A Review on the Control Parameters of Natural Convection in Different Shaped Cavities with and without Nanofluid
Abstract
:1. Introduction
2. Experimental Studies
3. Numerical Studies
3.1. Governing Equations
3.2. Thermophysical Properties of Fluids in Cavities
3.2.1. Air and Water
3.2.2. Nanofluids
3.2.3. Non-Newtonian Fluids
4. Effective Parameters on Heat Transfer in Cavities
4.1. Inclined Cavity
4.2. Adding a Fin to Cavity
4.3. Applying a Magnetic Field
4.4. Add Porous Media to the Cavity
5. Cavity with Two-Phase Approach
5.1. Eulerian–Eulerian Approach
5.1.1. Volume of Fluid Model
5.1.2. Mixing Model
5.1.3. Eulerian Model
5.2. Eulerian–Lagrangian Approach
6. Non-Rectangular Cavities
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
AR | Aspect ratio | Greek symbols | |
B0 | Magnetic field strength | Magnetic field angle | |
Cp | Specific heat | Thermal diffusivity | |
CVFEM | Control volume finite element method | Solid volume fraction | |
CVM | Control volume method | ε | porosity |
Da | Darcy number | Temperature | |
FDM | Finite difference method | Dynamic viscosity | |
FEM | Finite element method | Kinematic viscosity | |
FVM | Finite volume method | Density | |
g | Gravitational acceleration | σ | Electrical conductivity |
Gr | Grashof number | Cavity angle | |
h | Convection heat transfer coefficient | Subscripts | |
Ha | Hartmann number | ave | Average |
k | Thermal conductivity | c | Cold |
L | Enclosure length | h | Hot |
n | Power-law index | f | Pure fluid |
Nusselt number | nf | Nanofluid | |
P | Pressure | p | Particle |
Pr | Prandtl number | s | Surface |
Ra | Rayleigh number | W | Water |
Rd | Radiation parameter | ||
t | Time | ||
T | Temperature | ||
u, v | Velocity components in x and y directions | ||
x,y | Cartesian coordinates |
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References | Geometry | Type of Fluid | Parameter | Solver | Remark |
---|---|---|---|---|---|
[12] | air | Ra AR | Experimental | Radiation | |
[16] | air | Ra AR dp | Experimental | 3D | |
[25] | Fluid Pr = 6.62 | Ra Da | FEM Experimental | Entropy Generation Porous Layer | |
[18] | Water | Ra | Experimental | ||
[21] | air | Ra d | Experimental FDM | Fin 3D | |
[23] | Water air | Ra | CVFEM Experimental | 3D | |
[26] | air | E td h | Experimental | 3D Fin Radiation | |
[27] | air | Ra S | Experimental | Fin 3D |
ρ (kg/m3) | Cp (kJ/kg.K) | k (W/m.K) | μ (kg/m.s) | |
---|---|---|---|---|
Water [35] | 9.971 × 102 | 4.179 | 6.13 × 10−1 | 1 × 10−3 |
Air [36] | 1.169 | 1.0064 | 2.607 × 10−2 | 1.853 × 10−5 |
ρ (kg/m3) | Cp (kJ/kg.K) | k (W/m.K) | μ (kg/m.s) | |
---|---|---|---|---|
765.33 +1.8142 × T −0.0035 × T2 | 28.07 −0.2817 × T +0.00125 × T2 −2.48 × 10−6 × T3 +1.857 × T4 | −0.5752 + 0.006397 × T −8.151 × T2 | 0.0967 −8.207 × 10−4 × T + 2.344 × 10−6 T2 −2.244 × 10−9 × T3 | [23] Water |
