MatLab Bvp4c Technique to Compute Thermophoresis and Brownian Motion in Nanofluid Flow Over a Transient Stretching Sheet

This physical phenomenon examined the transport mechanisms of heat and mass within a nanofluid thin film. The nanofluid thin film is situated over an unsteady stretching sheet, which is one of the pioneering contributions to the field, focusing specifically on the flow dynamics of nanofluid thin films. This foundational framework is established by Buongiorno’s fluid model. The mathematical model is applied for the evaluation of the nanofluid film, which adeptly weaves in significant phenomena, including Brownian motion as well as thermophoresis. The mathematical model is achieved in the form of non-linear partial differential equations (PDEs) for computation with the help of computer applications. Firstly, the analytical framework of similarity transformations is applied to non-linear PDEs to convert them into ordinary differential equations (ODEs). Secondly, these ODEs have been critically examined and prepared for coding in MatLab by reducing their high order into first order. The software Mathematica and MatLab have been employed to solve the boundary value problem (BVP). The built-in BVP4c solver is applied to obtain accurate solutions in the form of graphs and numerical values. The current analysis yields significant results revealing that both the free surface temperature and the volume fraction of nanoparticles tend to increase in response to variations in both unsteady conditions and magnetic parameters. Furthermore, the outcomes demonstrate that the interaction among diverse nanofluid variables with the phenomenon of viscous energy loss contributes to a reduction in the overall heat transfer rate. The potential effect of these proficient thermal management techniques is crucial, especially in microelectronics and energy systems.