Study of heat transfer in a nanofluid layer using homotopy analysis method

Abstract

In this paper, we perform a weak nonlinear stability analysis to study the heat transfer in a
horizontal nanofluid layer. We consider a set of new boundary conditions for the nanoparticle
fraction, which is physically more realistic. The new boundary condition is based on the
assumption that the nanoparticle fraction adjusts itself so that the nanoparticle flux is zero on the
boundaries. The governing equations for this problem are reduced to Ginzburg–Landau equation
and solved by using homotopy analysis method (HAM). Obtained results are valid for the whole
solution domain with high accuracy. Nusselt number and Nanoparticle Nusselt number are
calculated for different values of parameters. The results have been depicted graphically.