Table 2 Correlations for boiling flow heat transfer coefficient

Warrier et al. [27]

FC-84

Small rectangular parallel channels of D_h = 0.75mm

Single-phase forced convection and subcooled and saturated nucleate boiling

3 < x <55%

$h_{\mathrm{tp}}=h_{\mathrm{sp}}\left(1+6{\mathrm{Bo}}^{\frac{1}{16}}-5.3\left(1-855\mathrm{Bo}\right){\chi }_{\mathrm{v},x}^{0.65}\right)\left(6\right)$ $h_{\mathrm{sp}}=0.023R{e}_{\mathrm{l}}^{0.8}P{r}_{\mathrm{l}}^{0.4}{\lambda }_{\mathrm{l}}/D_{\mathrm{h}}\left(7\right)$

Kandlikar and Balasubramanian [28]

Water, refrigerants, and cryogenic fluids

Minichannels and microchannels

Flow boiling

x <0.7 ~ 0.8

$\mathrm{Co}<0.65,h_{\mathrm{tp}}=h_{\mathrm{sp}}\left[1.136{\mathrm{Co}}^{-0.9}{\left(25F{r}_{\mathrm{lo}}\right)}^c+667.2{\mathrm{Bo}}_{\mathrm{lo}}^{0.7}\right]\left(8\right)$ $\mathrm{Co}>0.65,h_{\mathrm{tp}}=h_{\mathrm{sp}}\left[0.6683{\mathrm{Co}}^{-0.2}{\left(25F{r}_{\mathrm{lo}}\right)}^c+1058{\mathrm{Bo}}_{\mathrm{lo}}^{0.7}\right]\left(9\right)$

h_sp is calculated Equation 7

Sun and Mishima [29]

Water, refrigerants (R11, R12, R123, R134a, R141b, R22, R404a, R407c, R410a) and CO2

Minichannel diameters from 0.21 to 6.05 mm

Flow boiling laminar flow region

Re _L < 2,000 and Re _G < 2,000

$h_{\mathrm{tp}}=\frac{6R{e}_{\mathrm{lo}}^{1.05}{\mathrm{Bo}}^{0.54}{\lambda }_{\mathrm{l}}}{{\mathrm{We}}_{\mathrm{l}}^{0.191}{\left({\rho }_{\mathrm{l}}/{\rho }_g\right)}^{0.142}{D}_{\mathrm{h}}}\left(10\right)$

Bertsch et al. [30]

Hydraulic diameters ranging from 0.16 to 2.92 mm

Minichannels

Flow boiling and vapor quality

0 to 1

$h_{\mathrm{tp}}=\left(1-{\chi }_{\mathrm{v},x}\right)h_{\mathrm{nb}}+\left[1+80\left({\chi }_{\mathrm{v},x}^2-{\chi }_{\mathrm{v},x}^6\right)e^{-0.6{\mathrm{Co}}_{\mathrm{f}}}\right]h_{\mathrm{sp}}\left(11\right)$

h_nb is calculated by Cooper [35]:$h_{\mathrm{nb}}=55P_{\mathrm{R}}^{0.12-0.087ln\xi }{\left(-0.4343ln{P}_{\mathrm{R}}\right)}^{-0.55}{M}^{-0.5}{q}^{0.67}\left(12\right)$

h_sp = χ_v,xh_sp,go + (1 − χ_v,x)h_sp,lo (13)$h_{\mathrm{sp},\mathrm{ko}}=\left[3.66+\frac{0.0668R{e}_{\mathrm{ko}}P{r}_k{D}_{\mathrm{h}}/L}{1+0.04{\left(R{e}_{\mathrm{ko}}P{r}_k{D}_{\mathrm{h}}/L\right)}^{2/3}}\right]\frac{\lambda }{D_{\mathrm{h}}}\left(14\right)$${\mathrm{Co}}_{\mathrm{f}}=\sqrt{\frac{\sigma }{g\left({\rho }_{\mathrm{l}}-{\rho }_{\mathrm{g}}\right)D_{\mathrm{h}}^2}}\left(15\right)$

Temperature

−194°C to 97°C

Heat flux

4–1,150 kW/m²

Mass flux

20–3,000 kg/m²s

Lazarek and Black [31]

