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<p>This paper explores the complex dynamics of time-dependent, two-dimensional flow of an incompressible fractional Nadeem trigonometric non-Newtonian (NTNN) fluid experiencing cosine oscillations in a rectangular duct caused by an external magnetic field. The primary goal is to find practical analytical solutions for the fluid flow described by a time-fractional derivative-based initial-boundary value problem. A method employing both Laplace and double Fourier sine transforms is used to simplify the governing equations. A detailed parametric analysis is performed to examine how the fractional order α, rheological parameter <i>N</i>, oscillation frequency ω, time <i>t</i> and magnetic field strength <i>M</i> affect the velocity profile and shear stress of the fluid. The results indicate that increasing values of α, <i>N</i>, ω and <i>t</i> lead to higher fluid flow, while stronger magnetic fields produce a damping effect. In certain limiting cases, the model reduces to the conventional NTNN and classical Newtonian fluid flows, thereby confirming the versatility and robustness of the analytical solution.</p>

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Exact solutions for the magnetised flow of fractional NTNN fluid subject to an oscillating rectangular duct

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Sohail Nadeem,
  • Sobia Naz,
  • Bushra Ishtiaq,
  • Jehad Alzabut

摘要

This paper explores the complex dynamics of time-dependent, two-dimensional flow of an incompressible fractional Nadeem trigonometric non-Newtonian (NTNN) fluid experiencing cosine oscillations in a rectangular duct caused by an external magnetic field. The primary goal is to find practical analytical solutions for the fluid flow described by a time-fractional derivative-based initial-boundary value problem. A method employing both Laplace and double Fourier sine transforms is used to simplify the governing equations. A detailed parametric analysis is performed to examine how the fractional order α, rheological parameter N, oscillation frequency ω, time t and magnetic field strength M affect the velocity profile and shear stress of the fluid. The results indicate that increasing values of α, N, ω and t lead to higher fluid flow, while stronger magnetic fields produce a damping effect. In certain limiting cases, the model reduces to the conventional NTNN and classical Newtonian fluid flows, thereby confirming the versatility and robustness of the analytical solution.