Buildings.HeatTransfer.Convection.Functions.HeatFlux

Correlations for convective heat flux

Information

This package contains functions for the convective heat transfer. Input into the functions is the temperature difference between the solid and the fluid. The functions compute the convective heat flux, rather than the convective heat transfer coefficient. The reason is that the convective heat transfer coefficient is not differentiable around zero for certain flow configurations, such as buoyancy driven flow at a horizontal surface. However, the product of convective heat transfer coefficient times temperature difference is differentiable around zero.

Package Content

Name Description

constantCoefficient Constant convective heat transfer coefficient

wall Free convection, wall

floor Free convection, floor

ceiling Free convection, ceiling

raleigh Raleigh number with smooth transition to lower limit

BaseClasses Base classes for convective heat transfer coefficients

Name	Description
constantCoefficient	Constant convective heat transfer coefficient
wall	Free convection, wall
floor	Free convection, floor
ceiling	Free convection, ceiling
raleigh	Raleigh number with smooth transition to lower limit
BaseClasses	Base classes for convective heat transfer coefficients

Buildings.HeatTransfer.Convection.Functions.HeatFlux.constantCoefficient

Constant convective heat transfer coefficient

Information

This function computes the convective heat transfer coefficient as h=hCon, where hCon=3 is a default input argument. The convective convective heat flux is q_flow = h * dT, where dT is the solid temperature minus the fluid temperature.

Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).

Inputs

Type Name Default Description

TemperatureDifference dT Temperature difference solid minus fluid [K]

CoefficientOfHeatTransfer hCon 3 Constant for convective heat transfer coefficient [W/(m2.K)]

Type	Name	Default	Description
TemperatureDifference	dT		Temperature difference solid minus fluid [K]
CoefficientOfHeatTransfer	hCon	3	Constant for convective heat transfer coefficient [W/(m2.K)]

Outputs

Type Name Description

HeatFlux q_flow Convective heat flux from solid to fluid [W/m2]

Type	Name	Description
HeatFlux	q_flow	Convective heat flux from solid to fluid [W/m2]

Modelica definition

function constantCoefficient 
  "Constant convective heat transfer coefficient"
  extends Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux;
  input Modelica.SIunits.CoefficientOfHeatTransfer hCon = 3 
    "Constant for convective heat transfer coefficient";
algorithm 
  q_flow :=hCon*dT;
end constantCoefficient;

Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall

Free convection, wall

Information

This function computes the buoyancy-driven convective heat transfer coefficient for a wall as h=1.3*|dT|^0.3333, where dT is the solid temperature minus the fluid temperature. The convective convective heat flux is then q_flow = h * dT.

Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).

Inputs

Type Name Default Description

TemperatureDifference dT Temperature difference solid minus fluid [K]

Type	Name	Default	Description
TemperatureDifference	dT		Temperature difference solid minus fluid [K]

Outputs

Type Name Description

HeatFlux q_flow Convective heat flux from solid to fluid [W/m2]

Type	Name	Description
HeatFlux	q_flow	Convective heat flux from solid to fluid [W/m2]

Modelica definition

function wall "Free convection, wall"
  extends Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux;
algorithm 
  q_flow := noEvent(smooth(1, if (dT > 0) then 1.3*dT^1.3333 else -1.3*(-dT)^1.3333));

end wall;

Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor

Free convection, floor

Information

This function computes the buoyancy-driven convective heat transfer coefficient for a floor as h=k*|dT|^0.3333, where k=1.51 if the floor is warmer than the fluid, or k=0.76 otherwise, and where dT is the solid temperature minus the fluid temperature. The convective convective heat flux is then q_flow = h * dT.

Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).

