# 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

## Authors

• Shafaruniza Mahadi Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Cawangan Johor, Kampus Segamat, Johor, Malaysia
• Yeak Su Hoe Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81318 Johor Bahru, Johor, Malaysia
• Norazam Arbin Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Cawangan Johor, Kampus Segamat, Johor, Malaysia
• Faisal Salah Department of Mathematics, College of Science and Arts, King Abdul-Aziz University, Rabigh, Saudi Arabia

## Keywords:

Hybrid method, rotating frame, porous medium, magnetohydrodynamic, 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.

## Author Biographies

### Shafaruniza Mahadi, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Cawangan Johor, Kampus Segamat, Johor, Malaysia

shafa669@uitm.edu.my

### Yeak Su Hoe, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81318 Johor Bahru, Johor, Malaysia

s.h.yeak@utm.edu.my

### Norazam Arbin, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Cawangan Johor, Kampus Segamat, Johor, Malaysia

noraz574@uitm.edu.my

### Faisal Salah, Department of Mathematics, College of Science and Arts, King Abdul-Aziz University, Rabigh, Saudi Arabia

faisal19999@yahoo.com

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2021-09-26

## How to Cite

Mahadi, S., Yeak Su Hoe, Norazam Arbin, & Faisal Salah. (2021). 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. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 87(2), 90–105. https://doi.org/10.37934/arfmts.87.2.90105

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