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A numerical study of the unsteady mixed convection heat transfer characteristics of an Ag–water nanofluid confined within a square shape lid-driven cavity has been carried out. The Galerkin weighted residual of the finite element method has been employed to investigate the effects of the periodicity of sinusoidal boundary condition for a wide range of Grashof numbers (Gr) (105 to 107) with the parametric variation of sinusoidal even and odd frequency, N, from 1 to 6 at different instants (for τ = 0.1 and 1). It has been observed that both the Grashof number and the sinusoidal even and odd frequency have a significant influence on the streamlines and isotherms inside the cavity. The heat transfer rate enhanced by 90% from the heated surface as the Grashof number (Gr) increased from 105 to 107 at sinusoidal frequency N = 1 and τ = 1.