Line Set


A line set is essentially just a set of tubes of a reasonably long length that allows for fluid to be moved from one place to another. It is commonly insulated in order to decrease heat transfer between the tube and ambient.

Mathematical Description

(Source code, png, hires.png, pdf)


An energy balance over the control volume in the tube gives

(1)\dot m_r c_{p,r}dT=UdA(T_{\infty}-T)

where if T_{\infty} is greater than T, the differential dT is positive. Therefore separation of variables yields

(2)\frac{dT}{T_{\infty}-T}=\frac{UdA}{\dot m_r c_{p,r}}

and upon integration (with a u-substitution)

(3)-\left. \ln (T_{\infty}-T)\right|_{T_i}^{T_o}=\frac{UA}{\dot m_r c_{p,r}}

finally yields

(4)\frac{T_o-T_{\infty}}{T_i-T_{\infty}}=\exp\left(-\frac{UA}{\dot m_r c_{p,r}}\right)

and the outlet temperature from

(5)T_o=T_{\infty}+(T_i-T_{\infty})\exp\left(-\frac{UA}{\dot m_r c_{p,r}}\right)

(Source code, png, hires.png, pdf)


Based on the concentric geometry, the heat transfer network terms are given by

(6)R_{tube}=\frac{\ln(D_o/D_i)}{2\pi L k_{tube}}

(7)R_{insul}=\frac{\ln[(D_o+2t_{insul})/D_o]}{2\pi L k_{insul}}

(8)\mathrm{UA}_i=h_i\pi D_i L

\mathrm{UA}_o=h_o\pi (D_o+2t_{insul}) L

and the overall heat conductance is given by


The pressure drop and refrigerant charge are evaluated from section Single-phase refrigerant pressure drop, heat transfer and charge.


Variable Description
c_{p,r} Refrigerant specific heat [J/kg/K]
D_i Inner diameter of tube [m]
D_o Outer diameter of tube [m]
k_{insul} Thermal conductivity of insulation [W/m/K]
L Length of tube [m]
\dot m_r Refrigerant mass flow rate [kg/s]
R_{tube} Thermal resistance from tube [K/W]
R_{insul} Thermal resistance from insulation [K/W]
t_{insul} Thickness of insulation [m]
T_i Inlet temperature [K]
T_o Outlet temperature [K]
T_{\infty} Ambient temperature [K]
\mathrm{UA} Overall heat transfer conductance [W/K]
\mathrm{UA_i} Inner heat transfer conductance [W/K]
\mathrm{UA_o} Outer heat transfer conductance [W/K]
\alpha_i Inner heat transfer coefficient [W/m2/K]
\alpha_o Outer heat transfer coefficient [W/m2/K]

Component Class Documentation

class LineSet.LineSetClass(**kwargs)[source]

Return a list of parameters for this component for further output

It is a list of tuples, and each tuple is formed of items:
[0] Description of value [1] Units of value [2] The value itself

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