The characteristics of longitudinal dispersion enhancement by the flow oscillation are numerically studied according to various groove geometries in a 2-D channel in the present study. The length of expanded section l$_{1}$/h$_{1}$ is varied from 0 to 8.75. The oscillating flow condition is given at both side ends, i.e., u = Asin ($2{pi}ft$) The non-dimensional temperatures at both side ends are set to zero. The bottom and top walls are adiabatic. The local heat sources are located at the middle of the groove wall. In order to solve the governing equations, the SIMPIER algorithm is employed. The present results indicate that maximum longitudinal thermal dispersion can be achieved when the area ratio of the expanded section to the contracted section in the grooved channel becomes 1.