LBL logo

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, because the convective heat transfer coefficient is not differentiable around zero for some 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
Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling ceiling Free convection, ceiling
Buildings.HeatTransfer.Convection.Functions.HeatFlux.constantCoefficient constantCoefficient Constant convective heat transfer coefficient
Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor floor Free convection, floor
Buildings.HeatTransfer.Convection.Functions.HeatFlux.rayleigh rayleigh Rayleigh number with smooth transition to lower limit
Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall wall Free convection, wall
Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses BaseClasses Base classes for convective heat transfer coefficients

Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling

Free convection, ceiling

Information

This function computes the buoyancy-driven convective heat flux as

q̇ = h ΔT,

where ΔT is the solid temperature minus the fluid temperature and h is the convective heat transfer coefficient for a ceiling, computed as

h=k |ΔT|0.3333,

where k=1.51 if the fluid is warmer than the ceiling, or k=0.76 otherwise.

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

Inputs

TypeNameDefaultDescription
TemperatureDifferencedT Temperature difference solid minus fluid [K]

Outputs

TypeNameDescription
HeatFluxq_flowConvective 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.constantCoefficient Buildings.HeatTransfer.Convection.Functions.HeatFlux.constantCoefficient

Constant convective heat transfer coefficient

Information

This function computes the buoyancy-driven convective heat flux as

q̇ = h ΔT,

where ΔT is the solid temperature minus the fluid temperature and h is the convective heat transfer coefficient.

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

Inputs

TypeNameDefaultDescription
TemperatureDifferencedT Temperature difference solid minus fluid [K]
CoefficientOfHeatTransferhCon3Constant for convective heat transfer coefficient [W/(m2.K)]

Outputs

TypeNameDescription
HeatFluxq_flowConvective 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.floor Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor

Free convection, floor

Information

This function computes the buoyancy-driven convective heat flux as

q̇ = h ΔT,

where ΔT is the solid temperature minus the fluid temperature and h is the convective heat transfer coefficient for a floor, computed as

h=k |ΔT|0.3333,

where k=0.76 if the fluid is warmer than the floor, or k=1.51 otherwise.

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

Inputs

TypeNameDefaultDescription
TemperatureDifferencedT Temperature difference solid minus fluid [K]

Outputs

TypeNameDescription
HeatFluxq_flowConvective 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.rayleigh Buildings.HeatTransfer.Convection.Functions.HeatFlux.rayleigh

Rayleigh number with smooth transition to lower limit

Information

This function returns the Rayleigh number. The parameter RaMin is used to transition to a lower limit for the Rayleigh number. This is helpful to avoid a Rayleigh 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)).

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

TypeNameDefaultDescription
Lengthx Layer thickness [m]
Densityrho Mass density [kg/m3]
SpecificHeatCapacityc_p Specific heat capacity [J/(kg.K)]
DynamicViscositymu Dynamic viscosity [Pa.s]
ThermalConductivityk Thermal conductivity [W/(m.K)]
TemperatureT_a Temperature of surface a [K]
TemperatureT_b Temperature of surface b [K]
RealRa_min Minimum value for Rayleigh number

Outputs

TypeNameDescription
RealRaRayleigh number

Modelica definition

function rayleigh "Rayleigh number with smooth transition to lower limit" extends Modelica.Icons.Function; 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 Rayleigh number"; output Real Ra "Rayleigh 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 rayleigh;

Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall

Free convection, wall

Information

This function computes the buoyancy-driven convective heat flux as

q̇ = h ΔT,

where ΔT is the solid temperature minus the fluid temperature and h is the convective heat transfer coefficient for a wall, computed as

h=1.3 |ΔT|0.3333.

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

Inputs

TypeNameDefaultDescription
TemperatureDifferencedT Temperature difference solid minus fluid [K]

Outputs

TypeNameDescription
HeatFluxq_flowConvective 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;

Automatically generated Mon May 4 10:22:55 2015.