Analysis of three-dimensional boundary-layer nanofluid flow and heat transfer over a stretching surface by means of the homotopy analysis method

Abstract

In this paper, an investigation is made of the three-dimensional flow and heat transfer of a nanofluid in the boundary-layer region over a flat sheet stretched continuously in two lateral directions. With the help of a series of similarity transformations, this problem is reduced to a set of three coupled differential equations. The homotopy analysis method (HAM) is then applied to derive the explicit solutions for both the velocity and the temperature distributions. A mathematical analysis shows that these solutions decay exponentially at far field. Besides, the influences of the nanoparticle volume fraction ϕ on the velocity and temperature profiles, as well as the reduced local skin friction coefficients and the reduced local Nusselt numbers are studied. It is found that the heat transfer conductivity of the nanofluid is superior to that of the pure fluids.