A detailed analysis has been performed for a heterogeneous photocatalytic Taylor vortex reactor that uses flow instability to recirculate fluid continually from the vicinity of the rotating inner cylindrical surface (coated with catalyst) to the stationary outer cylindrical surface of an annulus. A detailed time accurate computation when the reactor is started impulsively shows the different stages of flow evolution and the effects of finite length of the reactor in creating eddies, the overall effects of which shows very high efficiency of photocatalytic conversion. The physical arrangement considered is such that pollutant degradation is maximized by a combination of the controlled periodic illumination effect and the motion of fluid particles in a specific regime of centrifugal instability. It was found out that optimum Reynolds's number is 380 as the system reaches steady state faster, number of vortices per unit length is more, vortices move faster towards center from end, and the magnitude of both axial and radial component of velocity is more than at higher or lower value of Reynolds's number.