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Dual Solutions for Nonlinear Flow Using Lie Group Analysis.

Muhammad Awais1, Tasawar Hayat2, Sania Irum1

  • 1Department of Mathematics, COMSATS Institute of Information Technology, Attock, 43600, Pakistan.

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|November 18, 2015
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Summary
This summary is machine-generated.

This study explores dual solutions in magnetohydrodynamic (MHD) flow of upper-convected Maxwell (UCM) fluids over shrinking walls. Findings reveal how parameters like Deborah number and wall mass transfer influence fluid velocity profiles.

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Area of Science:

  • Fluid Dynamics
  • Magnetohydrodynamics
  • Non-Newtonian Fluids

Background:

  • Magnetohydrodynamic (MHD) flow is crucial in various industrial applications.
  • Understanding non-Newtonian fluid behavior, like that of upper-convected Maxwell (UCM) fluids, is essential.
  • Investigating flow over porous shrinking surfaces presents unique challenges.

Purpose of the Study:

  • To analyze the existence of dual solutions for MHD flow of UCM fluid over a porous shrinking wall.
  • To explore the influence of physical parameters on the flow characteristics.
  • To provide insights into the complex flow behavior under different conditions.

Main Methods:

  • Lie group analysis was used to simplify the governing nonlinear differential equations.
  • Absolute invariants were explicitly computed.
  • A shooting method was employed for numerical solution construction.

Main Results:

  • Dual solutions for the velocity profile of the UCM fluid were successfully computed.
  • The impact of Deborah number, Hartman number, and wall mass transfer on dual solutions was analyzed.
  • Streamlines illustrating suction and blowing effects were visualized.

Conclusions:

  • The study confirms the existence of dual solutions in this specific MHD flow scenario.
  • Key parameters significantly affect the fluid's velocity profile and flow patterns.
  • The findings contribute to the understanding of non-Newtonian fluid dynamics in porous media.