In this paper, the and fully developed flow with heat and mass transfer in a fuel cell channel with rectangular cross-section is investigated. The rectangular channel is straight and has a porous wall and three non-porous walls. The governing equations including the momentum and energy equations solved by a two-dimensional code (quasi-three-dimensional), and the velocity, pressure and temperature distribution curve along the channel, and non-dimensional flow parameters such as the friction coefficient and the Nusselt number in different aspect ratios are calculated and plotted. For the flow, the non-slip boundary condition is used and for the heat transfer, the usual boundary conditions in the fuel cell so that on the porous wall, the constant heat flux boundary condition is used and three other non-porous walls, constant temperature boundary condition The results show that for a given aspect ratio, the friction coefficient in the injection condition is greater than suction condition, and by increasing the amount of injection and suction, the difference between them increases. In addition, the value of friction coefficient unit aspect ratio 1 (square cross-section) is minimal for suction and ejection. The value of the Nusselt number is minimal at unit aspect ratio for both suction and injection. Also, the distribution of velocity and temperature along the channel as well as of parameters along with injection and suction and without it in different aspect ratios are plotted and discussed.