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

The study focuses on the instability of local linear convective flow in an incompressible boundary layer caused by a rough rotating disk in a steady MHD flow of viscous nanofluid. Miklavčič and Wang's (Miklavčič and Wang, 2004) 9 MW roughness model are utilized in the presence of MHD of Cu-water nanofluid with enforcement of axial flows. This study will investigate the instability characteristics with the MHD boundary layer flow of nanofluid over a rotating disk and incorporate the effects of axial flow with anisotropic and isotropic surface roughness. The resulting ordinary differential equations (ODEs) are obtained by using von Kàrmàn (Kármán, 1921) 3 similarity transformation on partial differential equations (PDEs). Subsequently, numerical solutions are obtained using the shooting method, specifically the Runge-Kutta technique. Steady-flow profiles for MHD and volume fractions of nanoparticles are analyzed by the partial-slip conditions with surface roughness. Convective instability for stationary modes and neutral stability curves are also obtained and investigated by the formulation of linear stability equations with the MHD of nanofluid. Linear convective growth rates are utilized to analyze the stability of magnetic fields and nanoparticles and to confirm the outcomes of this analysis. Stationary disturbances are also considered in the energy analysis. The investigation indicates the correlation between instability modes Type I and Type II, in the presence of MHD, nanoparticles, and the growth rates of the critical Reynolds number. An integral energy equation enhances comprehension of the fundamental physical mechanisms. The factors contributing to convective instability in the system are clarified using this approach.