R113

Macrochannels 3.15 mm inner diameter tube

Saturated flow boiling

-

$N{u}_x=30R{e}_{\mathrm{lo}}^{0.857}{\mathrm{Bo}}^{0.714}\left(16\right)$

Gungor and Winterton [32]

Water and refrigerants (R-11, R-12, R-22, R-113, and R-114)

Horizontal and vertical flows in tubes and annuli D = 3 to 32 mm

Saturated and subcooled boiling flow

0.008 < p_sat < 203 bar; 12 < G < 61.518 kg/m²s; 0 < x < 173%; 1 < q < 91.534 kW/m²

h_tp = (SS₂ + FF₂)h_sp (17)

h_sp is calculated Equation 6

S = 1 + 3, 000Bo^0.86 (18)$F=1.12{\left(\frac{{\chi }_{\mathrm{v},x}}{1-{\chi }_{\mathrm{v},x}}\right)}^{0.75}{\left(\frac{{\rho }_{\mathrm{l}}}{{\rho }_{\mathrm{g}}}\right)}^{0.41}\left(19\right)$$S_2=\left\{\begin{array}{l}F{r}_{\mathrm{lo}}^{(0.1-2\mathrm{Fr}{}_{\mathrm{lo}})}\mathrm{if}\mathrm{horizontal}\mathrm{with}F{r}_{\mathrm{lo}}<0.05\\ 1\mathit{otherwise}\end{array}\right.\left(20\right)$$F_2=\left\{\begin{array}{l}F{r}_{\mathrm{lo}}^{\left(0.5\right)}\mathrm{if}\mathrm{horizontal}\mathrm{with}F{r}_{\mathrm{lo}}<0.05\\ 1o\mathrm{therwise}\end{array}\right.\left(21\right)$

Liu and Witerton [36]

Water, refrigerants and ethylene glycol

Vertical and horizontal tubes, and annuli

Subcooled and saturated flow boiling

-

$h_{\mathrm{tp}}=\sqrt{{\left(F{h}_{\mathrm{lo}}\right)}^2+{\left(S{h}_{\mathrm{nb}}\right)}^2}\left(22\right)$

h_nb is calculated by Cooper [35] (Equation 11)$F=0.35\left[1+{\chi }_{\mathrm{v},x}\frac{{\mu }_{\mathrm{l}}{C}_{\mathrm{p},\mathrm{l}}}{{\lambda }_{\mathrm{l}}}\left(\frac{{\rho }_{\mathrm{l}}}{{\rho }_{\mathrm{v}}}-1\right)\right]\left(23\right)$$S=\left[1+0.055F^{0.5}R{e}_{\mathrm{lo}}^{0.16}\right]\left(24\right)$

Kew and Cornwell [33]

R141b

Single tubes of 1.39–3.69 mm inner diameter

Nucleate boiling, confined bubble boiling, convective boiling, partial dry out

-

$h_{\mathrm{tp}}=30R{e}_{\mathrm{lo}}^{0.857}{\mathrm{Bo}}^{0.714}\frac{{\lambda }_{\mathrm{l}}}{D_{\mathrm{h}}}{\left(\frac{1}{1-{\chi }_{\mathrm{v},x}}\right)}^{0.143}\left(25\right)$

Yan and Lin [34]

R134a

28 parallel tubes 2 mm

Convective boiling

G = 50 to 200 kg/m²s; q = 0.5 to 2 W/cm²

$h_{\mathrm{tp}}=\left(C_1{\mathrm{Co}}^{C_2}+C_3{\mathrm{Bo}}^{C_4}F{r}_{\mathrm{lo}}\right){\left(1-{\chi }_{\mathrm{v},\mathrm{m}}\right)}^{0.8}{h}_{\mathrm{l}}\left(26\right)$

h_l = 4.364λ_l/D_h (27)$C_m=C_{m,1}{\mathrm{Re}}_{\mathrm{lo}}^{C_{m,2}}{T}_{\mathrm{R}}^{C_{m,3}}\left(28\right)$

The best fitting values for the constants C_m,1, C_m,2, and C_m,3 are listed in Table 3