Optimization and sensitivity analysis of unsteady MHD mixed convective heat transfer in a lid-driven cavity containing a double-pipe circular cylinder using nanofluids

The present investigation focuses on optimizing and conducting a response surface analysis for unsteady laminar mixed convective heat transfer in a rectangular lid-driven cavity with a heated double-pipe utilizing water-based graphene nanofluid. The effects of an inclined magnetic field and a partially heater on the right wall of the cavity have been analyzed in this research. Firstly, the governing equations along with precise boundary conditions have been transformed into dimensionless form, then the resulting non-linear partial differential equations (PDEs) have been solved using the finite element method with the Galerkin weighted residual approach. The computational outcomes are obtained for a variety of physical and governing parameters, such as solid volume fraction (δ), heater length ( HL ), Richardson number ( Ri ), Hartmann number ( Ha ), inclination of magnetic field (ϕ), and non-dimensional time (τ). The simulation results show that the aforementioned parameters significantly affect the temperature distribution, flow pattern, average fluid temperature (θ av ) inside the cavity, and average Nusselt number ( Nu av ) at the heated surface. Optimization and sensitivity of the parameters namely solid volume fraction (δ), Richardson number ( Ri ), and Hartmann number ( Ha ) have been performed by using the response surface methodology, which entails creating a correlation equation that connects input variables to output responses to improve Nu av for better heat transfer efficiency. Variations in the Richardson number ( Ri ) and solid volume fraction ( δ ) have a significant impact on the heat transfer rate, contrary to the findings. In addition, nanofluid's flow behavior is notably influenced by the magnetic field and its orientation. Furthermore, the heat transfer rate increases by 18.23 % as the solid volume fraction, δ , enhances from 0.001 to 0.03 and by 68.22 % as the heater length, HL , rises from 0.1 to 0.5. However, as the Hartmann number rises from 0 to 100, the average heat transfer across the cavity decreases by 17.46 %. Additionally, the Nu av inside the cavity is positively sensitive to Richardson number ( Ri ) and solid volume fraction (δ), whereas negatively sensitive to Hartmann's number ( Ha ).