The purpose of this study is the modeling a fibrous filter with random fibers, the simulation and the analysis of the effect of brownian and thermophoretic forces on the cupture of nanoparticles in the shallow fibrous micro-filters. In the present study is used from the one-way coupling, according to the motion of the particles is due to the motion of the base fluid. On this basis and in the euler approach,  the governing equations on the base fluid flow and heat transfer and in the lagrangian approach, differential equations governing on the dynamics of the particles (discrete phase) are obtained and solved numerically. In the lagrangian approach, the motion of nanoparticles and their Captured is simulated by using of the particle tracking and considering brownian and thermophoretic forces. The analysis of these equations was performed in view of euler and lagrange, considering small size in the finite element method (FEM). Next, a suitable method is provided for the numerical solution of the equations governing on the motion of nanoparticles and the simulation of the particle cupterd mechanisms, according to the type of equations and effective forces on the nanoscale. then, the results of this simulations are compared and validated with the previous research results. Finally, the results is provide for different gradients temperature, different size of the fiber and nanoparticles, density and fiber filtration layer in the form of design and efficiency diagrams. The results show that the dominant mechanism in the cupterd of particles below 100 nm is brownian diffusion. In this particles range, thermophoretic phenomenon has a little effect on the cupture of nanoparticle by filter fibers. Also, interception mechanism is more effective from brownian diffusion and thermophoretic mechanisms.