Magnetohydrodynamic fl ow in a permeable channel filled with nano fluid

In this paper, the problem of laminar magnetohydrodynamic nanouid owin 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 tominimize the residual. this investigation was compared with a numerical method (fourthorderrungekutte method) and found to be in excellent agreement. the base uid in thechannel is water containing copper as a nanoparticle. the eective thermal conductivityand viscosity of nanouid are calculated by the maxwell{garnetts (mg) and brinkmanmodels, respectively. the inuence of the three dimensionless numbers: the nanouidvolume fraction, hartmann number and reynolds number, are examined. the resultsindicate that velocity boundary layer thickness decreases with an increase in reynoldsnumber and nanoparticle volume fraction, and increases as hartmann number increases.