Metaheuristic optimization and sensitivity analysis of porous medium parameters for enhanced natural convection heat transfer under sinusoidal boundary conditions

In this study, natural convection flow within a porous cavity subjected to sinusoidal temperature boundary conditions is investigated using the multiple-relaxation-time Lattice Boltzmann Method. The main objective is to optimize and analyze the sensitivity of the porous medium characteristics to maximize heat transfer performance, expressed by the average Nusselt number. A design space is constructed based on four key parameters: porosity, Darcy number, Rayleigh number, and phase deviation. To efficiently explore this design space, a novel integrated framework is developed for the first time by combining Lattice Boltzmann Method, an Artificial Neural Network, and metaheuristic optimization algorithms, including Genetic Algorithm, Particle Swarm Optimization, and Grey Wolf Optimizer. Various tools were employed to implement the optimization process: initially, an artificial neural network was used for interpolation and regression, followed by several metaheuristic optimization algorithms such as genetic algorithm, particle swarm optimization, and grey wolf optimizer to identify the optimal design point. The multiple-relaxation-time Lattice Boltzmann method was applied to analyze and simulate the flow and heat transfer fields at each design point. The results indicate that the optimized configuration yields a maximum average Nusselt number, corresponding to specific values of porosity, Darcy number, Rayleigh number, and phase deviation. Among these, the Darcy number and phase deviation were found to have the most and least significant impact, respectively, on maximizing the average Nusselt number. These findings were further validated by the results of the global sensitivity analysis.