((3.484 − 1.317) × xv) | 1.034 −2.8488 × 10−4 × T +7.8168 10−7 × T2 −4.9707 × 10−10 × T3 +1.077 × −13 × T4 | −2.2765 × 10−3 +1.259 × 10−4 × T −1.481 × 10−7 × T2 +1.7355 × 10−10 × T3 −1.0666 × −13 T4 +2.476 × −17 × T5 | −9.8601 10−1 +9.0801 10−2 T −1.1763 10−4 T2 +1.2349 10−7 T3 −5.797 −11 T4 | [36] Dry air |
1.2933 −5.588 × 10−3 × T +3.860 × 10−5 × T2 −5.253 10−7 × T3 | 1.0045 +2.0506 × 10−3 × T −1.6315 × 10−4 × T2 +6.2123 × 10−6 × T3 −8.8304 × 10−8 × T4 +5.071 −11 T5 | 2.4007 10−2 +7.2784 10−5 T −1.788 10−2 T2 −1.3517 10−9 T3 −3.3224 −11 T4 | 1.7157 10−5 +4.7224 10−8 T −3.663 10−10 T2 +1.873 10−12 T3 −8.050 −14 T4 | [37] Saturated air |
References | Geometry | Type of Fluid | Parameter | Solver | Remark |
---|---|---|---|---|---|
[38] | air | Ra ε | FVM | Open Cavity Radiation | |
[39] | Water | Ra | CVFEM | ||
[40] | air | SC τ β w k | FDM | Thermophoresis Wave Wall | |
[41] | Air (H2O-CO2) | Ra type of gas | FVM | Radiation Turbulance | |
[43] | air | Ra d ε | CVFEM | Radiation Open Cavity | |
[42] | Type of gas | Ra | FDM | Radiation Transient | |
[44] | air | Ra | FDM | Transition | |
[45] | air | Ra AR h d | FVM | Radiation Fin | |
[46] | air | Ra d | FEM | Transient Fin | |
[47] | air | Ra Ha α | FEM | MHD Fin |
Correlation | Ref |
---|---|
Einstein [80] | |
Brinkman [81] | |
Batchelor [82] | |
Lundgren [83] | |
Graham [84] | |
Simha [85] | |
Mooney [86] | |
Eilers [87] | |
Saito [88] | |
Frankel and Acrivos [89] |
Ref | Correlation |
---|---|
Maxwell [104] | |
Wasp [105] | |
Bruggeman [106] | |
Hamiltonn and Crosse [107] | |
Koo and Kleinstreuer [108,109] | |
Avsec and Oblak [110] | |
Jang and Choi [111] | |
Pak and Cho [112] | |
Timofeeva et al. [113] |
References | Geometry | Type of Fluid | Parameter | Solver | Remark |
---|---|---|---|---|---|
[126] | Power-law non Newtonian | Ra n Pr rt | FVM | Open Cavity | |
[127] | Power-law non Newtonian | Ra AR Pr n w dp | LBM | Wave Wall | |
[128] | Power-law non Newtonian | Ra AR Da n α | FVM | Open Cavity Porous Layer Angel Cavity Entropy Generation | |
[129] | Viscoelastic fluid | Ra rd Pr e | FDM | Radiation | |
[130] | Power-law non Newtonian | Ra Ha n N | LBM | Entropy MHD Fin | |
[131] | Power-law non Newtonian | Gr Pr n δ | FEM | Fin | |
[132] | Power-law non Newtonian | Ra Ha AR n | LBM | MHD |
References | Geometry | Type of Fluid | Parameter | Solver | Remark |
---|---|---|---|---|---|
[144] | air | Gr α | LBM | Fin Inclined Cavity | |
[150] | Al2O3/W | Ra f α τ | FDM | Inclined Cavity Transient | |
[147] | nanofluid (water base) | Ra Da d h α | FDM | Thermophoresis Brownian Motion Inclined Cavity Porous Layer | |
