Intelligent predictive networks for Cattaneo-Christov heat and mass transfer dissipated Williamson fluid through double stratification

Abstract

This study aims to develop an efficient predictive model for Cattaneo-Christov heat and mass transformation of dissipative Williamson fluid with the effects of double stratification (CCHMT-DWF-DS) using the Levenberg-Marquardt Backpropagation (LMA-BP) algorithm. The under-consideration Williamson fluid flow is magneto-hydro-dynamic, incompressible and two-dimensional through a stretching sheet. The mathematical model of nonlinear partial differential equations for physical phenomena is transformed into ordinary differential equations by means of renowned similarity transformations. The solutions of physical problem are computed by bvp4c technique through MATLAB. The LMA-BP is employed to train a backward neural network capable of accurately predicting velocity, temperature, and concentration profiles under various physical conditions such as changes in the Hartmann number $Ha$, Prandtl number $\mathrm{Pr}$, Schmidt number $Sc$, Williamson parameter $\lambda$, the relaxation time of temperature ${\gamma }_1$, the relaxation time of concentration ${\gamma }_2$, temperature stratification ${\delta }_1$, and concentration stratification ${\delta }_2$ for generating a variety of graphical outcomes and statistics. This research is significant for its innovative use of the LMA-BP in analyzing the complex dynamics of non-Newtonian fluids specifically the Williamson fluid, alongside the Cattaneo-Christov heat and mass flux model. The obtaining graphs have been discussed in detail. The thermal and solutal relaxation factors reduce heat and mass flow while fluid motion is delayed by the time-dependent parameter $\lambda$ and further reduced by the Hartman number. The Cattaneo-Christov heat flux model enhances simulation accuracy by integrating temporal delays in heat transfer, proving beneficial for sophisticated industrial and scientific endeavors related to non-Newtonian fluids. This analysis offers a powerful predictive tool for applications in thermal management, industrial cooling systems, and biomedical fluid dynamics, advancing machine learning in fluid mechanics.