Correlation equations#

Group 1#

Florschuetz and Chao (1965) [1, 2]#

(1)#\[ \Nu_c = (4/\pi) \Ja \frac{\beta}{1-\beta} \]
(2)#\[ \beta = 1 - 4 \Ja \sqrt{\Fo_\o / \pi} \]

Group 3#

Isenberg and Sideman (1970) [2, 4]#

(3)#\[ \Nu_c = \left(1/\sqrt{\pi}\right) \Re_b^{1/2} \Pr^{1/3} \]
(4)#\[ \beta = \left( 1 - \left( 3/\sqrt{\pi} \right) \Re_\bo^{1/2} \Pr^{1/3} \Ja \Fo_\o \right) ^ {2/3}\]

Akiyama (1973) [2, 5]#

(5)#\[ \Nu_c = 0.37 \Re_b^{0.6} Pr^{1/3} \]
(6)#\[ \beta = \left( 1 - 1.036 \Re_\bo^{1/2} \Pr^{1/3} \Ja \Fo_\o \right) ^ {0.714} \]

Chen and Mayinger (1992) [2, 6]#

(7)#\[ \Nu_c = 0.185 \Re_\bo^{0.7} \Pr^{0.5} \]
(8)#\[ \beta = \left( 1 - 0.56 \Re_\bo^{0.7} \Pr^{0.5} \Ja \Fo_\o \right) ^ {0.9} \]
(9)#\[ 0 < \Re_b < 10\,000 ,\ 0 < \Ja < 80 ,\ 2 < \Pr < 15 \]

Kalman and Mori (2002) [2, 7]#

(10)#\[ \Nu_c = 0.0041 \Re_b^{0.855} \Pr^{0.855} \]
(11)#\[ \beta = \left( 1 - 0.0094 \Re_\bo^{0.855} \Pr^{0.855} \Ja \Fo_\o \right) ^ {0.873}\]
(12)#\[ 0.05 < \Re_b < 2\,000 ,\ 10 < \Pe < 20\,000 ,\ 3 < \Pr < 7.5 \]

Lucic and Mayinger (2010) [2, 8]#

(13)#\[ \Nu_c = 1.46 \Re_\bo^{0.61} \Ja^{-0.31} \Pr^{0.33} \]
(14)#\[ \beta = 1 - 2.92 \Re_\bo^{0.61} \Pr^{0.33} \Ja^{0.69} \Fo_\o \]
(15)#\[ 1\,000 < \Re_b < 3\,400 ,\ 10 < \Ja < 30 \]

Kim and Park (2011) [2, 9]#

(16)#\[ \Nu_c = 0.2575 \Re_b^{0.7} \Ja^{-0.2043} \Pr^{-0.4564} \]
(17)#\[ \beta = \left( 1 - 0.67 \Re_\bo^{0.7} \Pr^{-0.4564} \Ja^{0.7959} \Fo_\o \right) ^ {0.769}\]
(18)#\[ 1\,000 < \Re_b < 6\,000 ,\ 18 < \Ja < 36 ,\ 1.87 < \Pr < 2.03 \]

Al Issa et al. (2014) [2, 10]#

(19)#\[ \Nu_c = 0.0609 \Re_b^{0.89} \Pr^{0.33} \]
(20)#\[ \beta = \left( 1 - 0.135 \Re_\bo^{0.89} \Pr^{0.33} \Ja \Fo_\o \right) ^ {0.901} \]
(21)#\[ 2\,100 < \Re_b < 270\,000 ,\ 16 < \Ja < 35 ,\ 1.75 < \Pr < 1.9 \]

Tang et al. (2016) [2, 11]#

(22)#\[ \Nu_c = 4.34 \Re_b^{0.584} \Ja^{-0.419} \Pr^{0.333} \]
(23)#\[ \beta = \left(1 - 12.29 \Re_\bo^{0.584} \Pr^{0.333} \Ja^{0.581} \Fo_\o \right) ^ {0.706}\]
(24)#\[ 1\,000 < \Re_b < 30\,000 ,\ 45 < \Ja < 180 ,\ 2.1 < \Pr < 4.3 \]

Group 4#

Warrier et al. (2002) [2, 12]#

(25)#\[ \Nu_c = 0.6 \Re_b^{1/2} \Pr^{1/3} \left(1 - 1.2 \Ja^{9/10} \Fo_\o^{2/3} \right) \]
(26)#\[ \beta = \left( 1 - 1.8 \Re_\bo^{0.5} \Pr^{1/3} \Ja \Fo_\o \left( 1 - 0.72 \Ja^{0.9} \Fo_\o^{2/3} \right) \right) ^ {2/3}\]
(27)#\[ 20 < \Re_b < 700 ,\ 12 < \Ja < 100 ,\ 1.8 < \Pr < 2.9 \]

Yuan et al. (2009) [2, 3]#

(28)#\[ \Nu_c = 0.6 \Re_b^{1/2} \Pr^{1/3} (1 - \Ja^{0.1} \Fo_\o ) \]
(29)#\[ \beta = \left( 1 - 1.8 \Re_\bo^{0.5} \Pr^{1/3} \Ja \Fo_\o \left(1 - 0.5 \Ja^{0.1} \Fo_\o\right) \right) ^ {2/3}\]
(30)#\[ 335 < \Re_b < 1\,770 ,\ 0 < \Ja < 60 ,\ 1.71 < \Pr < 1.75 \]

Group 5#

Zeitoun et al. (1995) [2, 13]#

(31)#\[ \Nu_c = 2.04 \Re_b^{0.61} \alpha^{0.328} \Ja^{-0.308} \]
(32)#\[ \beta = \left( 1 - 5.67 \Re_\bo^{0.61} \alpha^{0.328} \Ja^{0.692} \Fo_\o \right) ^ {0.72}\]
(33)#\[ 2\,266 < \Re_b < 7\,953 \]