Fractional modeling and synchronization of ferrofluid on free convection flow with magnetolysis
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Fractional modeling and synchronization of ferrofluid on free convection flow with magnetolysis Aziz Ullah Awan1, Samia Riaz2 , Samina Sattar2 , Kashif Ali Abro3,4,a 1 Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan 2 Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan 3 Institute of Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State,
Bloemfontein, South Africa
4 Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology,
Jamshoro, Pakistan Received: 21 July 2020 / Accepted: 9 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The dispersion of ferromagnetism in free convection flow can lead the magnetization process in reduction due to misalignments of the magnetic domains. In this context, an intensive viscoelastic model is subjected to the magnetization process through non-integerorder differentiation based on singular kernel. The geometry of the problem is tackled for vertical tunnel on the basis of width d saturated by porous medium in which oscillating pressure gradient is invoked. The non-fractional governing equations have been treated for dimensionality of homogeneity. The fractionalized solutions for dimensionless velocity, temperature and Nusselt number have been investigated by employing the techniques of Laplace transforms with its inversion. The magnetized mathematical model has been disseminated for the sake of physical parameters subject the variants in fractional parameter. Finally, our results have been emphasized for rheological parameter so-called Peclet number, Reynolds number, magnetic parameter, Grashof number, Prandtl number on the variants of fractional time Caputo parameter.
1 Introduction The heat and flow properties of Newtonian and Non-Newtonian fluids are very different from each other. Non-Newtonian fluids have gained much attention of the researchers due to their vast applications in the applied areas such as in geophysics, chemical engineering and biological systems. Paper coating, food, plastic, fiber, greases and polymer are the behavior of non-Newtonian fluids in industry. Due to the complex flow behavior of non-Newtonian fluids, Navier–Stokes equations are not enough to describe their properties of. In this regard, many models have been presented [1–7]. Simple models such as Power law is used in those fluids where viscosity is shear dependent, and it can not presume the consequences of elasticity. Grade two or three models describe the consequences of elasticity, but in these models viscosity is not shear dependent [8,9]. These simple models can not predict the effect of stress relaxation.
a e-mail: [email protected] (corresponding author)
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Mixed convection has a vital role in the channel flow particularly in nuclear power and thermal. Mixed convection flow occurs in cha
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