Unsteady magnetohydrodynamic couple stress fluid flow from a shrinking porous sheet: Variational iteration method study

• Published in: Heat transfer (Hoboken, N.J. Print) Vol. 51; no. 2; pp. 2219 - 2236
• Main Authors: Reddy, G. Janardhana, Hiremath, Ashwini, Kumar, Mahesh, Bég, O. Anwar, Kadir, Ali
• Format: Journal Article
• Language: English
• Published: 01-03-2022
• Subjects: couple stress rheological liquid; MHD; polymer processing; shrinking sheet; unsteadiness; VIM
• ISSN: 2688-4534; 2688-4542
• DOI: 10.1002/htj.22397

Motivated by magnetic polymer manufacturing applications, the present research article examines theoretically the hydromagnetic boundary layer flow of an electrically conducting non‐Newtonian couple stress fluid due to a transient shrinking (contracting) porous sheet. The conservation partial differential equations for mass and momentum are rendered into a fifth‐order nonlinear ordinary differential equation via similarity transformations with associated boundary conditions. A semi‐analytical/numerical scheme employing Lagrangian multipliers and known as the variational iteration method (VIM) is implemented to solve the ordinary differential boundary value problem. Validation of the solutions is conducted by benchmarking against earlier Newtonian studies and very good agreement is achieved. A detailed assessment of the impact of couple stress (rheological), unsteadiness, magnetic body force parameter, and wall transpiration (suction/injection) parameter on flow characteristics is conducted with the aid of graphs. A significant deceleration in the flow is computed with increasing injection (acceleration is caused with greater suction) and acceleration is induced with higher unsteadiness parameter values. Increasing magnetic field (higher magnetic number) generates flow acceleration, rather than the customary deceleration, due to the shrinking sheet dynamics. A stronger couple stress effect manifests in strong retardation in the boundary layer flow and an increase in momentum (hydrodynamic|) boundary layer thickness. VIM demonstrates excellent convergence and accuracy and shows significant promise in studying further magnetic polymer fabrication flow problems.