Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Functions
Functions for convective heat transfer
Information
This package contains functions that are used to construct the models in Buildings.Fluid.HeatExchangers.RadiantSlabs.
Package Content
| Name | Description |
|---|---|
 AverageResistance
|
Average fictitious resistance for plane that contains the pipes |
 heatFlowRate
|
Heat flow rate for epsilon-NTU model |
Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Functions.AverageResistance
Average fictitious resistance for plane that contains the pipes
Information
This function computes a fictitious thermal resistance between the pipe outer wall and a fictitious, average temperature of the plane that contains the pipes. The equation is the same as is implemented in TRNSYS 17. Different equations are used for
-
floor heating systems (if
sysTyp == Buildings.Fluid.HeatExchangers.RadiantSlabs.Types.SystemType.Floor), -
radiant heating or cooling systems in ceilings and walls (if
sysTyp == Buildings.Fluid.HeatExchangers.RadiantSlabs.Types.SystemType.Ceiling_Wall_or_CapillaryanddisPip/dPipOut ≥ 5.8), and -
capillary tube systems (if
sysTyp == Buildings.Fluid.HeatExchangers.RadiantSlabs.Types.SystemType.Ceiling_Wall_or_CapillaryanddisPip/dPipOut < 5.8).
Limitations
The resistance Rx is based on a steady-state heat transfer analysis. Therefore, it is
only valid during steady-state.
For a fully dynamic model, a finite element method for the radiant slab would need to be implemented.
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| Distance | disPip | pipe distance [m] | |
| Diameter | dPipOut | pipe outside diameter [m] | |
| ThermalConductivity | k | pipe level construction element thermal conductivity [W/(m.K)] | |
| SystemType | sysTyp | Type of radiant system | |
| ThermalConductivity | kIns | floor slab insulation thermal conductivity [W/(m.K)] | |
| Thickness | dIns | floor slab insulation thickness [m] |
Outputs
| Type | Name | Description |
|---|---|---|
| ThermalInsulance | Rx | Thermal insulance [m2.K/W] |
Modelica definition
function AverageResistance
"Average fictitious resistance for plane that contains the pipes"
input Modelica.SIunits.Distance disPip "pipe distance";
input Modelica.SIunits.Diameter dPipOut "pipe outside diameter";
input Modelica.SIunits.ThermalConductivity k
"pipe level construction element thermal conductivity";
input Buildings.Fluid.HeatExchangers.RadiantSlabs.Types.SystemType
sysTyp "Type of radiant system";
input Modelica.SIunits.ThermalConductivity kIns
"floor slab insulation thermal conductivity";
input Modelica.SIunits.Thickness dIns "floor slab insulation thickness";
output Modelica.SIunits.ThermalInsulance Rx "Thermal insulance";
protected
Real cri(unit="1")
"Criteria used to select formula for computation of resistance";
Real infSum
"Approximation to infinite sum used to compute the thermal resistance";
Real alpha(unit="W/(m2.K)", min=0)
"Criteria used to select formula for computation of resistance";
Real fac "Factor used for systems in wall or ceiling, or for capillary tubes";
algorithm
if sysTyp == Buildings.Fluid.HeatExchangers.RadiantSlabs.Types.SystemType.Floor then
alpha := kIns/dIns;
if alpha >= 1.212 then
Modelica.Utilities.Streams.print("Warning: In RadiantAverageResistance, require alpha = kIns/dIns >= 1.212 W/(m2.K).\n" +
" Obtained alpha = " + String(alpha) + " W/(m2.K)\n" +
" kIns = " + String(kIns) + " W/(m.K)\n" +
" dIns = " + String(dIns) + " m\n" +
" For these values, the radiant slab model is outside its valid range.\n");
end if;
infSum := - sum(((alpha/k*disPip - 2*Modelica.Constants.pi*s)/
(alpha/k*disPip + 2*Modelica.Constants.pi*s))
*Modelica.Math.exp(-4*Modelica.Constants.pi*s*dIns/disPip)/s for s in 1:100);
Rx := disPip*(Modelica.Math.log(disPip/Modelica.Constants.pi/dPipOut) + infSum)
/(2*Modelica.Constants.pi*k);
fac := 0; // not needed.
