Mixed Convection of Silica–Molybdenum Disulphide/Water Hybrid Nanoliquid over a Rough Sphere
Abstract
:1. Introduction
- –
- combined convective flow over a rough sphere;
- –
- impact of molybdenum-silica/water hybrid nanofluid on flow structures and heat patterns;
- –
- effect of surface roughness on hydro- and thermodynamics.
2. Mathematical Analysis
3. Method of Analysis
4. Results and Discussion
5. Conclusions
- –
- the hybrid nanofluid augments the temperature, as well as Nusselt number at the wall;
- –
- velocity distribution is reduced, while friction at the surface enhances in the case of hybrid nanofluid;
- –
- slip exists near the surface of the sphere owing to roughness, which yields steep jump in the liquid velocity close to the border;
- –
- for enhancing magnitudes of small parameter, the friction at the surface and the Nusselt number are enhanced;
- –
- skin-friction parameter and the Nusselt number are boosted for hybrid nanoliquid on comparison with mono nanofluid and the base fluid;
- –
- skin-friction parameter and the Nusselt number have the highest values for blade-shaped nanoadditives and lowest value is found for spherical-formed nanoparticles.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
F | dimensionless velocity |
Nu | Nusselt number |
G | non-dimensional temperature |
g | gravity acceleration |
n | frequency parameter |
v | y-velocity projection |
r(x) | radius of the section normal to axis of the sphere |
Pr | Prandtl number |
U0 | reference velocity |
f | dimensionless stream function |
R | radius of the sphere |
Tw | temperature at the wall |
Re | Reynolds number |
Gr | Grashof number |
Ri | combined convection parameter |
T | temperature |
T∞ | ambient temperature |
u | x-velocity projection |
U∞ | free stream velocity constant |
x, y | Cartesian coordinates |
Ue | free stream velocity |
Greek symbols
α | small parameter |
step size in and η directions | |
ε | velocity ratio parameter |
, η | transformed variables |
νf | kinematic viscosity |
φ1 | volume fraction of silica nanoparticle |
φ2 | volume fraction of molybdenum disulphide nanoparticle |
ψ | dimensionless stream function |
Subscripts
f | base fluid |
hnf | hybrid nanofluid |
nf | mono nanofluid |
s1 | solid component for silica |
s2 | solid component for molybdenum disulphide |
, η | variables of the partial derivatives |
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Properties | Nanofluid | Hybrid Nanofluid |
---|---|---|
Dynamic viscosity | ||
Density | ||
Thermal conductivity | with | |
Thermal expansion coefficient | ||
Heat capacitance |
Properties | Water | SiO2 | MoS2 |
---|---|---|---|
cp (J·kg−1·K−1) | 4179 | 730 | 397.746 |
ρ (kg·m−3) | 997.1 | 2650 | 5060 |
k (W·m−1·K−1) | 0.613 | 1.5 | 34.5 |
Β × 10−5 (K−1) | 21.0 | 42.7 | 2.8242 |
Nanoparticles Type | Geometry Parameter |
---|---|
Spherical | 3.0 |
Bricks | 3.7 |
Cylindrical | 4.9 |
Platelets | 5.7 |
Blade | 8.6 |
Combined Convection Parameter (Ri) | Mono Nanofluid (φ1 = 0.1 and φ2 = 0.0) | Hybrid Nanofluid (φ1 = 0.1 and φ2 = 0.1) | |||
---|---|---|---|---|---|
Re1/2Cf | Re−1/2Nu | Re1/2Cf | Re−1/2Nu | ||
Ri = −2 | smooth surface (α = 0) | 1.91924 | 1.73737 | 2.76707 | 2.07747 |
Ri = 0 | 2.68659 | 1.85759 | 3.54184 | 2.18376 | |
Ri = 3 | 3.71230 | 1.99284 | 4.60356 | 2.30996 | |
Ri = 6 | 4.64655 | 2.10531 | 5.58725 | 2.41753 | |
Ri = 10 | 5.79680 | 2.22851 | 6.81020 | 2.54115 | |
Ri = −2 | rough surface (α = 0.25) | 115.67549 | 2.11400 | 150.75397 | 2.46100 |
Ri = 0 | 116.33356 | 2.19692 | 151.43079 | 2.53750 | |
Ri = 3 | 117.24895 | 2.30142 | 152.38640 | 2.63768 | |
Ri = 6 | 118.10291 | 2.39003 | 153.28743 | 2.72483 | |
Ri = 10 | 119.17278 | 2.49174 | 154.42511 | 2.82653 |
Nazar et al. [54] | Mohamed et al. [55] | Present Results | |||||||
---|---|---|---|---|---|---|---|---|---|
Ri = −1 | Ri = 0 | Ri = 1 | Ri = −1 | Ri = 0 | Ri = 1 | Ri = −1 | Ri = 0 | Ri = 1 | |
00 | 0.7870 | 0.8162 | 0.8463 | 0.7858 | 0.8150 | 0.8406 | 0.7918 | 0.8180 | 0.8426 |
100 | 0.7818 | 0.8112 | 0.8371 | 0.7809 | 0.8103 | 0.8362 | 0.7778 | 0.8139 | 0.8385 |
200 | 0.7669 | 0.7974 | 0.8239 | 0.7615 | 0.7967 | 0.8232 | 0.7729 | 0.8008 | 0.8254 |
300 | 0.7422 | 0.7746 | 0.8024 | 0.7719 | 0.7741 | 0.8018 | 0.7497 | 0.7792 | 0.8054 |
400 | 0.7076 | 0.7429 | 0.7725 | 0.7074 | 0.7425 | 0.7721 | 0.7134 | 0.7475 | 0.7737 |
500 | 0.6624 | 0.7022 | 0.7345 | 0.6624 | 0.7032 | 0.7354 | 0.6754 | 0.7081 | 0.7377 |
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Patil, P.M.; Shankar, H.F.; Sheremet, M.A. Mixed Convection of Silica–Molybdenum Disulphide/Water Hybrid Nanoliquid over a Rough Sphere. Symmetry 2021, 13, 236. https://doi.org/10.3390/sym13020236
Patil PM, Shankar HF, Sheremet MA. Mixed Convection of Silica–Molybdenum Disulphide/Water Hybrid Nanoliquid over a Rough Sphere. Symmetry. 2021; 13(2):236. https://doi.org/10.3390/sym13020236
Chicago/Turabian StylePatil, Prabhugouda M., Hadapad F. Shankar, and Mikhail A. Sheremet. 2021. "Mixed Convection of Silica–Molybdenum Disulphide/Water Hybrid Nanoliquid over a Rough Sphere" Symmetry 13, no. 2: 236. https://doi.org/10.3390/sym13020236