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Steady-State Solutions for Two Mixed Initial-Boundary Value Problems Which Describe Isothermal Motions of Burgers’ Fluids: Application

Author

Listed:
  • Constantin Fetecau

    (Section of Mathematics, Academy of Romanian Scientists, 050094 Bucharest, Romania
    These authors contributed equally to this work and are co-first authors.)

  • N. Ameer Ahammad

    (Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Dumitru Vieru

    (Department of Theoretical Mechanics, Technical University of Iasi, 700050 Iasi, Romania)

  • Nehad Ali Shah

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
    These authors contributed equally to this work and are co-first authors.)

Abstract

Steady-state solutions of two mixed initial-boundary value problems are presented in equivalent forms. They describe isothermal permanent motions of incompressible Burgers’ fluids over an infinite flat plate that applies time-dependent shear stresses to the fluid. More exactly, they are the first exact solutions for motions of Burgers’ fluids with differential expressions of the shear stress or velocity on the boundary. The obtained results are designed to make equivalent solutions for motions caused by an infinite plate moving in its plane at velocities that seem to be similar to previous shear stresses. It is simple to limit all results for the purpose of providing efficient results for incompressible Oldroyd-B, Maxwell, second grade and Newtonian fluids undergoing comparable motions. They may also be used to estimate how long it will take to get to a steady or permanent state.

Suggested Citation

  • Constantin Fetecau & N. Ameer Ahammad & Dumitru Vieru & Nehad Ali Shah, 2022. "Steady-State Solutions for Two Mixed Initial-Boundary Value Problems Which Describe Isothermal Motions of Burgers’ Fluids: Application," Mathematics, MDPI, vol. 10(19), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3681-:d:936265
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    Cited by:

    1. Constantin Fetecau & Abdul Rauf & Tahir Mushtaq Qureshi & Dumitru Vieru, 2022. "Steady-State Solutions for MHD Motions of Burgers’ Fluids through Porous Media with Differential Expressions of Shear on Boundary and Applications," Mathematics, MDPI, vol. 10(22), pages 1-15, November.

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