NEW RESULTS OF FRACTAL FRACTIONAL MODEL OF DRILLING NANOLIQUIDS WITH CLAY NANOPARTICLES

Ilyas Khan, Aisha M. Alqahtani, Arshad Khan, Dolat Khan, Abdul Hamid Ganie and Gohar Ali
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Ilyas Khan: Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
Aisha M. Alqahtani: ��Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia
Arshad Khan: ��Institute of Computer Sciences and Information Technology, The University of Agriculture, Peshawar
Dolat Khan: �Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Pakistan
Abdul Hamid Ganie: �Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Abha-Male 61421, Saudi Arabia
Gohar Ali: �Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Pakistan

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-9

Abstract: In recent years, a new idea of the fractal fractional derivative has been introduced. However, it is not used for the free convection flow drilling nanoliquid with clay nanoparticles. In this paper, we have deliberated this new approach of the fractal fractional derivative with a power-law kernel for heat transfer in a drilling nanofluid with clay nanoparticle in a vertical channel. Water is taken as the base fluid. The flow of the fluid is between two fixed vertical parallel plates such that one of them is constantly heated. The resulting problem is modeled with a fractal fractional derivative operator with a power-law kernel. As the exact solution to this problem is not possible, therefore, the Crank–Nicolson Finite Difference Scheme (CNFDS) is used for numerical solutions. This idea for the fractal fractional fluid problem is used here for the first time in the literature. Results are portrayed in the various graphs using Maple-15 software. The importance of both fractal and fractional parameters is discussed in detail. Results showed that the fractal fractional parameter gives a more general solution of the velocity and temperature for the fixed fractional operators. Therefore, a mutual approach of fractal fractional clarifies the memory of the function better than fractional only.

Keywords: Fractal Fractional Model; Drilling Nanoliquids; Clay Nanoparticles; CNFDS (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500244

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