Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis

Liaquat Ali Lund, Zurni Omar, Ilyas Khan, Seifedine Kadry, Seungmin Rho, Irshad Ali Mari and Kottakkaran Sooppy Nisar
Additional contact information
Liaquat Ali Lund: School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Kedah
Zurni Omar: School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Kedah
Ilyas Khan: Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam
Seifedine Kadry: Department of Mathematics and Computer Science, Beirut Arab University, 115020 Beirut, Lebanon
Seungmin Rho: Department of Software, Sejong University, Seoul 05006, Korea
Irshad Ali Mari: KCAET Khairpur Mir’s & FAE, Sindh Agriculture University, Tandojam 70060, Pakistan
Kottakkaran Sooppy Nisar: Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser 11991, Saudi Arabia

Energies, 2019, vol. 12, issue 24, 1-17

Abstract: In this study, first-order slip effect with viscous dissipation and thermal radiation in micropolar fluid on a linear shrinking sheet is considered. Mathematical formulations of the governing equations of the problem have been derived by employing the fundamental laws of conservations which then converted into highly non-linear coupled partial differential equations (PDEs) of boundary layers. Linear transformations are employed to change PDEs into non-dimensional ordinary differential equations (ODEs). The solutions of the resultant ODEs have been obtained by using of numerical method which is presented in the form of shootlib package in MAPLE 2018. The results reveal that there is more than one solution depending upon the values of suction and material parameters. The ranges of dual solutions are S ≥ S c i , i = 0 , 1 , 2 and no solution is S < S c i where S c i is the critical values of S . Critical values have been obtained in the presence of dual solutions and the stability analysis is carried out to identify more stable solutions. Variations of numerous parameters have been also examined by giving tables and graphs. The numerical values have been obtained for the skin friction and local Nusselt number and presented graphically. Further, it is observed that the temperature and thickness of the thermal boundary layer increase when thermal radiation parameter is increased in both solutions. In addition, it is also noticed that the fluid velocity increases in the case of strong magnetic field effect in the second solution.

Keywords: heat transfer; micropolar fluid; slip conditions; viscous dissipation; dual solutions; stability analysis (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.mdpi.com/1996-1073/12/24/4617/pdf (application/pdf)
https://www.mdpi.com/1996-1073/12/24/4617/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jeners:v:12:y:2019:i:24:p:4617-:d:294433

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

More articles in Energies from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().