The how and heat transfer of a dusty fluid within the annulus of circular cylinders under a pulsatile pressure gradient has been studied. Using Saffman’s model for the dusty fluid the problem has been solved analytically and results discussed with the help of graphs. It is observed that the velocity of the fluid as well as that of the particle phase decreases with decrease of annular gap and increases with decrease of frequency of oscillation. The rate of heat transfer of fluid at the outer wall decreases with decrease of annular gap but the effect is opposite at the inner wall. The heat transfer rate increases with decrease of frequency of oscillation at both walls and the effect of volume fraction of dust particles is appreciable at large values of frequency of oscillation.