The method of lines for solution of the carbon nanotubes engine oil nanofluid over an unsteady rotating disk
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The method of lines for solution of the carbon nanotubes engine oil nanofluid over an unsteady rotating disk Dumitru Baleanu1,2,3,a , R. Sadat4,b , Mohamed R. Ali5 1 Department of Mathematics, Cankaya University, Ankara, Turkey 2 Institute of Space Sciences, Magurele, Bucharest, Romania 3 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung,
Taiwan
4 Department of Mathematics, Zagazig Faculty of Engineering, Zagazig University, Zagazig, Egypt 5 Department of Mathematics, Benha Faculty of Engineering, Benha University, Benha, Egypt
Received: 20 May 2020 / Accepted: 7 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The main target of the present model is to find the idea of magneto-hydrodynamics incompressible nanofluid flow past over an infinite rotating disk. The effect of the magnetic field is existed to check the nanofluid flow. The single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) engine oil can be utilized despite carrier fluid for an unsteady rotating disk. Here, we transform the nonlinear system of differential equations to the dimensionless ordinary differential equation by using similarity transformation. Then, we use the numerical method of lines to solve the nonlinear ODE via the Runge–Kutta technique. The resultant of the velocity, Nusselt number and Skin friction is demonstrated under the effect of several factors. We note that when we increase the velocity of the rotating disk, fluid velocity and temperature are safely increased. Finally, we note that the outcomes obtained demonstrate that the SWCNTs nanofluids improved the heat transfer more than the MWCNTs.
1 Introduction The carbon nanotube (CNT) is desired for several scopes of engineering such as chemical and mechanical engineering. The concept of SWCNTs was settled by two schooling category [1, 2]. This investigation classified the CNTs into two portions denominated as (SWCNTs) and (MWCNTs). The thermophysical characteristic of the two classes of CNTs is performed from the tentative product in the immediate propriety utilizing engine oil like a standard fluid. The heat transmission through a flow of the fluid through the rotating disk is used in many fields such as fuel cells, medical tools and thermal energy manufacturing systems. Von Karman [3] approached the similarity transformation to constringe the system of PDE into System of ordinary differential equations by the dimensionless functions for the fluid flow over the rotating frame. Mustafa [4] devoted the exact solutions for transfer the mass and heat through MHD skid flow in nanofluids. Millsaps et al. [5] tested the heat transmit merits
a e-mail: [email protected] b e-mail: [email protected] (corresponding author)
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through the rotation of the disk. Rashidi et al. [6] explained the generation of entropy due to the porosity of the rotating d
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