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Dual Thermal Analysis of Fractional Convective Flow Through Aluminum Oxide and Titanium Dioxide Nanoparticles

Qasim Ali

Qasim Ali

Faculty of Natural Sciences, Department of Mathematics, University of ChakwalChakwal, Pakistan
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Ali, Qasim
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Rajai S. Alassar

Rajai S. Alassar

Faculty of Computing and Mathematics, Department of Mathematics, Interdisciplinary Research Center for Sustainable Energy Systems, King Fahd University of Petroleum & MineralsDhahran, Saudi Arabia
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Alassar, Rajai S.
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Irfan. A. Abro

Irfan. A. Abro

School of Materials Science and Engineering, Beijing Institute of TechnologyBeijing, China
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Abro, Irfan. A.
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Kashif. A. Abro

Kashif. A. Abro

Faculty of Sciences, Technology and Humanities, Department of Basic Sciences and Related Studies, Mehran University of Engineering and TechnologyJamshoro, Pakistan
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Abro, Kashif. A.
  
31 mar 2025
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Data publikacji: 31 mar 2025
Zakres stron: 32 - 43
Otrzymano: 05 sty 2024
Przyjęty: 11 mar 2024
DOI: https://doi.org/10.2478/ama-2025-0005
Słowa kluczowe
© 2025 Qasim Ali et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fig 1.

Geometry of the problem
Geometry of the problem

Fig. 2.

Plot of temperature field for both fractional models when Pr = 0.3, φ = 0.01 with (a): t = 0.1 and (b): t = 1.5
Plot of temperature field for both fractional models when Pr = 0.3, φ = 0.01 with (a): t = 0.1 and (b): t = 1.5

Fig. 3.

Temperature field for diverse values of (a): Prandtl number and (b): nanofluid with α, β = 0.5, φ = 0.01, and t = 0.1
Temperature field for diverse values of (a): Prandtl number and (b): nanofluid with α, β = 0.5, φ = 0.01, and t = 0.1

Fig. 4.

Effect of (α, β) on velocity for Pr = 0.3, M = 0.5, Gr = 4, θ=π4 \theta = {\pi \over 4} , w = 0.9, b = 0.5, δ=π4 \delta = {\pi \over 4} and (a): t = 0.1 (b): t = 1.5
Effect of (α, β) on velocity for Pr = 0.3, M = 0.5, Gr = 4, θ=π4 \theta = {\pi \over 4} , w = 0.9, b = 0.5, δ=π4 \delta = {\pi \over 4} and (a): t = 0.1 (b): t = 1.5

Fig. 5.

The effect of (a): Grashof number (b): Pr on velocity when α, β = 0.5, M = 0.5, θ=π4 \theta = {\pi \over 4} , w = 0.9, b = 0.5, δ=π4 \delta = {\pi \over 4} , t = 0.1
The effect of (a): Grashof number (b): Pr on velocity when α, β = 0.5, M = 0.5, θ=π4 \theta = {\pi \over 4} , w = 0.9, b = 0.5, δ=π4 \delta = {\pi \over 4} , t = 0.1

Fig. 6.

Effect of volume fraction φ on velocity for α, β = 0.5, Pr = 0.3, M = 0.5, Gr = 4, θ=π4 \theta = {\pi \over 4} , w = 0.9, b = 0.5, δ=π4 \delta = {\pi \over 4}
Effect of volume fraction φ on velocity for α, β = 0.5, Pr = 0.3, M = 0.5, Gr = 4, θ=π4 \theta = {\pi \over 4} , w = 0.9, b = 0.5, δ=π4 \delta = {\pi \over 4}

Fig. 7.

Variation in (a): magnetic parameter and (b): the inclination of magnetic field for velocity field with α, β = 0.5, Pr = 0.3, Gr = 4, w = 0.9, b = 0.5, δ=π4 \delta = {\pi \over 4} , t = 0.1
Variation in (a): magnetic parameter and (b): the inclination of magnetic field for velocity field with α, β = 0.5, Pr = 0.3, Gr = 4, w = 0.9, b = 0.5, δ=π4 \delta = {\pi \over 4} , t = 0.1

Fig. 8.

