Stability analysis of nanofluid flow past a moving thin needle subject to convective surface boundary conditions

In this research, the heat transfer performance of a nanofluid past a moving thin needle in the presence of thermal boundary condition is investigated. Three different types of nanoparticles, namely copper, alumina and titania are taken into consideration. The governing partial differential equations are transformed into nonlinear ordinary differential equations by using an appropriate similarity transformation. These equations are then solved numerically using bvp4c package in MATLAB software. The effect of the involved parameters of interest, including nanoparticle volume fraction, needle thickness, velocity ratio and convective parameter on the velocity and temperature profiles, as well as the skin friction coefficient and the local Nusselt number are illustrated through graphs. The stability of the dual solutions obtained has been conducted to know which of the upper branch or lower branch solution is linearly stable and physically relevant.