MHD effects on Casson fluid flow squeezing between parallel plates

Amal Al-Hanaya; Munirah Alotaibi; Mohammed Shqair; Ahmed Eissa Hagag; Amal Al-Hanaya; Munirah Alotaibi; Mohammed Shqair; Ahmed Eissa Hagag

doi:10.3934/math.20231507

AIMS Mathematics

2023, Volume 8, Issue 12: 29440-29452. doi: 10.3934/math.20231507

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MHD effects on Casson fluid flow squeezing between parallel plates

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671 Saudi Arabia
2.
Faculty of Science, Zarqa University, Zarqa 13110, Jordan
3.
Department of Basic Science, Faculty of Engineering, Sinai University, Ismailia, Egypt

Received: 20 August 2023 Revised: 03 October 2023 Accepted: 15 October 2023 Published: 30 October 2023
MSC : 35Qxx, 76Mxx

We introduce this work by studying the non-Newtonian fluids, which have huge applications in different science fields. We decided to concentrate on taking the time-dependent Casson fluid, which is non-Newtonian, compressed between two flat plates. in fractional form and the magnetohydrodynamic and Darcian flow effects in consideration using the semi-analytical iterative method created by Temimi and Ansari, known as TAM, this method is carefully selected to be suitable for studying the Navier-Stokes model in the modified form to express the studied case mathematically. To simplify the partial differential equations of the system to the nonlinear ordinary differential equation of order four the similarity transformations suggested by Wang (1976) are used. The TAM approach demonstrates a high degree of accuracy, efficiency, and convergence when applied to the resolution of both linear and nonlinear problems, and the results in this article are used to study the effect of the related factors like squeeze number Sq, Casson parameterβ, magnetohydrodynamic parameter Mg and permeability constant Mp and examining the skin friction coefficient effect. The velocity profile is studied numerically, which is tabulated and graphically represented to show and confirm the theoretical study. We can conclude that the success of the proposed method in studying time-dependent Casson fluid, which is non-Newtonian, compressed between two flat plates provides opportunities for additional study and advancements in fluid mechanics using the techniques.
- Casson fluid,
- squeezing,
- MHD fluid,
- Fractional Calculus,
- Semi-Analytical Iterative Approach,
- TAM method
Citation: Amal Al-Hanaya, Munirah Alotaibi, Mohammed Shqair, Ahmed Eissa Hagag. MHD effects on Casson fluid flow squeezing between parallel plates[J]. AIMS Mathematics, 2023, 8(12): 29440-29452. doi: 10.3934/math.20231507

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Abstract

We introduce this work by studying the non-Newtonian fluids, which have huge applications in different science fields. We decided to concentrate on taking the time-dependent Casson fluid, which is non-Newtonian, compressed between two flat plates. in fractional form and the magnetohydrodynamic and Darcian flow effects in consideration using the semi-analytical iterative method created by Temimi and Ansari, known as TAM, this method is carefully selected to be suitable for studying the Navier-Stokes model in the modified form to express the studied case mathematically. To simplify the partial differential equations of the system to the nonlinear ordinary differential equation of order four the similarity transformations suggested by Wang (1976) are used. The TAM approach demonstrates a high degree of accuracy, efficiency, and convergence when applied to the resolution of both linear and nonlinear problems, and the results in this article are used to study the effect of the related factors like squeeze number Sq, Casson parameterβ, magnetohydrodynamic parameter Mg and permeability constant Mp and examining the skin friction coefficient effect. The velocity profile is studied numerically, which is tabulated and graphically represented to show and confirm the theoretical study. We can conclude that the success of the proposed method in studying time-dependent Casson fluid, which is non-Newtonian, compressed between two flat plates provides opportunities for additional study and advancements in fluid mechanics using the techniques.

References

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