow = 0; else // Even if hCon is a step function with a step at zero, // the product hCon*dT is differentiable at zero with // a continuous first derivative if isCeiling then qN_flow = Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling(dT=dT); elseif isFloor then qN_flow = Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor(dT=dT); else qN_flow = Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall(dT=dT); end if; // Forced convection W = Buildings.Utilities.Math.Functions.regStep( x = v-v_small/2, y1 = Buildings.HeatTransfer.Convection.Functions.windDirectionModifier( azi=azi, dir=dir), y2 = 0.75, x_small=v_small/4); hF = 2.537 * W * R * 2 / A^(0.25) * Buildings.Utilities.Math.Functions.regNonZeroPower( x=v, n=0.5, delta=v_small); qF_flow = hF*dT; end if; q_flow = qN_flow + qF_flow; end Exterior;

Buildings.HeatTransfer.Convection.Interior

Model for a interior (room-side) convective heat transfer

Buildings.HeatTransfer.Convection.Interior

Information

This is a model for a convective heat transfer for interior, room-facing surfaces. The parameter conMod determines the model that is used to compute the heat transfer coefficient:

If conMod= Buildings.HeatTransfer.Types.InteriorConvection.Fixed, then the convective heat transfer coefficient is set to the value specified by the parameter hFixed.
If conMod= Buildings.HeatTransfer.Types.InteriorConvection.Temperature, then the convective heat tranfer coefficient is a function of the temperature difference. The convective heat flux is computed using
- for floors the function Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor
- for ceilings the function Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling
- for walls the function Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall

Extends from Buildings.HeatTransfer.Convection.BaseClasses.PartialConvection (Partial model for heat convection).

Parameters

Type	Name	Default	Description
Area	A		Heat transfer area [m2]
InteriorConvection	conMod	Buildings.HeatTransfer.Types...	Convective heat transfer model
CoefficientOfHeatTransfer	hFixed	3	Constant convection coefficient [W/(m2.K)]
Angle	til	til(displayUnit="deg")	Surface tilt [rad]
Initialization
TemperatureDifference	dT.start	0	= solid.T - fluid.T [K]

Connectors

Type	Name	Description
HeatPort_a	solid
HeatPort_b	fluid

Modelica definition

model Interior "Model for a interior (room-side) convective heat transfer" extends Buildings.HeatTransfer.Convection.BaseClasses.PartialConvection; constant Boolean homotopyInitialization = true "= true, use homotopy method"; parameter Buildings.HeatTransfer.Types.InteriorConvection conMod= Buildings.HeatTransfer.Types.InteriorConvection.Fixed "Convective heat transfer model"; parameter Modelica.SIunits.CoefficientOfHeatTransfer hFixed=3 "Constant convection coefficient"; parameter Modelica.SIunits.Angle til(displayUnit="deg") "Surface tilt"; protected constant Modelica.SIunits.Temperature dT0 = 2 "Initial temperature used in homotopy method"; final parameter Real cosTil=Modelica.Math.cos(til) "Cosine of window tilt"; final parameter Real sinTil=Modelica.Math.sin(til) "Sine of window tilt"; final parameter Boolean isCeiling = abs(sinTil) < 10E-10 and cosTil > 0 "Flag, true if the surface is a ceiling"; final parameter Boolean isFloor = abs(sinTil) < 10E-10 and cosTil < 0 "Flag, true if the surface is a floor"; initial equation assert(homotopyInitialization, "In " + getInstanceName() + ": The constant homotopyInitialization has been modified from its default value. This constant will be removed in future releases.", level = AssertionLevel.warning); equation if (conMod == Buildings.HeatTransfer.Types.InteriorConvection.Fixed) then q_flow = hFixed * dT; else // Even if hCon is a step function with a step at zero, // the product hCon*dT is differentiable at zero with // a continuous first derivative if homotopyInitialization then if isCeiling then q_flow = homotopy(actual=Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling(dT=dT), simplified=dT/dT0*Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling(dT=dT0)); elseif isFloor then q_flow = homotopy(actual=Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor(dT=dT), simplified=dT/dT0*Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor(dT=dT0)); else q_flow = homotopy(actual=Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall(dT=dT), simplified=dT/dT0*Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall(dT=dT0)); end if; else if isCeiling then q_flow = Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling(dT=dT); elseif isFloor then q_flow = Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor(dT=dT); else q_flow = Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall(dT=dT); end if; end if; end if; end Interior;