This investigation aims to analyze the effects of heat transport characteristics in the unsteady flow of nanofluids over a moving plate caused by a moving slot factor. The BRS variable is utilized for the purpose of analyzing these characteristics. The process of mathematical computation involves converting the governing partial differential equations into ordinary differential equations that have suitable similarity components. The Keller-Box technique is employed to solve the ordinary differential equations (ODEs) and derive the corresponding mathematical outcomes. Figures and tables present the relationship between growth characteristics and various parameters such as temperature, velocity, skin friction coefficient, concentration, Sherwood number, and Nusselt number. The results are assessed by comparing them to previous findings. The observation reveals that higher dimensionless reference temperature and variable values of the moving slot parameter have a suppressing effect on the velocity and temperature patterns of nanofluids. Higher values of the dimensionless reference temperature and moving slot parameter lead to enhancements in the Sherwood number, skin friction coefficient, and Nusselt number. The conductivity of the nanofluid is ultimately affected by these enhancements.

The primary aim of this research endeavor is to examine the characteristics of magnetohydrodynamic Williamson nanofluid flow past a nonlinear stretching surface that is immersed in a permeable medium. In the current analysis, the impacts of Soret and Dufour (cross-diffusion effects) have been attentively taken into consideration. Using appropriate similarity variable transformations, the governing nonlinear partial differential equations were altered into nonlinear ordinary differential equations and then solved numerically using the Runge Kutta Fehlberg-45 method along with the shooting technique. Numerical simulations were then perceived to show the consequence of various physical parameters on the plots of velocity, temperature, and concentration of the nanofluid flow. Boosting the magnetic, Williamson, porosity, and stretching sheet index parameters, the velocity of the fluid flow decreases. The temperature is enhanced as the Williamson and Brownian motion parameters upsurge, but it decreases as the Prandtl, thermophoresis, stretching sheet index, and Dufour parameters escalate. The concentration distribution decreases as the thermophoresis and magnetic parameters upsurge, but it escalates as the Soret, Schmidt, Brownian motion, and stretching sheet index parameters increase. Skin friction coefficient boosted as the stretching sheet index and magnetic parameters enhanced against the Williamson parameter. The findings from this study have been contrasted with earlier findings on local Nusselt numbers, which show substantial support and endorse the existing approach’s validity. The numerical values of the local Sherwood number gradually increase as the Schmidt, Soret, stretching sheet index, and thermophoresis parameters are upsurged.