[153] | Al2O3/W | Ra Rd γ φ Ha | FEFVM | Brownian Motion Inclined Cavity Radiation Fin MHD | |
[154] | Al2O3/W | Ra Rd γ φ Ha | FEFVM | Brownian Motion Inclined Cavity Radiation Entropy MHD | |
[155] | Al2O3/W | Ra γ φ Ha | FEFVM | Brownian Motion Inclined Cavity Entropy MHD |
References | Geometry | Type of Fluid | Parameter | Solver | Remark |
---|---|---|---|---|---|
[164] | Al2O3/W | Ra γ AR | FDM | Open Cavity Fin | |
[165] | SiO2-TiO2/W-EG | Ra AR | LBM | Entropy Fin | |
[184] | SiO2/W | Ra K α | FEM | Fin | |
[185] | Cu/W | Ra | FEM | Fin | |
[186] | Cu/W | Ra Ha | CVFEM | MHD Fin | |
[166] | Al2O3/W | Ra k d | FDM | Entropy Fin | |
[182] | Fluid Pr = 0.7 | Ra α | FVM | Fin | |
[158] | air | Gr h | CVFEM | Fin | |
[171] | fluid Pr = 0.71 | Ra | LBM | Radiation Fin | |
[172] | fluid Pr = 0.71 | Ra l | LBM | Radiation Fin | |
[183] | fluid Pr = 0.7 | Ra AR | FVM | Fin | |
[181] | Cu/W | Ra h ε | FVM | Fin | |
[180] | Cu/W Ag/W Al2O3/W TiO2/W | Ra γ | FVM | Fin | |
[187] | Al2O3/W TiO2/W | Ra AR | LBM | Fin |
References | Geometry | Type of Fluid | Parameter | Solver | Remark |
---|---|---|---|---|---|
[211] | Fe3O4/W | Ra Ha Da α | FDM | Porous Layer Open Cavity MHD | |
[199] | Cu/W | Ra Ha | LBM | 3D MHD | |
[200] | CuO/W Al2O3/W | Gr Ha k | FEM | MHD Entropy Brownian Motion | |
[201] | CNT/W | Ra Ha α w k | FEM | MHD | |
[203] | Fe3O4/W | Ra Ha α Ω | FVM | ||
[204] | Cu- Al2O3/W | Ra w Ha | LBM | Wave Wall Open Cavity MHD Hybrid Nanofluid | |
[210] | Cu/W | Ra w Ha | CVFEM | Wave Wall MHD Brownian Motion | |
[212] | Cu- Al2O3/W | Ra Ha q b d | FDM | MHD Hybrid Nanofluid | |
[208] | CuO/W | Ra Ha h | FEM | 3D MHD | |
[170] | Al2O3/W | Ra Da h | LBM | Porous Layer MHD 3D Brownian Motion Fin | |
[209] | CNT/W | Ra Ha α | FVM | MHD 3D | |
[213] | Al2O3/W | Ra Ha AR d | FVFDM | Entropy MHD | |
[214] | CuO/W | Ra Ha m | CVFEM | MHD | |
[215] | Al2O3/W | Ra Ha AR α | LBM | Entropy MHD Brownian Motion |
References | Geometry | Type of Fluid | Parameter | Solver | Remark |
---|---|---|---|---|---|
[223] | Al2O3/W | Ra Da AR | FDM | Porous Layer Open Cavity | |
[224] | Fe3O4/EG | Ra Rd Da | CVFEM | Radition Porous Layer | |
[228] | fluid Pr = 0.7 | Ra Da | FEM | Entropy Porous Layer | |
[205] | fluid | Ra Ha Da w | FEM | Porous Layer Wave Wall MHD | |
[206] | Water | Ha Da α | LBM | Porous Layer MHD Phase Devition | |
[229] | isotropic porous medium | Ra Df Sr Le n | FDM | Soret Dufour Unsteady Double Diffusive Porous Layer | |
[230] | CuO/W | Ra d h k ε | FEM | Porous Layer | |
[231] | Fe3O4/EG | Ra Rd Da V | CVFEM | Radiation Coulomb Forces Porous Layer Electric Field |
References | Geometry | Type of Fluid | Parameter | Solver | Remark |
---|---|---|---|---|---|
[167] | Cu/W | Ra Da | FVM | Fin Porous Layer Entropy Two-Phase | |
