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Theoretical analysis of heat transfer plays a vital role in updating the quality of heat exchanger products. Experiments cost more compared to computational costs. In this direction, this work is concerned with the unsteady and incompressible fluid flow with a rod inside a square cavity. The disturbance in the flow is induced by the motion of the top and bottom walls of the cavity. The maximum fluid flow will arise, which will help in reducing the temperature of the heated wall or rod in any physical situation. A single wall is considered to be heated, which produces heat in the neighboring fluid layers. A rod is placed to reduce the motion of the heated fluid coming from the heated wall at a high-temperature. The transmission of thermal energy along with fluid flow is carried out using the energy equation and the Navier–Stokes equation of motion, respectively. These equations are transformed to dimensionless form by appropriate parametrization and solved using the finite element method for different parameters such as Rayleigh number and Prandtl number, temperature and velocity fields and are presented graphically [ABSTRACT FROM AUTHOR]