Numerical Solution for Unsteady Acceleration MHD Third-Grade Fluid Flow in a Rotating Frame Through Porous Medium Over Semi-Infinite Boundary Condition with a Presence of Heat Transfer

Abstract

The aim of this work is to present a suitable numerical solution for unsteady non-Newtonian third-grade fluid which rotates at z -axis and pass through a porous medium. The fluid flows in magnetic field with constant acceleration and the semi-infinite boundary condition are highlighted. The fluid problem is also deal with heat transfer. The nonlinear partial differential equation is discretised using the finite difference method (FDM). The linear system obtained for three different domains (lengths). Consequently, the asymptotic interpolation method is merged to solve problems of large sizes. This hybrid method yielded results that satisfied the boundary condition that reaches zero as length grows to infinite length. For velocity profile and temperature distribution, a comparison of FDM and hybrid method is shown. It is discovered that the hybrid method produces better results than FDM for this infinitely large problem. Several analyses have been carried out to investigate the effect of various fluid parameter values. The findings reveal that as the porosity parameter increases, the velocity decreases. The Grashof and Prandtl numbers demonstrate the relationship to the temperature distributions. The effects of the magnetic field and the non-Newtonian parameters were also illustrated, as these parameters influence the velocity distribution of the fluid flow.

Theoretical Error Analysis of Hybrid Finite Difference–Asymptotic Interpolation Method for Non-Newtonian Fluid Flow

“…By using linearization and by assuming that Δa is very small, the equation is reduced to ½F ′ðaÞ − K½Δa 1 Δa 2 Δa 3 T = R, where K and R are a matrix with coefficient and a vector without coefficient of Δa i . Based on the findings obtained by Mahadi et al [26][27][28], the interest of this error analysis for asymptotic interpolation is Δa 1 . The comparison of Δa 1 and the error of solution is shown in Table 4.…”

“…Although the results are converging, the velocity profile began to slightly show a difference at η ≥ 2. Therefore, an asymptotic interpolation method is added to the system using a special function of y = a 1 + a 2 e −a 2 3 L [26][27][28]. The hybrid approach used the idea of the least square nonlinear to determine the best fit for each node.…”

“…The results fulfill the condition in (9) where the fluid's veloc-ity decreases as length increase. The validation of the hybrid method can be seen in [28].…”

“…Thereby, this current work presents a hybrid finite difference-asymptotic interpolation method to respond to its infinite boundary condition. This hybrid method has been applied in Mahadi et al [26][27][28]. The advantage of this hybrid method is the numerical solution obtained will be close to its exact solution.…”

An Investigation on Unsteady Flow of a Reactive Third-order material in a Cylindrical Channel Taking into Account Induced Electric Field and Variable Electrical Conductivity

“…Following the above assumption, the equation governing third-order fluid flow is given as [13,14,15,16]:…”