Convection boundary layer flow past a moving thin needle in a nanofluid with stability analysis

This study focuses on the problem of steady laminar boundary layer flow past a continuously moving thin needle in a nanofluid. Four different problems are considered by using two types of nanofluid model which are Tiwari and Das (2007) and Boungiorno (2006) models. The Tiwari and Das (2007) model is applied for the first two problems, namely (i) forced convection flow past a moving horizontal thin needle in a nanofluid with slip effect and convective boundary condition and (ii) mixed convection flow past a moving vertical thin needle in a nanofluid. Meanwhile, the Boungiorno (2006) model is considered for the next two problems, namely (iii) free convection flow past a moving horizontal thin needle in a nanofluid with chemical reaction and heat generation and (iv) mixed convection flow past a moving vertical thin needle in a nanofluid with the magnetic field effect. The governing coupled partial differential equations are transformed into nonlinear ordinary differential equations by adopting suitable similarity transformations. The bvp4c solver is used to solve the given system of equations through MATLAB software. The influences of the governing parameters which include the needle thickness, velocity ratio, mixed convection or buoyancy, nanoparticle volume fraction, Brownian motion, thermophoresis, slip, convective or Biot number, chemical reaction, heat generation and magnetic on the characteristics of the flow, heat and mass transfer are analyzed. The physical quantities of interest such as the skin friction coefficient, the heat and mass transfer rate as well as the velocity, temperature and concentration distribution are graphically presented through graphs, and discussed further with the variation of governing parameters. Since all the problems possess dual solutions, the stability analysis is performed to identify which of the solutions are linearly stable. Validation of the present work is done by comparing the current results with those available in the literature and found to be in an excellent agreement. It is noticed in this work that the decrement in the needle thickness increases the skin friction coefficient, heat and mass transfer rate as well as widening the domain of the dual solutions obtained. Also, the study shows that the dual solutions exist when the needle surface and the buoyancy force are against the direction of the fluid motion. In Tiwari and Das problems, it is noted that the addition of nanoparticle volume fraction offers a greater skin friction coefficient. It also increases the heat transfer rate for the thin surface of the needle, and in the meantime decreases the heat transfer rate for the thick surface of the needle. Meanwhile, for the Buongiorno problems, it is found that the higher Brownian motion rate diminishes the heat and mass transfer rate in the flow. Similarly, the heat transfer rate decreases with higher values of the thermophoresis parameter, while the opposite effect is seen for the mass transfer rate. It is noticed in the stability analysis that the solution for the upper branch is always stable. Meanwhile, the solution for the lower branch indicates both stable and unstable solutions for the problem of forced convection flow. Nevertheless, other problems such as free and mixed convection flow, the lower branch solution represents an unstable solution