Atangana–Baleanu fractional model for the flow of Jeffrey nanofluid with diffusion-thermo effects: applications in engine oil

Ali, Farhad; Murtaza, Saqib; Khan, İlyas; Sheikh, Nadeem Ahmad; Nisar, Kottakkaran Sooppy

doi:10.1186/s13662-019-2222-1

Cited by 29 publications

(16 citation statements)

References 42 publications

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“…They noticed that by adding these nanoparticles within the base fluids improved the characteristics of EO. Similarly, Ali et al [44] suspended silver nanoparticles in the engine oil base fluid. They noticed that by increasing the amount of nanoparticles, the collision of nanoparticles rises which results to boost up the heat transfer rate up to 15%.…”

Section: Introductionmentioning

confidence: 99%

A Time Fractional Model of Generalized Couette Flow of Couple Stress Nanofluid With Heat and Mass Transfer: Applications in Engine Oil

et al. 2020

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The aim of this study is to obtain the closed form solutions for the laminar and unsteady couple stress fluid flow. The fluid is allowed to flow between two infinite parallel plates separated by distance. Moreover, we have considered that the lower plate is moving with uniform velocity 0 U and upper plate is stationary. For this purpose, engine oil is taken as a base fluid and to enhance the efficiency of lubricating oil, Molybdenum disulphide nanoparticles are dispersed uniformly in the engine oil. The flow is formulated mathematically in terms of partial differential equations of order four. Furthermore, the derived system of partial differential equations are fractionalized by using the mostly used definition of Caputo-Fabrizio time fractional derivative. The more general exact solutions for velocity, temperature and concentration distributions are obtained by using the joint applications of Fourier and the Laplace transforms. The effect of different parameters of interest of the obtained general solutions are discussed by sketching graphs. Furthermore, substituting favorable limits of different parameters, four different limiting cases are recovered from our obtained general solutions i.e. (a) Couette flow (b) Classical couple stress fluid (c) Newtonian viscous fluid and (d) in the absence of thermal and concentration. Moreover, the effect of different physical parameters on the velocity, temperature and concentration distributions are discussed graphically. It is worth noting that couple stress parameter corresponds to a decrease in the velocity profile. In order to observe the differences clearly, all the figures are compared for integer order and fractional order which provide a more realistic approach as compared to the classical model. Additionally, skin friction is calculated at lower as well as upper plate. Nusselt number and Sherwood number are also tabulated. It is noticed that the rate of heat transfer of engine oil can be enhanced up to 12.38% and decrease in mass transfer up to 2.14% by adding Molybdenum disulphide nanoparticles in regular engine oil. INDEX TERMS Couple stress nanofluid (CSNF); Caputo-Fabrizo (CF); Fourier transform (FT); Generalized Couette flow; Laplace transform (LT); Molybdenum disulphide (MoS2).

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Section: Introductionmentioning

confidence: 99%

A Time Fractional Model of Generalized Couette Flow of Couple Stress Nanofluid With Heat and Mass Transfer: Applications in Engine Oil

et al. 2020

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“…e generalized results of peristaltic flow of the Jeffrey fluid in a cross-sectional area of a triangular duct with slip at the peristaltic boundary are obtained in [8]. ere are a few further efforts for the Jeffrey fluid in [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Generalized Thermal Flux Flow for Jeffrey Fluid with Fourier Law over an Infinite Plate

Asjad

Basit

Akgül

et al. 2021

Mathematical Problems in Engineering

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The unsteady flow of Jeffrey fluid along with a vertical plate is studied in this paper. The equations of momentum, energy, and generalized Fourier’s law of thermal flux are transformed to non-dimensional form for the proper dimensionless parameters. The Prabhakar fractional operator is applied to acquire the fractional model using the constitutive equations. To obtain the generalized results for velocity and temperature distribution, Laplace transform is performed. The influences of fractional parameters α , β , γ , thermal Grashof number Gr , and non-dimensional Prandtl number Pr upon velocity and temperature distribution are presented graphically. The results are improved in the form of decay of energy and momentum equations, respectively. The new fractional parameter contains the Mittag-Leffler kernel with three fractional parameters which are responsible for better memory of the fluid properties rather than the exponential kernel appearing in the Caputo–Fabrizio fractional operator. The Prabhakar fractional operator has advantage over Caputo–Fabrizio in the real data fitting where needed.

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“…Consider that Y i : J × V ⟶ P cp (R) satisfy (H 1 ), (H 2 ), and (H 4 ). Assume that, for all n ∈ N, T n are defined by the same way as (54) with respect to (42) and (43). Moreover, let…”

Section: Resultsmentioning

confidence: 99%

“…is derivative is related to the fading memory concept and frequently used to discuss and analyze the real-world phenomena such as fluid and nanofluid models (see [41][42][43] and references therein). Depending on the constant M(α), the corresponding integral is given by the following definition.…”

Section: Definition 7 (Mittag-leffler Function) E General Form Ofmentioning

confidence: 99%

A Countable System of Fractional Inclusions with Periodic, Almost, and Antiperiodic Boundary Conditions

Salem

Al-Dosari

2021

Complexity

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This article is dedicated to the existence results of solutions for boundary value problems of inclusion type. We suggest the infinite countable system to fractional differential inclusions written by D α ABC ν i t ∈ Y i t , ν i t i = 1 ∞ . The mappings y i t , ν i t i = 1 ∞ are proposed to be Lipschitz multivalued mappings. The results are explored according to boundary condition σ ν i 0 = γ ν i ρ , σ , γ ∈ ℝ . This type of condition is the generalization of periodic, almost, and antiperiodic types.

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Atangana–Baleanu fractional model for the flow of Jeffrey nanofluid with diffusion-thermo effects: applications in engine oil

Cited by 29 publications

References 42 publications

A Time Fractional Model of Generalized Couette Flow of Couple Stress Nanofluid With Heat and Mass Transfer: Applications in Engine Oil

A Time Fractional Model of Generalized Couette Flow of Couple Stress Nanofluid With Heat and Mass Transfer: Applications in Engine Oil

Generalized Thermal Flux Flow for Jeffrey Fluid with Fourier Law over an Infinite Plate

A Countable System of Fractional Inclusions with Periodic, Almost, and Antiperiodic Boundary Conditions

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