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43 lines
7.5 KiB
TeX
43 lines
7.5 KiB
TeX
\documentclass[10pt,a4paper]{article}
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\usepackage[latin1]{inputenc}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{amssymb}
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\usepackage{graphicx}
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\usepackage[hmargin=0.5in, vmargin = 0.5in, paperwidth = 20in, paperheight = 20in]{geometry}
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\author{Ian Bell, Vincent Lemort, ULg}
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\begin{document}
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\centering
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\begin{tabular}{ccp{3in}p{8 in}}
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\hline\hline
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Fluid & Reference & $\eta^0$ & $\eta^r$ \\
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\hline
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Nitrogen, argon, oxygen air & (data) Lemmon and Jacobsen 2004 & $\eta^0 = \dfrac{0.0266958\sqrt{MT}}{\sigma^2\Omega(T^*)}$\newline$\Omega(T^*)=\exp\left(\sum_{i=0}^{4}b_i[\ln T^*]^i\right)$ & $\eta^r = \sum_{i=1}^NN_i\tau^{\tau_i}\delta^{d_i}\exp(-\gamma_i\delta^{l_i})$\\\hline
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Ammonia & (data) Fenghour 1995 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\Game(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = B_{BV}\rho\eta^0(T) + \Delta\eta$\newline$\Delta\eta = \sum_i b_i(T)\rho^i$\\\hline
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Carbon Dioxide & (data) Vesovic 1990 & $\eta^0 = \dfrac{1.00697\sqrt{T}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \Delta\eta$\newline$\Delta\eta_g = \sum_ie_i\rho^i$ \newline$\Delta\eta = \frac{\Delta\eta_g}{1+\exp[-Z(T-T_s)]}+\frac{\Delta\eta_g}{\lbrace 1+\exp[Z(T-T_s)][1+\exp[Z(\rho-\rho_s)]\rbrace}+\frac{\eta_l-\eta^0}{\lbrace 1+\exp[Z(T-T_s)]\rbrace\lbrace 1+\exp[-Z(\rho-\rho_s)]\rbrace}$ \newline $B = 18.56+0.014T$ \newline $\frac{1}{\eta_l-\Delta\eta_c} = B(T)[\frac{1}{\rho}-V_0(T)] \newline $V_0(T) = 7.41e-4-3.3e-7T$ \\\hline
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Dimethyl Ether & Meng 2012 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & \eta^r = \Delta\eta$\newline$\Delta\eta = \sum_{i=0}^{1}n_i\tau^{t_i}\delta^{d_i} + \sum_{i=2}^{6}n_i\tau^{t_i}\delta^{d_i}\exp(-\delta^{p_i})$\\\hline
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Ethane & Friend 1991 & $\eta^0 = \dfrac{12.0085\sqrt{t}}{\Omega^{(2,2)*}(t)}$ \newline $\Omega^{(2,2)*}(t) = \left[\sum_i C_it^{(i-1)/3-1} \right]^{-1}& $\Delta\eta = 15.977\left[\displaystyle\sum_i g_i\delta^{r_i}\tau^{s_i}\right]\left[1+\displaystyle\sum_{i=10}^{11}g_i\delta^{r_i}\tau^{s_i}\right]^{-1}$\\\hline
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Ethanol & Kiselev 2005 & $\eta^0 = \sum_i a_i T^{n_i}& \eta^r = B_{RF}\rho\eta^0(T)+\Delta \eta$ \newline $\Delta\eta = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_2+g_3\sqrt{\tau}$\\\hline
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Helium & Arp 1998 & NASTY & NASTY \\\hline
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Hydrogen & Muzny 2013 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2S^*(T^*)}$\newline$S^*(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = B_{RF}\rho\eta^0(T) + \Delta\eta$\newline$\Delta\eta = c_1\rho_r^2\left[c_2T_r+c_3/T_r+\frac{c_4\rho_r^2}{c_5+T_r}+c_6\rho_r^6\right]$\\\hline
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SF6 & Quinones-Cisneros 2012 & $\eta^0 = \sum_i d_i T_r^{n_i}$ & FRICTION THEORY\\\hline
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H2S & Quinones-Cisneros 2012 & $\eta^0 = 8.7721\dfrac{\sqrt{T}}{S^*(T^*)}$ \newline $S^*(T^*) = \sum_i \frac{\alpha_i}{T^{*i}}$ & FRICTION THEORY\\\hline
