Unsteady MHD flow of a fractional second grade fluid in a channel passing through a porous medium subject to a time-dependent motion of the bottom plate

• Published in: International journal of modern physics. B, Condensed matter physics, statistical physics, applied physics Vol. 38; no. 17
• Main Authors: Ullah, Ikram, Ul Haq, Sami, Khan, Zar Ali
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 10.07.2024; World Scientific Publishing Co. Pte., Ltd
• Subjects: Equilibrium flow; Fluid dynamics; Fluid flow; Graphs; Initial conditions; Integral transforms; Magnetohydrodynamic flow; Magnetohydrodynamics; Parameters; Plates (structural members); Porous media; Reynolds number; Shear stress; Steady state; Time dependence; Unsteady flow; Varnishes; Viscous fluids; MHD; Side walls; second-grade fluid channel; shear stress; exact solution; integral transformation
• ISSN: 0217-9792; 1793-6578
• DOI: 10.1142/S0217979224502138

The velocity of an unsteady flow of a viscous fluid of the second-grade MHD-type enclosed between two parallel side walls perpendicular to a plate was obtained by applying the integral transformation. The fluid is required to move by the plate, which over time t = 0 + subjected the fluid to shear stress. The solutions satisfy the given equation as well as the boundary and initial conditions, and they were separated into two types: steady state and transient state. Furthermore, through h → ∞ , we are able to recover the results found in the literature for motion across an infinite plate. Graphs depict the effect of the side walls and the time it takes to reach the steady state. The solutions are shown in graphs and discussed physically to examine the impact of different flow parameters. It is found that the fluid velocity decreases with an increasing fractional parameter β and second-grade parameter α . Also, it is noticed that the fluid velocity decreases with increasing values of Reynolds number and effective permeability. Numerous industrial products, including honey, paints, varnishes, coffee, chocolate and jelly, use this type of fluid flow concept.