The behavior of unsteady mixed convection flow of Cu-water based nanofluids is investigated numerically inside a square lid-driven partially heated flow below. Dual Reciprocity Boundary Element Method is used to solve stream function-vorticity form of the governing equations of the problem. The need of time integration scheme is eliminated by transforming the vorticity transport and energy equations to modified Helmholtz equations. This procedure also diminishes the stability problems. The numerical results are given for several values of Reynolds number (Re), Rayleigh number (Ra), heat source location (D), heat source length (B) and solid volume fraction (phi). The steady-state results are in good agreement with the results available in the literature.