Dual solutions in biomagnetic fluid flow and heat transfer over a nonlinear stretching/shrinking sheet: Application of lie group transformation method

Mohammad Ferdows; Ghulam Murtaza; Jagadis C. Misra; Efstratios E. Tzirtzilakis; Abdulaziz Alsenafi; Mohammad Ferdows; Ghulam Murtaza; Jagadis C. Misra; Efstratios E. Tzirtzilakis; Abdulaziz Alsenafi

doi:10.3934/mbe.2020264

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 4852-4874. doi: 10.3934/mbe.2020264

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Research article

Dual solutions in biomagnetic fluid flow and heat transfer over a nonlinear stretching/shrinking sheet: Application of lie group transformation method

1.
Research group of Fluid Flow Modeling and Simulation, Department of Applied Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
2.
Department of Mathematics, Comilla University, Comilla-3506, Bangladesh
3.
Central for Healthcare Science and Technology, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India
4.
Department of Mechanical Engineering, University of the Peloponnese, Patras, Greece
5.
Department of Mathematics, kuwait University P.O. Box 5969, Safat 13060, Kuwait

Received: 13 May 2020 Accepted: 08 July 2020 Published: 13 July 2020

Of concern in the paper is a theoretical investigation of boundary layer flow of a biomagnetic fluid and heat transfer on a stretching/shrinking sheet in the presence of a magnetic dipole. The problem has been treated mathematically by using Lie group transformation. The governing nonlinear partial differential equations are thereby reduced to a system of coupled nonlinear ordinary differential equations subject to associated boundary conditions. The resulting equations subject to boundary conditions are solved numerically by using bvp4c function available in MATLAB software. The plots for variations of velocity, temperature, skin friction and heat transfer rate have been drawn and adequate discussion has been made. The study reveals that the problem considered admits of dual solutions in particular ranges of values of the suction parameter and nonlinear stretching/shrinking parameter. A stability analysis has also been carried out and presented in the paper. This enables one to determine which solution is stable that can be realized physically, and which is not. The results of the present study have been compared with those reported by previous investigators to ascertain the validity/reliability of the computational results.
- dual solutions,
- stability analysis,
- biomagnetic fluid,
- magnetic dipole
Citation: Mohammad Ferdows, Ghulam Murtaza, Jagadis C. Misra, Efstratios E. Tzirtzilakis, Abdulaziz Alsenafi. Dual solutions in biomagnetic fluid flow and heat transfer over a nonlinear stretching/shrinking sheet: Application of lie group transformation method[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4852-4874. doi: 10.3934/mbe.2020264

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Abstract

Of concern in the paper is a theoretical investigation of boundary layer flow of a biomagnetic fluid and heat transfer on a stretching/shrinking sheet in the presence of a magnetic dipole. The problem has been treated mathematically by using Lie group transformation. The governing nonlinear partial differential equations are thereby reduced to a system of coupled nonlinear ordinary differential equations subject to associated boundary conditions. The resulting equations subject to boundary conditions are solved numerically by using bvp4c function available in MATLAB software. The plots for variations of velocity, temperature, skin friction and heat transfer rate have been drawn and adequate discussion has been made. The study reveals that the problem considered admits of dual solutions in particular ranges of values of the suction parameter and nonlinear stretching/shrinking parameter. A stability analysis has also been carried out and presented in the paper. This enables one to determine which solution is stable that can be realized physically, and which is not. The results of the present study have been compared with those reported by previous investigators to ascertain the validity/reliability of the computational results.

References

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