Comparison of ordinary and fractional velocity when (a): α, β → 0.5 and (b): α, β → 1
Comparison of ordinary and fractional velocity when (a): α, β → 0.5 and (b): α, β → 1

Fig. 9.

Comparison of (a): nanofluids and (b): numerical techniques for the velocity field
Comparison of (a): nanofluids and (b): numerical techniques for the velocity field

Numerical analysis of Nusselt number as well as skin friction for CF and AB derivatives

α, β Nu by CF Nu by AB Cf by AB Cf by CF
0.1 0.5352 0.5309 0.1836 0.1824
0.2 0.5276 0.5204 0.1751 0.1553
0.3 0.5151 0.5053 0.1611 0.1335
0.4 0.4972 0.4842 0.1423 0.1127
0.5 0.4730 0.4558 0.1203 0.0934
0.6 0.4411 0.4193 0.0965 0.0777
0.7 0.4000 0.3761 0.0728 0.0677
0.8 0.3502 0.3326 0.0513 0.0637
0.9 0.2965 0.2996 0.0359 0.0654

j_ama-2025-0005_tab_004

Symbol Quantity Unit
w Velocity (m/s)
t Time (s)
T Temperature (K)
knf Thermal conductivity of nanofluid (W/mk)
T Temperature (K)
T∞ Ambient temperature (K)
Gr Grashof number (−)
M Dimensionless magnetic parameter (−)
Pr Prandtl number (−)
q Laplace transform variable (−)
Bo Strength of magnetic field (kg/s2)
Cp Specific heat at constant pressure (J/kgK)
b Slip parameter (−)
Cf Skin friction (−)
Nu Nusselt number (−)

j_ama-2025-0005_tab_005

μnf Dynamic viscosity (Pa-s)
α, β Fractional parameters (−)
α1 Second-grade parameter (−)
βT Volumetric coefficient of expansion (−)
ρnf Density of nanofluid (kg/m3)
θ The angle of magnetic inclination (−)
δ The inclination angle of the plate (mol/m3)
βT Volumetric coefficient of expansion (−)
σnf Electrical conductivity of nanofluid (−)
ρf Density of fluid (kg/m3)
ρs Density of solid (kg/m3)
φ The volume fraction of nanofluid (−)

A comparison of solutions with two diverse approaches

ξ Temperature by Stehfest Temperature by Tzou Velocity by Stehfest Velocity by Tzou
0.1 0.9471 0.9471 0.7001 0.6999
0.2 0.8971 0.8971 0.7856 0.7854
0.3 0.8496 0.8496 0.8532 0.8530
0.4 0.8046 0.8046 0.9053 0.9051
0.5 0.7619 0.7619 0.9438 0.9436
0.6 0.7215 0.7215 0.9707 0.9705
0.7 0.6831 0.6831 0.9875 0.9872
0.8 0.6468 0.6468 0.9956 0.9954
0.9 0.6123 0.6123 0.9964 0.9961

Thermophysical characteristics of base fluids (water and blood) and nanoparticles [ 6,38]_

Material H2O Blood Al2O3 TiO2
ρ(kgm−3) 997.1 1053 1600 4250
Cp(kg−1k−1) 0.4179 3594 796 686.2
K(Wm−1k−1) 0.613 0.492 3000 8.9528
BT×10−5(k−1) 21 0.18 44 0.90
Język:
Angielski
Częstotliwość wydawania:
4 razy w roku
Dziedziny czasopisma:
Inżynieria, Elektrotechnika, Elektronika, Inżynieria mechaniczna, Mechanika, Bioinżynieria i inżynieria biomedyczna, Biomechanika, Inżynieria lądowa, Inżynieria środowiska
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