For the purpose of numerical simulations, we will use finite difference approximation to solve non-dimensional Navier-Stokes equations (NSEs) expressed by stream functions in the case of vorticity. The fluid flow inside T - shaped cavity is movement subject to laminar flow. The equations of motion and energy of the viscous fluid flow apply for a steady state of incompressible fluids. The fluid mechanics under this boundary is simulated in two dimensional domains" x and y". Under these boundary conditions we simulate the streamlines, vorticity, temperature distribution and velocity vector in x-y plane. The cavity driven by the horizontal velocities and solve the problem under two cases depends on the direction of velocities "parallel and anti-parallel wall motions". During the motion of the fluid inside the cavity, some vertices vorticity will appear, these vertices indicate that position and change its positions under changing the Reynolds numbers. The viscous fluid motion and energy are simulated under the Prandtl number is equal 1.96 and the Reynolds numbers taken at " Re=1, Re=100, Re=400, Re=800, Re=1200 and Re=2000".