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The present numerical study is conducted to investigate MHD mixed convection flow and heat transfer characteristics in a double-lid driven cavity with a heat-generating solid square block. The cavity horizontal walls are adiabatic while both the vertical lids are maintained at a uniform temperature Tc and velocity V0. The present study simulates a reasonable system such as air-cooled electronic equipment with a heat component or an oven with heater. Emphasis is sited on the influences of the position of the block in the cavity. The transport governing equations are solved employing the finite element formulation based on the Galerkin method of weighted residuals. The computation is carried out for a wide range of relevant parameters such as location of the block and Richardson number. Results are presented for the effect of aforesaid parameters on the contours of streamline and isotherm. Besides, the heat transfer rate in terms of the average Nusselt number and temperature of the fluid and block center are offered for the mentioned parametric values. The obtained results demonstrate that the flow and thermal field are strongly influenced by the above mentioned parameters.