A Fourth-Order Compact Finite Difference Scheme for Solving the Time Fractional Carbon Nanotubes Model.

N H Sweilam,Waleed Abdel Kareem,Zafer M Asker,Khloud R Khater

doi:10.1155/2022/1426837

Abstract

In this work, we deal with unsteady magnetohydrodynamic allowed convection inflow of blood with a carbon nanotubes model; the single and multiwalled carbon nanotubes of human blood are used as a based fluid. Two numerical methods used to study this model are the weighted average finite difference method and the nonstandard compact finite difference method. The proportional Caputo hybrid operator has been used to fractionalize the proposed model. Stability analysis has been construed by a kind of John von Neumann stability analysis. Numerical results are presented in diverse graphs, which manifest that the method is successful in solving the proposed model.

Highlights

Fractional calculus (FC) is a generalization of the integerorder calculus
To clarify the performance of the proposed method for solving the suggested model, we will study the effects of various flow parameters (α, φ, c, M, K, Pr, and Gr) that are distinguished in multifigures identifying the temperature and velocity profiles for blood. e influences of all the above parameters are displayed for human blood (SWCNTs and multiple-walled CNTs (MWCNTs)); the Pr is taken 21 and 25, respectively
(iv) Figure 5 shows the actions of the magnetic number on the velocity for both single wall and multiwall carbon nanotubes (CNTs), where it is a nondimensional number of the constant magnetic field that is the cause of Lorentz force that obverses the nanofluid velocity and resists motion, with the increasing M and the velocity decreasing in both cases

Summary

Introduction

Fractional calculus (FC) is a generalization of the integerorder calculus. Researchers try to solve problems with α-order derivatives and integrals, where there are several definitions for derivatives of order α [1, 2]. Oberlin et al [7] were the first to initiate the carbon nanotubes (CNTs) as nanoparticles in 1976. CNTs are one of the nanomaterials that are vastly used in such parts in the last years. CNTs have been used for thermal defence as thermal boundary materials. In 1995, a novel magnificence of warmth transferring fluids that may be engineered via placing metal nanoparticles in conventional heat transfer fluids became initiated by Choi [9]. 3D nanofluid waft with heat and mass transferring analysis is over a linear straight floor with convective boundary conditions Khan et al [10] discussed the slip waft of Eyring-Powell nanoliquid film containing graphene nanoparticles. 3D nanofluid waft with heat and mass transferring analysis is over a linear straight floor with convective boundary conditions

Methods

Results

Conclusion