Stability Analysis of Mixed Convection Flow towards a Moving Thin Needle in Nanofluid

The problem of steady laminar mixed convection flow and heat transfer past a moving vertical thin needle in nanofluid for both assisting and opposing cases is analyzed in this paper. Three types of nanoparticles including copper, titania and alumina are taken into consideration. The nonlinear ordinary differential equations for momentum and energy have been transformed by adopting the similarity transformation in linear form. The problem is solved numerically using an implemented package called bvp4c in MATLAB software. The numerical computations are carried out for various parameters of interest, which consists of the velocity ratio parameter, mixed convection parameter, nanoparticle volume fraction parameter and the needle size. A stability analysis of the solution is performed showing that the upper branch solution is stable, while the lower branch solution is unstable. Validation of the present work is done by comparing the current results with those available in the existing literature and found to be in excellent agreement.