Gyrotactic microorganism's and heat transfer analysis of water conveying MHD SWCNT nanoparticles using fourth-grade fluid model over Riga plate

In this study, we explore the intricate conduct of gyrotactic microorganisms in a magnetohydrodynamic (MHD) nanofluid flow across a Riga plate, using the fourth-grade fluid model. The comprehensive investigation encompasses a few influential parameters, including non-dimensional viscoelastic parameter α1, cross-viscous parameter α2 third-grade fluid parameters α3, fourth-grade fluid parameters α4, fourth-grade fluid parameter α5, Modified Hartman number M, local Reynolds number Re, and the inverse Darcy number Da⁻¹. Furthermore, the effects of slip parameters S₁,S₂,S₃ and thermophoretic parameter τ on velocity, temperature, and concentration profiles are inspected. The conclusions demonstrate that the manipulation of these parameters leads to substantial modifications in the patterns of fluid flow, heat transfer, and concentration distributions. The findings offer significant contributions to the understanding of the intricate dynamics of gyrotactic microorganisms in magnetohydrodynamic (MHD) nanofluid flows, hence enhancing our comprehension of their behaviours and interactions. This research contributes to the enhancement of knowledge regarding fluid flows influenced by biological factors and exhibits sizable potential for a wide range of applications.