Study of heat transfer and flow of nanofluid in permeable channel in the presence of magnetic field

In this paper, laminar fluid flow and heat transfer in channel with permeable walls in the presence of a transverse magnetic field is investigated. Least square method (LSM) for computing approximate solutions of nonlinear differential equations governing the problem. We have tried to show reliability and performance of the present method compared with the numerical method (Runge-Kutta fourth-rate) to solve this problem. The influence of the four dimensionless numbers: the Hartmann number, Reynolds number, Prandtl number and Eckert number on non-dimensional velocity and temperature profiles are considered. The results show analytical present method is very close to numerically method. In general, increasing the Reynolds and Hartman number is reduces the nanofluid flow velocity in the channel and the maximum amount of temperature increase and increasing the Prandtl and Eckert number will increase the maximum amount of theta.