Application of artificial neural networks to the Cattaneo–Christov heat flux model in Jeffrey fluid flow with gyrotactic microorganisms over a stretching cylinder with variable fluid properties

The accurate modeling of heat and mass transfer in non-Newtonian fluids containing gyrotactic microorganisms is essential for applications in biotechnology, chemical engineering, and environmental processes. Existing studies rarely combine the Cattaneo–Christov heat flux model with Jeffrey fluid flow, gyrotactic microorganisms, and variable fluid properties in cylindrical geometries. This work fills that gap by formulating and analyzing such a model over a stretching cylinder, incorporating double stratification, heat generation, and chemical reactions. Due to the cylindrical geometry, mathematical formulations are based on cylindrical coordinates. The governing PDEs are reduced to ODEs via similarity transformations and solved using MATLAB’s bvp4c. An Artificial Neural Network (ANN) with the Levenberg–Marquardt algorithm (ANN-LMM) is trained on these solutions to provide rapid, accurate predictions of velocity, temperature, concentration, and microorganism distributions. The novelty of this study lies in integrating gyrotactic microorganism transport with the Cattaneo–Christov model for Jeffrey fluids and validating the ANN as an efficient surrogate to numerical solvers. The analysis reveals that the skin friction coefficient increases with the Deborah number ( β ) and curvature parameter ( α ) but decreases with the retardation times ratio ( λ 1 ) and stagnation variable ( A ). Furthermore, the density of motile microorganisms profile decreases with increasing values of the bio-convection Lewis number ( L e ), concentration difference parameter ( Ω ), bio-convection Peclet number ( P e ), and motile density stratification parameter ( S 2 ). Furthermore, the ANN is utilized to predict and verify the fluid velocity, temperature, concentration, and motile microorganism distribution across different parametric conditions. The sensitivity analysis was applied at the end, after the ANN, to classify the important parameters that have real significance.