Neural network prediction of double-diffusive bioconvection in a rotating porous medium under internal heat, chemical reaction and gravity modulation

Exploring the classical three-dimensional problem, this work focuses on the stability of bioconvection in a rotating horizontal porous medium that is permeable and isotropic. The research adopts a novel perspective by examining the influence of internal heating, chemical reactions and gravity modulation within a double-diffusive fluid system characterized by gyrotactic micro-organisms. To analyze the instability characteristics, linear and weakly nonlinear stability analyses are employed. The linear stability analysis involves deriving a differential eigenvalue problem, which is then solved using the normal mode method. For the eigenvalue problem, an artificial neural network is used to predict the critical thermal Rayleigh number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msubsup> </mml:math> ), demonstrating strong agreement between numerical predictions and analytical solutions. The results indicate that an increase in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msubsup> </mml:math> enhances system stability by increasing the cell eccentricity. The cubic Ginzburg–Landau equation, solved using the Runge–Kutta method, provides insights into the nonlinear evolution of convection amplitude. Heat and mass transfer are analysed via Nusselt and Sherwood numbers, with graphical representations of their variations. The onset and development of convection, driven by temperature and solute concentration differences, generate convection cells. These cells are visualized through streamlines, isotherms, isohalines and micro-organism growth patterns, highlighting interactions between thermal, solutal and biological transport mechanisms.