Series solutions of non-Newtonian nanofluids with Reynolds' model and Vogel's model by means of the homotopy analysis method

Heat transfer plays an important role in the handling and processing of non-Newtonian nanofluids. In this paper, the fully developed flowof an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid in coaxial cylinders is studied. Two illustrative models of variable viscosity, namely (i) Reynolds’ model and (ii) Vogel’s model, are considered. Analytic solutions of velocity, temperature, and nanoparticle concentration are first developed by the homotopy analysismethod (HAM), and then the role of pertinent parameters is illustrated graphically. Convergence of the obtained series solutions has been discussed explicitly and the recurrence formulae for finding the coefficients are also given in each case. © 2011 Elsevier Ltd. All rights reserved.