Existence and stability of heat and fluid flow in the presence of nanoparticles along a curved surface by mean of dual nature solution

This study examines the possible existence and stability of the heat transfer solutions due to unsteady nanofluid flow over a curved surface. Alumina oxide (Al2O3) is considered as one of the important nanoparticles due to its potential use in various fields like purification of water, ceramics and insulation products. It is considered that the small quantity of nanoparticles is incorporated in the Ethylene Glycol to form the nanofluid. Mathematical form of the problem is obtained by using the fundamental laws of motion and heat transfer. These equations are modified for the presence of solid concentrations in an ordinary liquid. The complicated coupled unsteady system is transformed into non-dimensional form by the use of relevant transformations. The solution of nonlinear problem is produced by the use of numerical scheme, available in the form of BVP4C package in MATLAB. In the case of surface shrinking towards the surface, a reverse flow situation is also developed, and requires careful selection of solution by examining the stability of solution. Detailed stability analysis is carried, and critical values are determined for the possible existence of dual solutions. Moreover, various parameters variation is also analyzed by plotting graphs and tables. The numerical values are also calculated for the reduced Nusselt number and skin friction values caused due to variation in various flow parameters. Results have shown that for the curved shrinking surfaces, one should expect multiple solutions for a set of parameter values like mass suction, curvature, nanoparticles volume fraction and unsteadiness. The isotherms suggest linear decay of heat away from the surface. (C) 2019 Elsevier Inc. All rights reserved.