Chapter 4 - Homotopy Analytical Method

Abstract

In this chapter, the homotopy analysis method (HAM) is introduced for solving nonlinear differential equations arising in modern fluid problems. Involved problems include unsteady flow and radiation heat transfer of magnetohydrodynamic fluid over a horizontal continuously stretching surface, flow and heat transfer of nanofluids over a porous rotating disk with velocity slip and temperature jump, mixed convection boundary layer heat transfer of power law fluid over a moving conveyor along an inclined plate, and the MHD thermosolutal Marangoni convection heat and mass transfer of power law fluids driven by a power law temperature and a power law concentration. The effects of power law fluid viscosity on temperature field are taken into account here by us by assuming that the temperature field is similar to a velocity field with a modified Fourier's law. Approximate analytical solutions are obtained by using HAM and the effects of involved parameters on the velocity, temperature, and concentration fields are analyzed in detail.