Machine learning study for three-dimensional magnetohydrodynamics Casson fluid flow with Cattaneo-Christov heat flux using linear regression technique: Application in engineering science and technology

Abstract

This paper explores Casson fluid three-dimensional laminar steady flow across an expanding layer, including Cattaneo-Christov and magnetohydrodynamic impact. A similarity transformation is carried out and leads to a set of coupled ordinary differential equations representing the governing equations that are numerically solved using bvp4c in MATLAB. The paper uses artificial neural networking-based Levenberg-Marquardt scheme and machine learning-based linear regression model defined by Y=p1∗x+p2, which examine the interactions between the important parameters and fluid behavior. For scenario 1, the greatest coefficient of determination value is 0.9315, indicating a solid fit and effective analysis of the underlying pattern. The velocity profile depicts a reduction with an increase in the Casson fluid parameter, representing higher resistance to deformation. In contrast, in the concentration profile, a reduction with an increase in Lewis number is noted, showing lower mass transfer rates because of dominant thermal diffusion. Isothermal and contour plots of the Nusselt number show significant heat transfer variations, helping to analyze the thermal management aspects. The zero-error line indicates the least amount of error when the Casson fluid parameter is used, and the mean square error value ranges from 10‗−6 to 10‗−10. The Lewis number and heat flux indicate greater sensitivity to the Sherwood number and Nusselt number, respectively. Applications range from advanced energy-efficient technology, such as heat exchangers and cooling electronics, to healthcare and medical fields, such as medical bills, insurance, the simulation of blood flow in specific medical equipment, industries or food manufacturing systems, etc. To provide techniques for forecasting or a deeper knowledge of complex fluid dynamics for a variety of practical engineering and research objectives, the study integrates a numerical approach with machine learning.