  We study the critical dynamics of hyper-cubic finite size system in the
presence of quenched short-range correlated disorder. By using the random $T_c$
model A for the critical dynamics and the renormalization group method in the
vicinity of the upper critical dimension $d=4$, we derive in first order of
$\epsilon$ the expression for the relaxation time. Its finite-size scaling
behavior is discussed both analytically and numerically in details. This was
made possible by analyzing carefully the finite--size effects on the Onsager
kinetic coefficient. The obtained results are compared to those reported in the
literature.
