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 |
| rayleigh
| Rayleigh number with smooth transition to lower limit |
 BaseClasses
| Base classes for convective heat transfer coefficients |
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 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
Outputs
| 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;
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 heat flux is then
q_flow = h * dT.
Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).
Inputs
Outputs
| 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;
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 heat flux is then
q_flow = h * dT.
Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).
Inputs
Outputs
| 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;
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 heat flux is then
q_flow = h * dT.
Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).
Inputs
Outputs
| 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;
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)).
Inputs
Outputs
| Type | Name | Description |
|---|
| Real | Ra | Rayleigh number |
Modelica definition
function rayleigh
"Rayleigh 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 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;
Automatically generated Thu Oct 24 15:10:21 2013.
