Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer

Abstract

The recent study was concerned with employing the finite element method for heat and mass transfer of MHD Maxwell nanofluid flow over the stretching sheet under the effects of radiations and chemical reactions. Moreover, the effects of viscous dissipation and porous plate were considered. The mathematical model of the flow was described in the form of a set of partial differential equations (PDEs). Further, these PDEs were transformed into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. Rather than analytical integrations, numerical integration was used to compute integrals obtained by applying the finite element method. The mesh-free analysis and comparison of the finite element method with the finite difference method are also provided to justify the calculated results. The effect of different parameters on velocity, temperature and concentration profile is shown in graphs, and numerical values for physical quantities of interest are also given in a tabular form. In addition, simulations were carried out by employing software that applies the finite element method for solving PDEs. The calculated results are also portrayed in graphs with varying sheet velocities. The results show that the second-order finite difference method is more accurate than the finite element method with linear interpolation polynomial. However, the finite element method requires less number of iterations than the finite difference method in a considered particular case. We had high hopes that this work would act as a roadmap for future researchers entrusted with resolving outstanding challenges in the realm of enclosures utilized in industry and engineering.

Unveiling the Power of Implicit Six-Point Block Scheme: Advancing numerical approximation of two-dimensional PDEs in physical systems

“…By applying the matrix inverse approach to solve the matrix Eq (8) for the unknown coefficients of z i , i = 0(1)8, where J = Θ −1 Z, or with the use of computer-aided tools like Mathematica 11.0. The obtained values are then used to replace (6) and set x = ϕh+x n+5 in order to get the form's continuous function;…”

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Compressible Non-Newtonian Fluid Based Road Traffic Flow Equation Solved by Physical-Informed Rational Neural Network

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Design of Finite Difference Method and Neural Network Approach for Casson Nanofluid Flow: A Computational Study

“…The proposed numerical scheme could solve various partial differential equations commonly encountered in science and engineering. Upon the conclusion of this study, it is feasible to suggest alternative applications for the present methods in conjunction with their existing uses [42][43][44][45]. Furthermore, the suggested approach is user-friendly and has the potential to be utilized when resolving a wider range of partial differential equations in the fields of science and engineering.…”