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 47 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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“…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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“…Haq et al [13] explored the e ects of magnetic eld with water functionalized metallic nanoparticles for squeezed ow over a sensor surface. In short, this study includes few latest references on nano uids [14][15][16], modern fractional derivatives [17][18][19][20][21][22], heat transfer [23][24][25][26][27], nanoparticles [28][29][30][31], porosity and magnetic eld [32][33][34][35][36][37], and few di erent circumstances [38][39][40][41][42][43]. Motivated by the above research work on nano uids, the purpose of this study is to investigate the analytic and mathematical performance of micropolar nano uid to enhance heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer on Fractionalized Micropolar Nanofluid over Oscillating Plate via Caputo-Fabrizio Fractional Operator

Yıldırım

Abro

2019

Scientia Iranica

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Nano uids and the enhancement of heat transfer in real systems have proved to be a widely researched area of nanotechnology; other areas of particular interest to researchers include the improvement of thermal conductivity, thermophoresis phenomenon, dispersion of nanoparticles volume fraction, and few others. Based on the touch of nanotechnology, this study investigates the analytic and mathematical performance of micropolar nano uid in the enhancement of heat transfer. The base uid is taken for the purpose of thermal conductivity subject to two types of nanoparticles: copper and silver. The mathematical analysis of the micropolar nano uid was carried out by invoking the non-integer order derivative and transform methods. By applying a mathematical tool to the equations of micropolar nano uid, the solutions were explored for temperature, microrotation, and velocity. In order to meet the physical aspects of the problem based on micropolar nano uid, the comparison of velocity eld of micropolar nano uid for the suspension of ethylene glycol into silver and that of ethylene glycol into copper is made to enhance the rate of heat transfer.

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Thermodynamics of magnetohydrodynamic Brinkman fluid in porous medium

Cited by 47 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

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

Heat Transfer on Fractionalized Micropolar Nanofluid over Oscillating Plate via Caputo-Fabrizio Fractional Operator

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