Weak nonlinear thermo bioconvection: Heat transfer via artificial neural network

The present study undertakes an analytical exploration of the onset of regular and chaotic thermo-bioconvection in a suspension of gravitactic microorganisms. Additionally, it employs a machine learning approach for numerical computation and prediction of heat transfer rates. The two-dimensional flow governing dynamics are modeled using the Hamilton-Crosser model for microorganisms. The amplitude of convection is determined by solving the cubic Ginzburg-Landau equation derived by applying the Lorenz technique. Stationary curves are plotted with thermal Rayleigh number and wave number, while Nusselt numbers are depicted over a range of time. The onset of chaotic motion is briefly discussed through Lyapunov plots and a bifurcation diagram. Further, to predict the heat transfer rate with multiple interconnected parameters, an artificial neural network is trained with the Levenberg-Marquardt algorithm to understand the underlying patterns of simulated data. The trained neural network is then employed to estimate the Nusselt number for various values of bioconvection Rayleigh number, bioconvection Lewis number, and bioconvection Péclet number. The values obtained from the artificial neural network models are compared with numerical data for validation and are found to be in good agreement. The findings of weak non-linear stability indicate that chaotic motion emerges in the system at the Hopf-Rayleigh number of 24.635, and fast-swimming microorganisms significantly increase the heat transfer rate. The coefficient of correlation is higher than 0.99, supporting the accuracy of developed ANN models to predict the Nusselt number with high accuracy. This observation supports the potential utilization of microbes in heat transfer applications.