| Summary: | Understanding fluid dynamics and heat transfer is crucial for designing and improving various engineering systems. This study examines the heat transfer characteristics of a buoyancy-driven natural convection flow that is laminar and incompressible. The investigation also considers entropy generation (<i>E<sub>gen</sub></i>) within an octagonal cavity subject to a cold cylinder inside the cavity. The dimensionless version of the governing equations and their corresponding boundary conditions have been solved numerically using the finite element method, employing triangular mesh elements for discretization. The findings indicated that incorporating a cold cylinder inside the octagonal cavity resulted in a higher heat transfer (HT) rate than in the absence of a cold cylinder. Furthermore, using the heat flux condition led to a higher average Nusselt number (<i>Nu<sub>avg</sub></i>) and a lower Bejan number (<i>Be</i>) than the isothermal boundary condition. The results also showed that HT and <i>E<sub>gen</sub></i> were more significant in the Al<sub>2</sub>O<sub>3</sub>-H<sub>2</sub>O nanofluid than the basic fluids such as air and water, and HT increased as χ increased. The current research demonstrates that employing the heat flux condition and incorporating nanoparticles can enhance the rate of HT and <i>Egen</i>. Furthermore, the thermo-fluid system should be operated at low <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>a</mi></mrow></semantics></math></inline-formula> to achieve greater HT effectiveness for nanofluid concerns.
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