Convection Dynamics of Nanofluids for Temperature and Magnetic Field Variations
This paper studies nonlinear stability and convection dynamics of temperature and magnetic variation on electrical conductivity of nanofluids. The system in Cartesian coordinates comprises a fluidic layer deals with exterior magnetic field, gravity and he
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Abstract This paper studies nonlinear stability and convection dynamics of temperature and magnetic variation on electrical conductivity of nanofluids. The system in Cartesian coordinates comprises a fluidic layer deals with exterior magnetic field, gravity and heat subjection in a chamber. The partial differential equations have been obtained from the equations of sustentation of energy and momentum; then, these equations are converted to three-dimensional differential equations set of nonlinear system similar to Lorenz equations. Applying time series and stability concept to investigate the consequence of temperature with magnetic force through Rayleigh and Hartmann numbers on the chaos transposition has been investigated for aluminum trioxide (Al2 O3 ), titanium dioxide (TiO2 ), zinc oxide (ZnO), silicon dioxide (SiO2 ) and copper oxide (CuO) nanofluids. Some kind of magnetic cooling has been observed which is indicated by the stabilization of chaos in nanofluid convection with the increase in the applied field or the Hartmann number. As the value of Rayleigh number increases, then system transits from stable to chaotic stage, and once the chaotic phase begins, system stability cannot be restored by controlling Rayleigh number. It is observed that among all nanofluids, CuO resists to chaotic stage for longer time in response to increase in temperature and Al2 O3 requires least increase in magnetic field intensity to get restored from chaotic to stable phase. It is concluded that variations in temperature and magnetic field cause transition of system from stable to chaotic and back to stable state, and also the electrical conductivity for different nanofluids decreases and increases, respectively. This phenomenon has a wider application in pharmacy, biosciences, health sciences, environment and in all fields of engineering. Keywords Phase portrait · Chaotic phase · Rayleigh number · Hartmann number · Nanofluids R. Bhardwaj · M. Chawla (B) Non-Linear Dynamics Research Lab, University School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University, Dwarka, Delhi 110078, India e-mail: [email protected] R. Bhardwaj e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 D. Gupta et al. (eds.), International Conference on Innovative Computing and Communications, Advances in Intelligent Systems and Computing 1165, https://doi.org/10.1007/978-981-15-5113-0_20
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R. Bhardwaj and M. Chawla
1 Introduction For the last few decades, the significance of chaotic behavior of dynamical (moving) system has been developing in nature. Chaos in conduction dynamics plays a vital role and has a vast application in the evolvement of dynamical systems in electrical, mechanical, magneto-mechanical, biological, chemical reaction or fluid flows. The extensive study on way to chaos in fluidic layer has been discussed by Lorenz [1] in which Bénard problem studied to figure the unpredicted weather convention. Lorenz considered a system of 2-D fluid chambers, which were cool down and heat up from below;
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