A semi-analytical and intelligent computing paradigm for thermal rheological response of biological nanofluid with brownian and thermophoresis diffusion effects

Abstract

This paper presents a novel feed advance neural network domain using the intelligent Bayesian regularized scheme to generate a numerical solution of the effect of Brownian and thermophoresis diffusion influence on Marangoni convection flow of Biological nanofluid along a sheet with thermophoretic particle deposition and induced magnetic field. The proposed model has significant implications for biological and technical applications based on heat and mass transfer. It enhances synovial nanofluid performance under produced magnetic fields, making it useful for drug delivery systems, targeted therapy, and artificial joint lubrication. Furthermore, the addition of thermophoretic particle deposition, Brownian motion, and Marangoni convection makes it perfect for microfluidic devices, cancer hyperthermia treatment, and advanced cooling systems that demand precise control over nanoparticle transport and thermal management. The numerical outcomes are presented as tables and graphs using the Homotopy analysis method (HAM). Variations in flow characteristics include velocity, temperature, solutal field profiles. The results show that the thermal field expands as the magnetic factor rises and the velocity profile declines. © 2026 The Authors