Powell-Eyring fluid flow over a stratified sheet through porous medium with thermal radiation and viscous dissipation

W. Abbas; Ahmed M. Megahed; W. Abbas; Ahmed M. Megahed

doi:10.3934/math.2021780

AIMS Mathematics

2021, Volume 6, Issue 12: 13464-13479. doi: 10.3934/math.2021780

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Research article

Powell-Eyring fluid flow over a stratified sheet through porous medium with thermal radiation and viscous dissipation

W. Abbas ¹,
Ahmed M. Megahed ^{2
,
,}

1.
Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science, Technology and Maritime Transport, Cairo, Egypt
2.
Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

Received: 19 July 2021 Accepted: 06 September 2021 Published: 18 September 2021
MSC : 65L10, 76A05, 76D50, 76S05

The present study explores the effects of viscous dissipation, the thermal dependent conductivity and the thermal dependent viscosity on the steady motion of a Powell-Eyring fluid over a stratified stretching sheet which embedded in a porous medium. The fact that the nature of non-Newtonian flows problems are highly nonlinear equations has been taken into consideration here and this was the motive objective to determine numerical solutions. So, the emphasis is on the methodology adopted for obtaining numerical solutions that yielded after employing the Chebyshev spectral method. The temperature distributions and the velocity components are evaluated by solving numerically the boundary value problems that correspond to the proposed problem. Then, some figures have been plotted to elucidates the effect of different physical parameters appearing in the problem on both the temperature and the velocity profiles. The presence of the thermal radiation and the viscous dissipation in the fluid flow are shown to have quite a dramatic effect on the temperature profiles. In culmination, cooling process in nuclear reactors and geothermal engineering especially in the presence of thermal stratification phenomenon can be adopted as an application of this study. The theoretical and the observed results provide a fairly good qualitative agreement.
- Eyring-Powell fluid,
- thermal stratification,
- chebyshev spectral method,
- thermal radiation,
- porous medium
Citation: W. Abbas, Ahmed M. Megahed. Powell-Eyring fluid flow over a stratified sheet through porous medium with thermal radiation and viscous dissipation[J]. AIMS Mathematics, 2021, 6(12): 13464-13479. doi: 10.3934/math.2021780

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Abstract

The present study explores the effects of viscous dissipation, the thermal dependent conductivity and the thermal dependent viscosity on the steady motion of a Powell-Eyring fluid over a stratified stretching sheet which embedded in a porous medium. The fact that the nature of non-Newtonian flows problems are highly nonlinear equations has been taken into consideration here and this was the motive objective to determine numerical solutions. So, the emphasis is on the methodology adopted for obtaining numerical solutions that yielded after employing the Chebyshev spectral method. The temperature distributions and the velocity components are evaluated by solving numerically the boundary value problems that correspond to the proposed problem. Then, some figures have been plotted to elucidates the effect of different physical parameters appearing in the problem on both the temperature and the velocity profiles. The presence of the thermal radiation and the viscous dissipation in the fluid flow are shown to have quite a dramatic effect on the temperature profiles. In culmination, cooling process in nuclear reactors and geothermal engineering especially in the presence of thermal stratification phenomenon can be adopted as an application of this study. The theoretical and the observed results provide a fairly good qualitative agreement.

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