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The objective of the current research paper is to investigate the effects of surface roughness on magnetohydrodynamic nonlinear mixed convection nanofluid flow over vertically moving plate. The highly coupled dimensional nonlinear partial differential equations (NPDE) are converted into dimensionless NPDE along with the boundary conditions with the help of non-similar transformations. The resulting set of dimensionless nonlinear PDE’s are solved by using Quasilinearization technique and implicit finite difference method. Impacts of various dimensionless parameters, namely, Brownian diffusion (Nb), nonlinear mixed convection ( ), nanoparticle buoyancy ratio (Nr), Lewis number (Le), thermophoresis (Nt), frequency (n), magnetic (M) and small parameter ( ) are studied in detail on profiles as well as gradients. The results reveal that increasing values of  increase the velocity profile, while increasing values of Nr decrease the same. Further, increasing values of and n exhibit sinusoidal variations on skin-friction coefficient, heat and nanoparticle mass transfer rates. Moreover, the presence of nonlinear mixed convection parameter has significant effects on fluid flow compared to its absence. In addition to this, rate of heat transfer is analyzed in presence and absence of nanoparticles.

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