. 2020 Sep 16;10(9):1855. doi: 10.3390/nano10091855

Table 5.

Proposed correlations for natural thermo-convection of nanofluids in different cavities.

Researchers	NF	Geometry	Correlation
Ali et al. [152]	Al₂O₃/W	Vertical cylinders	$N u = (7.899 - 8.571 \times 10^{- 9} R a^{*}) \times (1.0 - 15.283 φ + 387.681 φ^{2}) A R^{0.5}$
Ho et al. [145]	Al₂O₃/W	Vertical squares	$N u_{n f} = C R a_{n f}^{n} {(P r_{n f, h} / P r_{n f})}^{m} {(β r_{n f, h} / β r_{n f})}^{p}$
Cadena-de la Peña et al. [151]	AIN and TiO₂/mineral oil	Opened vertical annular	$N u = 0.496 R a^{*}^{0.17} K^{(\frac{1.582}{k} + 2.463)} A R^{- 0.541}$ Maximum deviation = 1.6%
Ali et al. [5]	Al₂O₃/W	Vertical cylinders	$N u = 1.426 {(R a^{*})}^{0.119} (1 + 44.097 φ - 6943.36 φ^{2}) A R^{0.137}$
Ghodsinezhad et al. [15]	Al₂O₃/W	Square	$N u = 0.6091 {(R a)}^{0.235} {(φ)}^{0.00584}$ (for φ ≤ 0.1) $N u = 0.482 {(R a)}^{0.2356} {(φ)}^{- 0.026}$ (for φ ≥ 0.1); R² = 0.94
Ilyas et al. [147]	f-Al₂O₃/THO	Rectangular	$N u = C {(R a)}^{0.04} {(1 - φ)}^{- 0.015}$ ; 228 ≤ Pr ≤ 592; 0.97 ≤1− $φ$ (wt. frac.) ≤ 1; $C = 4.17 {(\frac{P r_{r}}{P r_{r} - 0.343})}^{2.51} (\frac{P r_{r}}{K_{r}^{3.76} β_{r}^{3.483}})$
Nnanna et al. [54]	Al₂O₃/DIW	Rectangular	$N u = 16.4 e^{- R a ϵ φ (e^{- m φ})}$ ε = 4 × 10⁻⁷; m = 11; 10⁵ ≤ φRae^−mφ ≤ 10⁶
Babu and Rao [156]	Al₂O₃/DIW	Vertical cylinder	$N u = 1.349 {(R a)}^{0.22}$ (0 < φ < 0.10 vol.%); R² = 0.995 $N u = 1.246 {(R a)}^{0.224}$ (0.1 < φ < 0.60 vol.%); R² = 0.997
Choudhary and Subudhi [139]	Al₂O₃/DW	Square	$N u = 0.1199 P r^{- 1 / 2} {(R a)}^{1 / 4} + 2.17 \times 10^{3} P r^{- 1 / 7} {(R a)}^{3 / 7}$ (φ < 0.01 vol.%) $N u = 0.132 P r^{- 1 / 2} {(R a)}^{1 / 4} + 1.66 \times 10^{3} P r^{- 1 / 7} {(R a)}^{3 / 7}$ (φ < 0.10 vol.%) ${(\frac{δ_{t h}}{H})}_{N F} = 122.55 {(R a)}^{- 0.427}$ ; (φ < 0.01 vol.%) ${(\frac{δ_{t h}}{H})}_{N F} = 44.873 {(R a)}^{- 0.3728}$ ; (φ < 0.10 vol.%)
Rao and Babu [156]	Al₂O₃/W	Cylinder	$N u = 1.349 {(R a)}^{0.22}$ (0 $\leq φ \leq 0.1$ ) $N u = 1.246 {(R a)}^{0.224}$ (0.1 $\leq φ \leq 0.6$ )
Giwa et al. [36]	Fe₂O₃-Al₂O₃/DIW	Rectangular	$N u = 0.721 {(R a)}^{0.2429} φ^{- 0.0613}$
Haddad et al. [158]	ZnO/W	Hemisphere	$N u (α) = κ (α) {(R a)}^{b (a)} P r^{m}$ $κ (α) = 6 \times 10^{- 6} α^{2} - 8 \times 10^{- 4} α + 0.4$ $b (α) = - 3 \times 10^{- 7} α^{2} + 2 \times 10^{- 6} α + 0.223$ ; $m = - 0.03$ Valid for $5.21 \times 10^{7} \leq R a \leq 7.29 \times 10^{10}$ ; $0 ° \leq α \leq 180 °$ ; $3.95 \leq P r \leq 6.07$
Giwa et al. [157]	Al₂O₃-MWCNT/DIW	Square	$N u = 6.47 \times 10^{- 4} {(R a)}^{0.5928} R^{0.00169}$
Umar et al. [160]	ZrO₂/water	Triangular and rectangular	$N u = 16.22 {(\frac{R a D_{h}}{x})}^{0.0696}$ and $N u = 10.09 {(\frac{R a D_{h}}{x})}^{0.0702}$