From e73380e802c3b742765dc702790239adf55d9182 Mon Sep 17 00:00:00 2001
From: Casper <c.jansen@ascee.nl>
Date: Tue, 25 May 2021 10:58:02 +0200
Subject: [PATCH] Added eq:kappa and renamed indices of eq:Phi(_mn)

---
 lrftubes.lyx | 108 ++++++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 94 insertions(+), 14 deletions(-)

diff --git a/lrftubes.lyx b/lrftubes.lyx
index 7397351..f1bf2ab 100644
--- a/lrftubes.lyx
+++ b/lrftubes.lyx
@@ -2343,8 +2343,8 @@ Dynamic viscosity of a gas mixture
 \end_layout
 
 \begin_layout Standard
-The dynamic viscosity of a gas mixture can be derived from the dynamic viscosity
- of pure gases as 
+The dynamic viscosity of a gas mixture can be derived from the dynamic viscositi
+es of pure gases as 
 \begin_inset CommandInset citation
 LatexCommand cite
 after "p. 27"
@@ -2356,42 +2356,42 @@ literal "false"
 :
 \begin_inset Formula 
 \begin{equation}
-\mu_{\mathrm{mix}}=\sum_{n=0}^{N-1}\frac{x_{n}\mu_{n}}{\sum_{m=0}^{N-1}\Phi_{nm}x_{m}},\label{eq:mumix}
+\mu_{\mathrm{mix}}=\sum_{α=0}^{N-1}\frac{x_{α}\mu_{α}}{\sum_{β=0}^{N-1}\Phi_{αβ}x_{β}},\label{eq:mumix}
 \end{equation}
 
 \end_inset
 
 where 
-\begin_inset Formula $\mu_{n}$
+\begin_inset Formula $\mu_{α}$
 \end_inset
 
-denotes the pure substance dynamic viscosity of species 
-\begin_inset Formula $n$
+ is the dynamic viscosity of pure chemical species 
+\begin_inset Formula $α$
 \end_inset
 
-, and 
-\begin_inset Formula $x_{n}$
+ and 
+\begin_inset Formula $x_{α}$
 \end_inset
 
 denotes its mole fraction in the mixture.
  
-\begin_inset Formula $\Phi_{mn}$
+\begin_inset Formula $\Phi_{αβ}$
 \end_inset
 
  is defined as:
 \begin_inset Formula 
 \begin{equation}
-\Phi_{mn}=\frac{1}{\sqrt{8}}\left(1+\frac{M_{n}}{M_{m}}\right)^{-1/2}\left[1+\left(\frac{\mu_{n}}{\mu_{m}}\right)^{1/2}\left(\frac{M_{m}}{M_{n}}\right)^{1/4}\right]^{2},
+\Phi_{αβ}=\frac{1}{\sqrt{8}}\left(1+\frac{M_{α}}{M_{β}}\right)^{-1/2}\left[1+\left(\frac{\mu_{α}}{\mu_{β}}\right)^{1/2}\left(\frac{M_{β}}{M_{α}}\right)^{1/4}\right]^{2},\label{eq:Phi_mn}
 \end{equation}
 
 \end_inset
 
 where 
-\begin_inset Formula $M_{i}$
+\begin_inset Formula $M_{α}$
 \end_inset
 
  is the molar mass of species 
-\begin_inset Formula $i$
+\begin_inset Formula $α$
 \end_inset
 
 .
@@ -2407,7 +2407,7 @@ reference "eq:mumix"
 \end_inset
 
  can efficiently be solved by noting that 
-\begin_inset Formula $d_{n}=\sum_{m=0}^{N-1}\Phi_{nm}x_{m}$
+\begin_inset Formula $d_{α}=\sum_{β=0}^{N-1}\Phi_{αβ}x_{β}$
 \end_inset
 
  is a matrix-vector product, which can be written as 
@@ -2417,6 +2417,65 @@ reference "eq:mumix"
 .
 \end_layout
 
+\begin_layout Subsubsection
+Thermal conductivity of a gas mixture
+\end_layout
+
+\begin_layout Standard
+The thermal conductivity of a gas mixture can be derived from the thermal
+ conductivities of pure gases as 
+\begin_inset CommandInset citation
+LatexCommand cite
+after "p. 276"
+key "bird_transport_2007"
+literal "false"
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\begin{equation}
+k_{mix}=\sum_{α=0}^{N-1}\frac{x_{α}k_{α}}{\sum_{β=0}^{N-1}\Phi_{αβ}x_{β}}\label{eq:kappamix}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+where 
+\begin_inset Formula $k_{α}$
+\end_inset
+
+ is the thermal conductivity of pure chemical species 
+\begin_inset Formula $α$
+\end_inset
+
+ and 
+\begin_inset Formula $x_{α}$
+\end_inset
+
+denotes its mole fraction in the mixture and 
+\begin_inset Formula $\Phi_{αβ}$
+\end_inset
+
+is identical to that appearing in the viscosity equation, see 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:Phi_mn"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+.
+\end_layout
+
 \begin_layout Subsection
 Combustion
 \end_layout
@@ -7015,6 +7074,27 @@ Membrane
 A membrane is a mechanical 
 \end_layout
 
+\begin_layout Section
+Hole
+\end_layout
+
+\begin_layout Standard
+series_impedance.py/class CircHoleNeck(SeriesImpedance)
+\end_layout
+
+\begin_layout Standard
+Behaves like an acoustic mass with losses.
+ It represents holes in sheet material, which can form the neck of a Helmholtz
+ resonator.
+ Hole-hole interaction is neglected.
+ The resistance term is an approximation.
+\end_layout
+
+\begin_layout Standard
+Usable for connecting volumes to eachother or volumes to ducts, to form
+ Helmholtz resonators.
+\end_layout
+
 \begin_layout Section
 End corrections and discontinuities
 \begin_inset CommandInset label
@@ -9606,7 +9686,7 @@ n
 \end_layout
 
 \begin_layout Standard
-The coarse 0impedance of a Helmholtz resonator repeated here:
+The coarse impedance of a Helmholtz resonator repeated here:
 \begin_inset Formula 
 \begin{equation}
 Z(\omega)=\underbrace{i\omega m_{A}+R_{v}}_{Z_{h}}+\frac{\rho_{0}c_{0}^{2}}{i\omega V},