[176] | Al2O3/W | Nt Nb Nr Ra Da Le Nh d γ | FEM | Wavewall Porous Medium Two-Phase Brownian Motion Fin | |
[169] | Al2O3/W | Ra k d | FDM | Thermophoresis Brownian Motion Two-Phase Fin | |
[168] | Al2O3/W | Ra d k | FDM | Fin Two-Phase | |
[145] | Cu/W | Ra Da α | FVM | Two-Phase Porous Layer Inclined Cavity |
Ref | Geometry |
---|---|
Astanina et al. [211]] | Examined a trapezoidal cavity |
Rahimi et al. [165] | L-shaped cavity |
Izadi et al. [173] | Inverted T cavity |
Dutta and Biswas [25] | Quarter circle cavity |
Ahmed et al. [227] | Cone cavity |
Lugarini et al. [43] | C-shaped cavity |
Zhang et al. [256] | Circular cavity |
Guestal et al. [257] | Circular cavity |
Armaghani et al. [213] | T-shaped cavity |
Enayati et al. [258] | Cylindrical cavity |
Snoussi et al. [259] | U-shaped cavity |
Ho et al. [44] | Cylindrical cavity |
Bhowmick et al. [252] | V-shaped cavity |
Mo et al. [187] | U-shaped cavity |
Malekpour et al. [260] | I-shaped cavity |
Sheikholeslami et al. [231] | Circular sectot between two circles |
Almudhaf et al. [229] | Trapezoidal cavity |
Amrani et al. [45] | Triangular cavity |
References | Geometry | Type of Fluid | Parameter | Solver | Remark |
---|---|---|---|---|---|
[250] | SiO2-TiO2/W-EG | Ra | LBM | Hybrid Nanofluid Entropy | |
[261] | CuO/W | Ra T AR | FDM | Thermophoresis Brownian Motion | |
[251] | Nanofluid (Water base) | Ra Le Nr Nb Nt | FDM | Transient Thermophoresis Brownian Motion | |
[262] | CuO/W | Ra | FDM | ||
[252] | fluid Pr = 0.71 | Ra AR Pr | FVM | Transient | |
[263] | Al2O3/W | Ra | LBM | Radiation | |
[264] | fluid Pr = 7 | Ra Da Le n | FVM | 3D | |
[257] | Cu/W TiO2/W | Ra h | FVM | Hybrid Nanofluid | |
[265] | CuO/W | Ra | LBM | Entropy 3D | |
[259] | Cu/W Al2O3/W | Ra | FVM | 3D |
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Rostami, S.; Aghakhani, S.; Hajatzadeh Pordanjani, A.; Afrand, M.; Cheraghian, G.; Oztop, H.F.; Shadloo, M.S. A Review on the Control Parameters of Natural Convection in Different Shaped Cavities with and without Nanofluid. Processes 2020, 8, 1011. https://doi.org/10.3390/pr8091011
Rostami S, Aghakhani S, Hajatzadeh Pordanjani A, Afrand M, Cheraghian G, Oztop HF, Shadloo MS. A Review on the Control Parameters of Natural Convection in Different Shaped Cavities with and without Nanofluid. Processes. 2020; 8(9):1011. https://doi.org/10.3390/pr8091011
Chicago/Turabian StyleRostami, Sara, Saeed Aghakhani, Ahmad Hajatzadeh Pordanjani, Masoud Afrand, Goshtasp Cheraghian, Hakan F. Oztop, and Mostafa Safdari Shadloo. 2020. "A Review on the Control Parameters of Natural Convection in Different Shaped Cavities with and without Nanofluid" Processes 8, no. 9: 1011. https://doi.org/10.3390/pr8091011