Chaotic characteristics of thermal convection at smaller verse larger Prandtl number through fractal and fractional differential operators from nanofluid

ABSTRACT

Nanofluids with a smaller and larger Prandtl number reflect the dominations of thermal diffusivity and momentum diffusivity, respectively. This fact shows how much heat is carried away by how much fluid through transference from one point to another point. For the sake of the above fact, the thermal convection at a smaller versus larger Prandtl number through fractal and fractional differential operators is investigated from the nanofluid on the basis of certain nanoparticles and base fluid. The nanofluid as a base fluid is ethylene glycol and nanoparticles are titanium dioxide, copper, silver and aluminium oxide. For the first time in the literature, mathematical modeling is proposed via fractal and fractional differential operators of Caputo-Fabrizio and Atangana-Baleanu. The numerical schemes of chaotic models have been presented by invoking the Adams-Bashforth-Moulton method as a powerful technique for simulations. The thermophysical properties of the nanofluid have been traced out chaotically by comparative analysis of fractal and fractional differential operators of Caputo-Fabrizio and Atangana-Baleanu. Finally, two-dimensional chaotic attractors, three-dimensional chaotic attractors and each type of nanoparticle have been discussed for smaller, medium and larger values of Prandtl number by emphasizing the role of fractal and fractional differential operators.

KEYWORDS:

• Role of Prandtl number
• fractal and fractional differential operators
• nanofluid and nanoparticles
• numerical schemes and simulations

Acknowledgments

The authors acknowledge the Deanship of Scientific Research at King Faisal University for the financial support under RAE’D track (Grant No. 207009).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author(s) reported that there is no funding associated with the work featured in this article.

Notes on contributors

Kashif Ali Abro

Dr. Kashif Alli Abro received his Bachelor’s degree in Mathematics from University of Sindh Jamshoro Pakistan, and M.Phil. and PhD in Applied Mathematics from the NED University of Engineering and Technology, Karachi, Pakistan. Whilst he did his post doctorate in Applied Mathematics from the University of the Free State, Bloemfontein, South Africa. He is presently working as an Assistant Professor in the Department of Basic Sciences and related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan. His research interests are: Fractional Calculus (Modern Fractional Operators) and Modern Control Engineering. He is also author of 117 international research papers.

Basma Souayeh

Basma Souayeh is currently working in Physics Department at King Faisal University as an Associate Professor and a Scientific Researcher. She is also a member of Fluid Mechanics Laboratory in Tunisia. She has completed her BS Degree in University of Tunis El Manar, Tunisia. Ms Degree and Ph. D degree (URPF Lab) done in the same University, in years 2010, 2012 & 2017, respectively. She has been involved in teaching and research since 2012. Her research skills focused on the following areas: Computational physics, Mechanical Engineering, Thermal Engineering, Energy, Computational Fluid Mechanics, Numerical Simulation, Numerical Modeling, CFD Simulation, Finite Volume Method, Finite Difference Method, Engineering Thermodynamics, Energy Engineering, Heat and Mass Transfer, Nanofluids, CFD coding, Fluid flow and Mechanics.

Kamran Malik

Dr. Kamran Malik received his Bachelor’s, Master's, M.Phil. and PhD degree (in Applied Mathematics) from University of Sindh Jamshoro Pakistan, He is presently working as an Assistant Professor in the Department of Mathematics, Government College University Hyderabad, Pakistan. His research interests are: strength of materials, quadrature, cubature, numerical analysis. He is also author of 11 international research papers.

Abdon Atangana

Dr. Abdon Atangana received his B.Sc. Bachelor (Pure Mathematics), B.Sc. Honors (Applied Mathematics), M.Sc. (Applied Mathematics), PhD (Geohydrology) from University of the Free State South Africa. He is currently a full research professor at the Faculty of Natural and Agriculture Science in University of the Free State South Africa. His research interests are fractional calculus and control system identifications.