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

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

Acta Mechanica et Automatica
Volume 19 (2025): Issue 1 (March 2025)
By: Qasim Ali,  Rajai S. Alassar,  Irfan. A. Abro and  Kashif. A. Abro  
Open Access
|Mar 2025

Figures & Tables

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, βNu by CFNu by ABCf by ABCf by CF
0.10.53520.53090.18360.1824
0.20.52760.52040.17510.1553
0.30.51510.50530.16110.1335
0.40.49720.48420.14230.1127
0.50.47300.45580.12030.0934
0.60.44110.41930.09650.0777
0.70.40000.37610.07280.0677
0.80.35020.33260.05130.0637
0.90.29650.29960.03590.0654

j_ama-2025-0005_tab_004

SymbolQuantityUnit
wVelocity(m/s)
tTime(s)
TTemperature(K)
knfThermal conductivity of nanofluid(W/mk)
TTemperature(K)
T∞Ambient temperature(K)
GrGrashof number(−)
MDimensionless magnetic parameter(−)
PrPrandtl number(−)
qLaplace transform variable(−)
BoStrength of magnetic field(kg/s2)
CpSpecific heat at constant pressure(J/kgK)
bSlip parameter(−)
CfSkin friction(−)
NuNusselt number(−)

j_ama-2025-0005_tab_005

μnfDynamic viscosity(Pa-s)
α, βFractional parameters(−)
α1Second-grade parameter(−)
βTVolumetric coefficient of expansion(−)
ρnfDensity of nanofluid(kg/m3)
θThe angle of magnetic inclination(−)
δThe inclination angle of the plate(mol/m3)
βTVolumetric coefficient of expansion(−)
σnfElectrical conductivity of nanofluid(−)
ρfDensity of fluid(kg/m3)
ρsDensity of solid(kg/m3)
φThe volume fraction of nanofluid(−)

A comparison of solutions with two diverse approaches

ξTemperature by StehfestTemperature by TzouVelocity by StehfestVelocity by Tzou
0.10.94710.94710.70010.6999
0.20.89710.89710.78560.7854
0.30.84960.84960.85320.8530
0.40.80460.80460.90530.9051
0.50.76190.76190.94380.9436
0.60.72150.72150.97070.9705
0.70.68310.68310.98750.9872
0.80.64680.64680.99560.9954
0.90.61230.61230.99640.9961

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

MaterialH2OBloodAl2O3TiO2
ρ(kgm−3)997.1105316004250
Cp(kg−1k−1)0.41793594796686.2
K(Wm−1k−1)0.6130.49230008.9528
BT×10−5(k−1)210.18440.90
DOI: https://doi.org/10.2478/ama-2025-0005 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
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Language: English
Page range: 32 - 43
Submitted on: Jan 5, 2024
Accepted on: Mar 11, 2024
Published on: Mar 31, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Non-singularized derivative,
Mixed convection flow with nanoparticles,
Heat transfer of inclined plate,
Integral transforms
Related subjects:
Engineering,
Electrical engineering,
Electronics,
Mechanical engineering,
Mechanics,
Bioengineering and biomedical engineering,
Biomechanics,
Civil engineering,
Environmental engineering

© 2025 Qasim Ali, Rajai S. Alassar, Irfan. A. Abro, Kashif. A. Abro, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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