Correlation equations#

Group 1#

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

(1)#$${\mathit{Nu}}_c=(4/\pi )\mathit{Ja}\frac{\beta }{1-\beta }$$

(2)#$$\beta =1-4\mathit{Ja}\sqrt{{\mathit{Fo}}_{\mathit{0}}/\pi }$$

Group 3#

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

(3)#$${\mathit{Nu}}_c=\left(1/\sqrt{\pi }\right){\mathit{Re}}_b^{1/2}{\mathit{Pr}}^{1/3}$$

(4)#$$\beta ={(1-\left(3/\sqrt{\pi }\right){\mathit{Re}}_{\mathit{b}\mathit{0}}^{1/2}{\mathit{Pr}}^{1/3}\mathit{Ja}{\mathit{Fo}}_{\mathit{0}})}^{2/3}$$

Akiyama (1973) [2, 5]#

(5)#$${\mathit{Nu}}_c=0.37{\mathit{Re}}_b^{0.6}P{r}^{1/3}$$

(6)#$$\beta ={(1-1.036{\mathit{Re}}_{\mathit{b}\mathit{0}}^{1/2}{\mathit{Pr}}^{1/3}\mathit{Ja}{\mathit{Fo}}_{\mathit{0}})}^{0.714}$$

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

(7)#$${\mathit{Nu}}_c=0.185{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.7}{\mathit{Pr}}^{0.5}$$

(8)#$$\beta ={(1-0.56{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.7}{\mathit{Pr}}^{0.5}\mathit{Ja}{\mathit{Fo}}_{\mathit{0}})}^{0.9}$$

(9)#$$0<{\mathit{Re}}_b<10000,0<\mathit{Ja}<80,2<\mathit{Pr}<15$$

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

(10)#$${\mathit{Nu}}_c=0.0041{\mathit{Re}}_b^{0.855}{\mathit{Pr}}^{0.855}$$

(11)#$$\beta ={(1-0.0094{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.855}{\mathit{Pr}}^{0.855}\mathit{Ja}{\mathit{Fo}}_{\mathit{0}})}^{0.873}$$

(12)#$$0.05<{\mathit{Re}}_b<2000,10<\mathit{Pe}<20000,3<\mathit{Pr}<7.5$$

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

(13)#$${\mathit{Nu}}_c=1.46{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.61}{\mathit{Ja}}^{-0.31}{\mathit{Pr}}^{0.33}$$

(14)#$$\beta =1-2.92{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.61}{\mathit{Pr}}^{0.33}{\mathit{Ja}}^{0.69}{\mathit{Fo}}_{\mathit{0}}$$

(15)#$$1000<{\mathit{Re}}_b<3400,10<\mathit{Ja}<30$$

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

(16)#$${\mathit{Nu}}_c=0.2575{\mathit{Re}}_b^{0.7}{\mathit{Ja}}^{-0.2043}{\mathit{Pr}}^{-0.4564}$$

(17)#$$\beta ={(1-0.67{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.7}{\mathit{Pr}}^{-0.4564}{\mathit{Ja}}^{0.7959}{\mathit{Fo}}_{\mathit{0}})}^{0.769}$$

(18)#$$1000<{\mathit{Re}}_b<6000,18<\mathit{Ja}<36,1.87<\mathit{Pr}<2.03$$

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

(19)#$${\mathit{Nu}}_c=0.0609{\mathit{Re}}_b^{0.89}{\mathit{Pr}}^{0.33}$$

(20)#$$\beta ={(1-0.135{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.89}{\mathit{Pr}}^{0.33}\mathit{Ja}{\mathit{Fo}}_{\mathit{0}})}^{0.901}$$

(21)#$$2100<{\mathit{Re}}_b<270000,16<\mathit{Ja}<35,1.75<\mathit{Pr}<1.9$$

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

(22)#$${\mathit{Nu}}_c=4.34{\mathit{Re}}_b^{0.584}{\mathit{Ja}}^{-0.419}{\mathit{Pr}}^{0.333}$$

(23)#$$\beta ={(1-12.29{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.584}{\mathit{Pr}}^{0.333}{\mathit{Ja}}^{0.581}{\mathit{Fo}}_{\mathit{0}})}^{0.706}$$

(24)#$$1000<{\mathit{Re}}_b<30000,45<\mathit{Ja}<180,2.1<\mathit{Pr}<4.3$$

Group 4#

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

(25)#$${\mathit{Nu}}_c=0.6{\mathit{Re}}_b^{1/2}{\mathit{Pr}}^{1/3}(1-1.2{\mathit{Ja}}^{9/10}{\mathit{Fo}}_{\mathit{0}}^{2/3})$$

(26)#$$\beta ={(1-1.8{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.5}{\mathit{Pr}}^{1/3}\mathit{Ja}{\mathit{Fo}}_{\mathit{0}}(1-0.72{\mathit{Ja}}^{0.9}{\mathit{Fo}}_{\mathit{0}}^{2/3}))}^{2/3}$$

(27)#$$20<{\mathit{Re}}_b<700,12<\mathit{Ja}<100,1.8<\mathit{Pr}<2.9$$

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

(28)#$${\mathit{Nu}}_c=0.6{\mathit{Re}}_b^{1/2}{\mathit{Pr}}^{1/3}(1-{\mathit{Ja}}^{0.1}{\mathit{Fo}}_{\mathit{0}})$$

(29)#$$\beta ={(1-1.8{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.5}{\mathit{Pr}}^{1/3}\mathit{Ja}{\mathit{Fo}}_{\mathit{0}}(1-0.5{\mathit{Ja}}^{0.1}{\mathit{Fo}}_{\mathit{0}}))}^{2/3}$$

(30)#$$335<{\mathit{Re}}_b<1770,0<\mathit{Ja}<60,1.71<\mathit{Pr}<1.75$$

Group 5#

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

(31)#$${\mathit{Nu}}_c=2.04{\mathit{Re}}_b^{0.61}{\alpha }^{0.328}{\mathit{Ja}}^{-0.308}$$

(32)#$$\beta ={(1-5.67{\mathit{Re}}_{\mathit{b}\mathit{0}}^{0.61}{\alpha }^{0.328}{\mathit{Ja}}^{0.692}{\mathit{Fo}}_{\mathit{0}})}^{0.72}$$

(33)#$$2266<{\mathit{Re}}_b<7953$$