Abstarct: in this thesis, enhancement of Heat transfer in a two dimensional channel with infinite depth is investigate numerically. Two symmetric and isothermal parallel plates are considered as heat sources of the channel. Nano fluid, as the operating fluid, enters the channel with uniform velocity profile and specific temperature. The governing continuity, momentum and energy equations for laminar flow are derived and districted using a Finite Volume (FV) Method, applying First order Upwind Difference Skip (FUDS), and solved with SIMPLE algorithm. Nano fluid is assumed to be at two phase mixture model. A detailed study is conducted to highlight the influence of DA number and Nano particles’ volume fraction. The results indicate that using Nano fluid conclude Nu number enhancement by pressure gradient as well as Nano particles’ volume fraction increments simultaneously. Also channel is fully filled with the Aluminum’s mextal foam as the porous medium in order to enhance Nu number. Darcy-Brinkman equation is employed for porous medium. results reveal that also presence of porous medium modify Nu but unfavorably conducted to noticeably higher pressure gradient. Result addressing the increasing Nu and pressure gradient are conclude to reduction of Da number. Finally combination of Nano fluid and porous medium is recommended to optimize Nu and pressure gradient.it can be concluded that to achieve optimum results and avoiding higher pressure gradient, it is necessary to set select appropriate DA number