Inputs

Type Name Default Description

TemperatureDifference dT Temperature difference solid minus fluid [K]

Type	Name	Default	Description
TemperatureDifference	dT		Temperature difference solid minus fluid [K]

Outputs

Type Name Description

HeatFlux q_flow Convective heat flux from solid to fluid [W/m2]

Type	Name	Description
HeatFlux	q_flow	Convective heat flux from solid to fluid [W/m2]

Modelica definition

function floor "Free convection, floor"
  extends Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux;

algorithm 
  q_flow  := noEvent(smooth(1, if (dT>0) then 1.51*dT^1.3333 else -0.76*(-dT)^1.3333));
end floor;

Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling

Free convection, ceiling

Information

This function computes the buoyancy-driven convective heat transfer coefficient for a ceiling as h=k*|dT|^0.3333, where k=1.51 if the fluid is warmer than the ceiling, or k=0.76 otherwise, and where dT is the solid temperature minus the fluid temperature. The convective convective heat flux is then q_flow = h * dT.

Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).

Inputs

Type Name Default Description

TemperatureDifference dT Temperature difference solid minus fluid [K]

Type	Name	Default	Description
TemperatureDifference	dT		Temperature difference solid minus fluid [K]

Outputs

Type Name Description

HeatFlux q_flow Convective heat flux from solid to fluid [W/m2]

Type	Name	Description
HeatFlux	q_flow	Convective heat flux from solid to fluid [W/m2]

Modelica definition

function ceiling "Free convection, ceiling"
  extends Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux;

algorithm 
   q_flow  := noEvent(smooth(1, if (dT>0) then 0.76*dT^1.3333 else -1.51*(-dT)^1.3333));
end ceiling;

Buildings.HeatTransfer.Convection.Functions.HeatFlux.raleigh

Raleigh number with smooth transition to lower limit

Information

This function returns the Raleigh number. The parameter RaMin is used to transition to a lower limit for the Raleigh number. This is helpful to avoid a Raleigh number of zero or to avoid an expression for a convection coefficient that has an infinite derivative near zero, i.e., if h=f(Ra^(1/2)).

Inputs

Type Name Default Description

Length x Layer thickness [m]

Density rho Mass density [kg/m3]

SpecificHeatCapacity c_p Specific heat capacity [J/(kg.K)]

DynamicViscosity mu Dynamic viscosity [Pa.s]

ThermalConductivity k Thermal conductivity [W/(m.K)]

Temperature T_a Temperature of surface a [K]

Temperature T_b Temperature of surface b [K]

Real Ra_min Minimum value for Raleigh number

Type	Name	Description
Length	x	Layer thickness [m]
Density	rho	Mass density [kg/m3]
SpecificHeatCapacity	c_p	Specific heat capacity [J/(kg.K)]
DynamicViscosity	mu	Dynamic viscosity [Pa.s]
ThermalConductivity	k	Thermal conductivity [W/(m.K)]
Temperature	T_a	Temperature of surface a [K]
Temperature	T_b	Temperature of surface b [K]
Real	Ra_min	Minimum value for Raleigh number

Outputs

Type Name Description

Real Ra Raleigh number

Type	Name	Description
Real	Ra	Raleigh number

Modelica definition

function raleigh 
  "Raleigh number with smooth transition to lower limit"
 input Modelica.SIunits.Length x "Layer thickness";
 input Modelica.SIunits.Density rho "Mass density";
 input Modelica.SIunits.SpecificHeatCapacity c_p "Specific heat capacity";
 input Modelica.SIunits.DynamicViscosity mu "Dynamic viscosity";
 input Modelica.SIunits.ThermalConductivity k "Thermal conductivity";
 input Modelica.SIunits.Temperature T_a "Temperature of surface a";
 input Modelica.SIunits.Temperature T_b "Temperature of surface b";
 input Real Ra_min "Minimum value for Raleigh number";
 output Real Ra "Raleigh number";
protected 
 Modelica.SIunits.TemperatureDifference dT "Temperature difference";
algorithm 
  dT :=abs(T_a - T_b);
  Ra := rho^2*x^3*Modelica.Constants.g_n*c_p*dT/((T_a+T_b)/2*mu*k);
  Ra := Buildings.Utilities.Math.Functions.smoothMax(x1=Ra, x2=Ra_min, deltaX=Ra_min/10);
end raleigh;

Automatically generated Fri Nov 4 08:28:36 2011.