Instability analysis of Reynolds nanofluid model for boundary layer flow of MHD NTNN fluid over a rotating disk with isotropic and anisotropic roughness

This work investigates the linear convective instability of magnetohydrodynamics MHD Nadeem trigonometric non-Newtonian (NTNN) fluid of Reynolds nanofluid over rough rotating disks with incompressible boundary-layer flows, using the MHD NTNN model to consider the effects of yield stress and shear-thinning on complicated fluids. We incorporate surface roughness effects with the NTNN model. New steady-flow profiles are derived, and shear-dependent viscosity is considered by extending the partial-slip roughness model. Linear stability analyses show the stabilizing effect of non-Newtonian fluids in the presence of certain types of surface roughness. This is observed in changes to the critical Reynolds number and the rates at which instabilities grow. When surface roughness, magnetic fields (MHD), Non-Newtonian, and nanofluids interact, Type I (inviscid crossflow) instability mode shows enhanced stabilization. Additionally, these factors show an effect on energy dissipation, total energy, and production terms, which further support this assumption. A similarity solution is used to simplify and numerically solve the governing nonlinear ordinary differential equations. The base flow solutions are computed using the BVP4C technique, which is based on a fourth-order Runge-Kutta scheme. The stability equations are then solved using the Chebyshev collocation method, which yields disturbance eigenfunctions and neutral stability curves for convective instabilities. Accordingly, across a range of parameter values, the neutral curves of convective instabilities in boundary-layer flow over a rotating disk can be determined, yielding information on the stability behaviour under different physical situations. The physical mechanisms are explained by an integral energy equation analysis, which shows that even in the presence of non-Newtonian effects, surface roughness and viscosity enhanced by nanoparticles maintain energy balance and flow stability. The findings presented in this study contribute to the knowledge of stability in boundary-layer flows, which can have significant implications for various fields such as fluid engineering and nanofluid methods.