Thermodynamics of magnetohydrodynamic Brinkman fluid in porous medium

Siyal, Ambreen; Abro, Kashif Ali; Solangi, Muhammad Anwar

doi:10.1007/s10973-018-7897-0

Cited by 43 publications

(12 citation statements)

References 45 publications

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“…They claimed that new strange behaviors of the attractors were not possible by only classical differentiations. In short, the study can be continued for the charming and effective role of fractional calculus in applied engineering problems, 20–31 but we include here recent attempt in categorically as epidemiology, 32–39 heat and mass transfer, 40–44 fluid mechanics, 45–47 nanofluids, 48–51 and electrical engineering 52–55 . Motivating by above discussion, our aim is to propose the controlling analysis and coexisting attractors provided by memristor through highly nonlinear for mathematical relationships of governing differential equations.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of memristor through fractal‐fractional differential operators: A numerical study

Abro

Atangana

2020

Math Methods in App Sciences

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The newly generalized energy storage component, namely, memristor, which is a fundamental circuit element so called universal charge‐controlled mem‐element, is proposed for controlling the analysis and coexisting attractors. The governing differential equations of memristor are highly nonlinear for mathematical relationships. The mathematical model of memristor is established in terms of newly defined fractal‐fractional differential operators so called Atangana‐Baleanu, Caputo‐Fabrizio, and Caputo fractal‐fractional differential operator. A novel numerical approach is developed for the governing differential equations of memristor on the basis of Atangana‐Baleanu, Caputo‐Fabrizio, and Caputo fractal‐fractional differential operator. We discussed chaotic behavior of memristor under three criteria such as (i) varying fractal order, we fixed fractional order; (ii) varying fractional order, we fixed fractal order; and (ii) varying fractal and fractional orders simultaneously. Our investigated graphical illustrations and simulated results via MATLAB for the chaotic behaviors of memristor suggest that newly presented Atangana‐Baleanu, Caputo‐Fabrizio, and Caputo fractal‐fractional differential operators generate significant results as compared with classical approach.

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Section: Introductionmentioning

confidence: 99%

Mathematical analysis of memristor through fractal‐fractional differential operators: A numerical study

Abro

Atangana

2020

Math Methods in App Sciences

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“…In 34 Fetecau studied unsteady flow of an Oldroyd-B fluid generating by a constantly accelerating plate between two side walls. Sajad et al 35…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of (Cu−Al2O3) water based Maxwell hybrid nanofluids with Caputo-Fabrizio fractional derivative

Ahmad

Imran

Nazar

2020

Advances in Mechanical Engineering

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In this article, a free convection flow of [Formula: see text] hybrid Maxwell nanofluids through a channel formed by two infinite vertical plates have been studied. Together with the the energy balance and heat source, a fractional model of Maxwell fluid is considered. To develop an analytical exact solution for velocity field, only the Caputo-Fabrizio definition of non-integral derivative together with application of Laplace transform method has been used. Some graphical presentation and discussion are made to see the effects of hybrid nanofluids and non-dimensional parameters on velocity boundary layer. As a result, a dual behavior of velocity was exposed due to fractional parameter for large and small times. A comparison between two kind of non-Newtonian fluids has been made and found that Brinkman fluid is more viscous than Maxwell fluid. Also, by letting Brinkman and Maxwell parameters zero, they coincides and the results obtained for Newtonian fluid showed graphically. The obtained results are realistic from the fractional model as by adjusting the values of fractional parameter can be compared with some experimental data.

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“…They solved the second order homogeneous differential equation and generated the gamma function among the solutions of velocities and shears stresses. Although the studies of circular pipe and different fractional approaches can be continuous yet we end here by citing here few recent attempts, for instance, circular cylinder [17][18][19][20][21] and modern fractional differentiations (Caputo, [22][23][24] Caputo-Fabrizio, [25][26][27][28][29][30] Atangana-Baleanu 31,32,34,35 and comparison of Atangana-Baleanu and Caputo-Fabrizio [36][37][38][39][40][41][42] ). Motivating by above significant contribution, our aim is to incorporate the new comparative analysis based on modern fractional differentiation on infinite helically moving pipe.…”

Section: Introductionmentioning

confidence: 99%

Use of Atangana–baleanu Fractional Derivative in Helical Flow of a Circular Pipe

2020

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There is no denying fact that helically moving pipe/cylinder has versatile utilization in industries; as it has multi-purposes, such as foundation helical piers, drilling of rigs, hydraulic simultaneous lift system, foundation helical brackets and many others. This paper incorporates the new analysis based on modern fractional differentiation on infinite helically moving pipe. The mathematical modeling of infinite helically moving pipe results in governing equations involving partial differential equations of integer order. In order to highlight the effects of fractional differentiation, namely, Atangana–Baleanu on the governing partial differential equations, the Laplace and Hankel transforms are invoked for finding the angular and oscillating velocities corresponding to applied shear stresses. Our investigated general solutions involve the gamma functions of linear expressions. For eliminating the gamma functions of linear expressions, the solutions of angular and oscillating velocities corresponding to applied shear stresses are communicated in terms of Fox- H function. At last, various embedded rheological parameters such as friction and viscous factor, curvature diameter of the helical pipe, dynamic analogies of relaxation and retardation time and comparison of viscoelastic fluid models (Burger, Oldroyd-B, Maxwell and Newtonian) have significant discrepancies and semblances based on helically moving pipe.

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Thermodynamics of magnetohydrodynamic Brinkman fluid in porous medium

Cited by 43 publications

References 45 publications

Mathematical analysis of memristor through fractal‐fractional differential operators: A numerical study

Mathematical analysis of memristor through fractal‐fractional differential operators: A numerical study

Mathematical modeling of (Cu−Al2O3) water based Maxwell hybrid nanofluids with Caputo-Fabrizio fractional derivative

Use of Atangana–baleanu Fractional Derivative in Helical Flow of a Circular Pipe

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