This paper designs a non-collocated space sampling sensing and actuation methods for a class of convective diffusion equations with Neumann conditions. The non-collocated design is achieved by rationally allocating the regions of action of controllers and sensors. Luenberger-type observers estimate the system state by finite number of measurements, and output feedback is constructed by replacing the state values with the estimated values to reach the local exponential stabilization of the system. This paper demonstrates the feasibility of such non-collocated controller and observer design strategies and implements numerical simulations by using the finite difference method.