Magnetohydrodynamic fl ow in a permeable channel fi lled with nano fluid

In this paper, the problem of laminar magnetohydrodynamic nano uid ow in a porous channel is investigated. The Optimal Homotopy Asymptotic Method (OHAM) is used to solve this problem. In order to lessen CPU time, the Galerkin method is used to minimize the residual. This investigation was compared with a numerical method (fourthorder Rungekutte method) and found to be in excellent agreement. The base uid in the channel is water containing copper as a nanoparticle. The eective thermal conductivity and viscosity of nano uid are calculated by the Maxwell{Garnetts (MG) and Brinkman models, respectively. The in uence of the three dimensionless numbers: The nano uid volume fraction, Hartmann number and Reynolds number, are examined. The results indicate that velocity boundary layer thickness decreases with an increase in Reynolds number and nanoparticle volume fraction, and increases as Hartmann number increases.