Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

Symmetry Reductions of Boundary Layer Equations of Second Grade Fluids

Document Type : Original Article

Author
Emeritus Prof, Mechanical Engineering Department, Manisa Celal Bayar University
Abstract
Boundary layer flow of a second grade fluid is considered. Symmetry analysis has been applied to the equations. The arbitrary functions are the outer velocity appearing in the equations and the two functions in the boundary conditions. The specific forms of the outer velocity for which the principal Lie algebra extends is discussed first. For generalized boundary conditions with three arbitrary functions including the outer velocity, a further group classification is presented. The boundary conditions include classical no slip boundary layer flow, stretching/shrinking sheet flow, Falkner-Skan flow, flow with suction/injection, stagnation point flow and prescribed wall velocities. Group classification results are summarized in tables to guide the researchers. While the main aim in this study is to present a complete group classification for the outer velocity and the generalized boundary conditions, specific boundary conditions are also treated as an example. Flow due to stretching of the permeable plate with suction/injection is considered. With the aid of symmetries, the partial boundary value problem is reduced to an ordinary boundary value problem. It is shown that the reduced boundary value problem possesses exact solutions. While the impermeable wall and permeable wall with suction leads to one solution within the exponential family, the injection case leads to two solutions within the exponential family. This work can be used as a reference work in determining the existence of similarity transformations under various flow conditions for second grade fluids.
Keywords
Subjects

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Articles in Press, Accepted Manuscript
Available Online from 10 November 2026

  • Receive Date 26 September 2026
  • Revise Date 16 October 2026
  • Accept Date 07 November 2026
  • First Publish Date 10 November 2026
  • Publish Date 10 November 2026