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Propane & (data) Vogel 1998 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta_h = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_1(1+g_2\tau^{1/2})$\\\hline
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n-Butane & Vogel 1999 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta_h = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_1(1+\displaystyle\sum_{l=2}g_l\tau^{(l-1)/2})$ \\\hline
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Isobutane & Vogel 2000 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta_h = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_1(1+\displaystyle\sum_{l=2}g_l\tau^{(l-1)/2})$ \\\hline
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R123 & (data) Tanaka 1996 & $\eta^0 = \displaystyle\sum_{i}a_iT_i$ & $\eta^r = \eta^1\rho+\Delta\eta$ \newline $\eta^1 = b_0+b_1T$\newline$\Delta\eta = \frac{a_0}{\rho-\rho_0}+\frac{a_0}{\rho_0}+a_1\rho+a_2\rho^2+a_3\rho^3$\\\hline
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R134a & Huber 2003 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = c_1\delta+\left(\frac{c_2}{\tau^6}+\frac{c_3}{\tau^2}+\frac{c_4}{\sqrt{\tau}}+c_5\tau^2\right)\delta^2+c_6\delta^3+c_7\left(\frac{1}{\delta_0-\delta}-\frac{1}{\delta_0}\right)$ \newline $\delta_0(\tau)=\frac{c_{10}}{1+c_8\tau+c_9\tau^2}$\\\hline
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n-Dodecane & (data) Huber 2004 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+c_1\left(\frac{\delta}{\delta_0-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=c_2 +c_3\sqrt{\tau}$\\\hline
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Octane, nonane, decane & (data) Huber 2004 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+c_1\left(\frac{\delta}{\delta_0-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=c_2 +c_3\sqrt{\tau}$\\\hline
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R125 & (data) Huber 2006 & $\eta^0 = \dfrac{5}{16}\sqrt{\dfrac{MkT}{\pi N}}\dfrac{1}{\sigma^2\Omega^*(T^*)}$\newline $\Omega(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+c_1\left(\frac{\delta}{\delta_0-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=c_2 +c_3\sqrt{\tau}$\\\hline
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Water & Huber 2009 & & \\\hline
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R152A & (data) Krauss 1996 & $\eta^0 = \dfrac{5}{16}\sqrt{\dfrac{MkT}{1000\pi N}}\dfrac{10^{24}}{\sigma^2\Omega^*(T^*)}=\dfrac{0.2169614\sqrt{T}}{\sigma^2\Omega(T^*)}$\newline $\Omega(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\dfrac{\Delta\eta}{H_c} = \displaystyle\sum_{i=1}^{4}E_i\left(\frac{\rho}{\rho_c}\right)^i + \frac{E_5}{\rho/\rho_c-E_6}+\frac{E_5}{E_6}$\\\hline
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R23 & Shan 2000 & $\eta^0 = \frac{5}{16}\sqrt{\frac{MkT}{1000\pi N}}\frac{10^{24}}{\sigma^2\Omega^*(T^*)}$\newline $\Omega(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & \\\hline
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R404A, R410A, R507, R407 & Geller 2000 & $\eta^0 = \sum_i A_iT^i$&$\eta^r = \sum_j b_j\rho^j$ \\\hline
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n-Hexane & (data) Michailidou 2013 &$\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2S(T^*)}$\newline$S(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$& $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = (\rho_r^{2/3}T_r^{1/2})\left\lbrace\dfrac{c_0}{T_r}+\dfrac{c_1}{c_2+T_r+c_3\rho_r^2}+\dfrac{c_4(1+\rho_r)}{c_5 + c_6T_r+c_7\rho_r+\rho_r^2+c_8\rho_rT_r} \right\rbrace$ \\\hline
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\hline\hline
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\end{tabular}
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For a description of the conversion between $\mathfrak{S}$ and $\Omega$, see Vesovic 1990 ($CO_2$). Basically $\Omega = (5/4)\mathfrak{S}$.
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\end{document} |