Finite element and neural computations for energy system containing conductive solid body and bottom circular heaters utilizing Ag–MgO (50:50)/water hybrid nanofluid

Abstract

This study investigates the natural convection of a hybrid nanofluid containing Ag–MgO (50:50) nanoparticles in water in a trapezoidal enclosure under the influence of Lorentz force. The cavity is heated from below by two semi-circular heaters containing a conductive solid body at the center. Galerkin finite element method is used to analyze the effects of various parameters such as Rayleigh number (103≤Ra≤106), conductivity ratio (10−2≤kr≤102), nanoparticle volume fraction (0≤ζ≤2%), Hartmann number (0≤Ha≤100), aligned magnetic field with angle (0o≤λ≤60o), side of solid central body (0.1L≤Ls≤0.4L) and diameter of circular heater (0.05L≤Dc≤0.4L) on heat transfer. The average Nusselt number decreases by 15%–20% with increasing cavity angle from 5 to 20 degrees (at Ra=5×104 and Ha=5), but adding just 1% of hybrid nanoparticles results in a 10% boost in heat transfer. Various training algorithms, including BFGS quasi-Newton, Resilient backpropagation, One step secant, Conjugate gradient, Bayesian regularization, and Levenberg Marquardt, are compared based on accuracy and computational time for input data generated from seven controlling parameters of heat transfer. Finally, the Levenberg Marquardt algorithm is used on two data sets for hot and cold walls with optimal neurons, and the genetic algorithm is used to predict the optimal values of the Nusselt number in a search space, which are verified with the particle swarm optimization algorithm. The minimum and maximum values for hot walls (Case I) were found to be 3.8005 and 17.5341, respectively, while for cold walls (Case II), the values were 0.9213 and 4.4434, respectively. These findings are significant for designing and optimizing cooling systems in various industries, including aerospace, automotive, and electronics.