Sensitivity study on convective heat transfer in a driven cavity with star-shaped obstacle and hybrid nanofluid using response surface methodology

Sensitivity analysis is significant for understanding and measuring the impact of various parameters and input variables on heat transfer phenomena. The main objective of the current work is to examine the sensitivity of a numerical analysis of mixed convection in a lid-driven square cavity with a magnetic field. The cavity also contains a heated, star-shaped obstacle and is filled with a hybrid nanofluid. The sensitivity analysis was conducted employing the statistical response surface methodology (RSM), while the numerical simulations used the Galerkin weighted residual finite element approach to solve the governing PDEs. The study investigates the impacts of four dimensionless factors: <i>Ri</i>, <i>Re</i>, <i>Ha</i>, and <i>ϕ</i>. The numerical observation was made that there exists an upward trend between the average heat transfer rate with <i>Ri, Re,</i> and <i>ϕ</i>, while there exists a downward trend with <i>Ha</i>. Furthermore, the average heat transfer rate increases by almost half (49.54 %) when <i>ϕ</i> increases from 1 % to 10 % and decreases by 5.97 % when the <i>Ha</i> increases from 0 to 60. Finally, the statistical investigation of the current model and testing techniques imply that <i>R</i> ^<i>2</i> values for the response function are high (98.72 %), suggesting that this model is appropriate for estimating <i>Nu</i>.