elseif sysTyp == Buildings.Fluid.HeatExchangers.RadiantSlabs.Types.SystemType.Ceiling_Wall_or_Capillary then
// Branch for radiant ceilings, radiant walls, and systems with capillary heat exchangers
cri := disPip/dPipOut;
fac := if (cri >= 5.8) then Modelica.Math.log(cri/Modelica.Constants.pi) else (cri/Modelica.Constants.pi/3);
Rx := disPip/2/Modelica.Constants.pi/k * fac;
else
assert(sysTyp == Buildings.Fluid.HeatExchangers.RadiantSlabs.Types.SystemType.Floor or
sysTyp == Buildings.Fluid.HeatExchangers.RadiantSlabs.Types.SystemType.Ceiling_Wall_or_Capillary,
"Invalid value for sysTyp in \"Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Functions.AverageResistance\"
Check parameters of the radiant slab model.");
cri := 0;
fac := 0;
Rx := 1;
end if;
end AverageResistance;
Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Functions.heatFlowRate
Heat flow rate for epsilon-NTU model
Information
This function computes the heat flow rate for the radiant slab.
Extends from Modelica.Icons.Function (Icon for functions).
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| Temperature | T_a | Temperature at port_a [K] | |
| Temperature | T_b | Temperature at port_b [K] | |
| Temperature | T_s | Temperature of solid [K] | |
| Temperature | T_f | Temperature of fluid control volume [K] | |
| SpecificHeatCapacity | c_p | Specific heat capacity [J/(kg.K)] | |
| ThermalConductance | UA | UA value [W/K] | |
| MassFlowRate | m_flow | Mass flow rate from port_a to port_b [kg/s] | |
| MassFlowRate | m_flow_nominal | Nominal mass flow rate from port_a to port_b [kg/s] |
Outputs
| Type | Name | Description |
|---|---|---|
| HeatFlowRate | Q_flow | Heat flow rate [W] |
Modelica definition
function heatFlowRate "Heat flow rate for epsilon-NTU model"
extends Modelica.Icons.Function;
input Modelica.SIunits.Temperature T_a "Temperature at port_a";
input Modelica.SIunits.Temperature T_b "Temperature at port_b";
input Modelica.SIunits.Temperature T_s "Temperature of solid";
input Modelica.SIunits.Temperature T_f "Temperature of fluid control volume";
input Modelica.SIunits.SpecificHeatCapacity c_p "Specific heat capacity";
input Modelica.SIunits.ThermalConductance UA "UA value";
input Modelica.SIunits.MassFlowRate m_flow
"Mass flow rate from port_a to port_b";
input Modelica.SIunits.MassFlowRate m_flow_nominal
"Nominal mass flow rate from port_a to port_b";
output Modelica.SIunits.HeatFlowRate Q_flow "Heat flow rate";
protected
Modelica.SIunits.MassFlowRate m_abs_flow "Absolute value of mass flow rate";
Modelica.SIunits.Temperature T_in "Inlet fluid temperature";
Real eps "Heat transfer effectiveness";
algorithm
m_abs_flow :=noEvent(abs(m_flow));
T_in :=smooth(1, noEvent(if m_flow >= 0 then T_a else T_b));
if m_abs_flow > 0.15*m_flow_nominal then
// High flow rate. Use epsilon-NTU formula.
eps := 1-Modelica.Math.exp(-UA/m_abs_flow/c_p);
Q_flow :=eps*(T_s-T_in)*m_abs_flow*c_p;
elseif (m_abs_flow < 0.05*m_flow_nominal) then
// Low flow rate. Use heat conduction to temperature of the control volume.
Q_flow :=UA*(T_s-T_f);
else
// Transition. Use a once continuously differentiable transition between the
// above regimes.
eps := 1-Modelica.Math.exp(-UA/m_abs_flow/c_p);
Q_flow := Buildings.Utilities.Math.Functions.spliceFunction(
pos=eps*(T_s-T_in)*m_abs_flow*c_p,
neg=UA*(T_s-T_f),
x=m_abs_flow/m_flow_nominal-0.1,
deltax=0.05);
end if;
end heatFlowRate;