Numerical solution of nanofluid flow over a permeable stretching and shrinking surface using BVP4C solver

This study investigates nanofluid flow over a permeable stretching/shrinking surface using BVP4C. This study utilises copper and silver nanoparticles to examine how well the two nanoparticles transfer heat. The aim of this study is to apply the similarity transformation to convert the partial differential equation (PDE) to an ordinary differential equation (ODE). The objective is to solve nanofluid flow over a permeable stretching/shrinking surface by using BVP4C. BVP4C in MATLAB software is then used to solve this equation numerically. The study then compares the results between the previous method which is the shooting method, and BVP4C, thus identifying the impact of copper and silver nanoparticles on the stretching/shrinking surface that influence the efficiency of heat transfer by analysing and measuring the nanoparticles in velocity profile, temperature profile, skin friction coefficient and local Nusselt number. The comparison demonstrates strong agreement between the computed skin friction coefficient and local Nusselt number obtained using BVP4C. The obtained result indicates that in the stretching case, the velocity profile, temperature profile, and boundary layer thickness decrease, but in the shrinking case, the velocity profile, temperature profile, and boundary layer thickness increase. In addition, the skin friction coefficient of silver is higher than that of copper, which contributes to a decrease in the velocity boundary layer. Meanwhile, the local Nusselt number of silver nanoparticles are higher than that of copper, indicating a higher rate of heat transfer for silver.