Heatline and sensitivity analysis of MHD nanofluid convection in a square enclosure with a circular heater: A comparative study using FEM, RSM, and ANN approaches

The heat transport in a square enclosure with a heated inner circular cylinder and nanofluid under the influence of magnetohydrodynamic (MHD) effects inside is investigated numerically in this work. The enclosure's top and bottom walls are thermally insulated, and the vertical walls are kept at a low temperature. A circular surface that generates internal heating induces thermal convection. To solve the steady-state natural convection problem, the two-dimensional mass, momentum, and energy equations are used. The finite element method (FEM) based on the Galerkin weighted residual approach, is incorporated to solve the governing equations. The radius of the circular heater ( 0.1 ≤ r ≤ 0.6 ), the Hartmann number ( 0 ≤ H a ≤ 60 ), the Rayleigh number ( 10 3 ≤ R a ≤ 10 6 ), and the nanoparticle volume fraction ( 0 ≤ ϕ ≤ 0.1 ) are all varied to conduct a thorough investigation. Heatlines, streamlines, isotherms, and 2D and 3D contour plots are used to display the thermal and flow behavior under various conditions. Response surface methodology (RSM) and Artificial Neural Networks (ANN) are employed to predict and optimize the average Nusselt number ( Nu av ), a key indicator of heat transfer efficiency, thereby enhancing thermal performance. In addition, sensitivity analysis (SA) is performed to evaluate how each input parameter affects Nu (average); the findings are displayed in two and three dimensions. By employing FEM data for optimization, the optimum parameter set is determined to be R a = 10 6 , H a = 0 , r = 0.1 , and ϕ = 0.1 , with a maximum N u (average) of 20.41. Moreover, with a coefficient of determination ( R 2 ) of 0.99 and a mean squared error (MSE) of 0.012, the ANN model demonstrates its efficacy as a reliable substitute for RSM by achieving a high prediction accuracy.