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The main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.

The non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

The results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.

AI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

This study aims to focuse on the flow behavior of a specific nanofluid composed of blood-based iron oxide nanoparticles, combined with motile gyrotactic microorganisms, in a ciliated channel with electroosmosis.

This study applies a powerful mathematical model to examine the combined impacts of bio convection and electrokinetic forces on nanofluid flow. The presence of cilia, which are described as wave-like motions on the channel walls, promotes fluid propulsion, which improves mixing and mass transport. The velocity and dispersion of nanoparticles and microbes are modified by the inclusion of electroosmosis, which is stimulated by an applied electric field. This adds a significant level of complexity.

To ascertain their impact on flow characteristics, important factors such as bio convection Rayleigh number, Grashoff number, Peclet number and Lewis number are varied. The results demonstrate that while the gyrotactic activity of microorganisms contributes to the stability and homogeneity of the nanofluid distribution, electroosmotic forces significantly enhance fluid mixing and nanoparticle dispersion. This thorough study clarifies how to take advantage of electroosmosis and bio convection in ciliated micro channels to optimize nanofluid-based biomedical applications, such as targeted drug administration and improved diagnostic processes.

First paper discussed “Numerical Computation of Cilia Transport of Prandtl Nanofluid (Blood-Fe₃O₄) Enhancing Convective Heat Transfer along Micro Organisms under Electroosmotic effects in Wavy Capillaries”.