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_Capillary and disPip/dPipOut ≥ 5.8), and
capillary tube systems (if sysTyp == Buildings.Fluid.HeatExchangers.RadiantSlabs.Types.SystemType.Ceiling_Wall_or_Capillary and disPip/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	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	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;