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)#\[
2\,266 < \Re_b < 7\,953
\]