Thermal Assessment of Maxwell–Sutterby fluid with gyrotactic microorganisms and activation energy effects induced by Riga plate via Levenberg–Marquardt algorithm

• Heat transfer is enhanced using Maxwell–Sutterby nanofluid flow over a Riga plate with joule heating and thermal radiation. • Nonlinear ODEs are solved using MATLAB’s bvp5c with the shooting method and Levenberg–Marquardt algorithm. • Nusselt number and fluid temperature rise with increasing Brownian motion, Hartmann number, thermophoresis, and radiation. • Statistical graphs and error histograms validate results for velocity, temperature, concentration, and microbe profiles. Enhancing thermal performance, nanofluids improve heat transfer efficiency in various biomedical engineering and industry applications. A steady flow of bioconvected Maxwell Sutterby nanofluid flow through the Riga plate is deliberated with heat and mass transferal in the presence of motile microorganisms. The impact of Joule heating magnetic field and time thermal conductivity is part of this investigation. For the motivation of the problem, the role of thermal radiation and activation energy, along with the convective boundary conditions, are considered. Appropriate similarity variables are assumed to renovate the set of controlling PDEs into nonlinear ODEs, which are then treated numerically via bvp5c MATLAB code with the help of the shooting method and Levenberg–Marquardt backpropagation algorithm. Regression-based statistical graphs and error histograms are used to examine the accuracy of the current technique. The influence of the prominent variables on non-dimensional velocity, non-dimensional energy, non-dimensional concentration and non-dimensional motile micro germs profiles is expounded via graphs, tables and literature. It is noted that the Nusselt number significantly rose as the values of Brownian motion, Hartmann number, and thermal radiation improved. The temperature of the fluid rises with higher values of thermophoresis, magnetic field, thermal radiation and Brownian motion.