The purpose of this study is to determine the effect of oscillating flow in a conduit in the absence of secondary flow on the rate of mass transfer to the wall, and the parameters that influence the magnitude of the change in the flux. Flow in an artery is pulsatile in nature and it will be shown in a later section that the model discussed in this paper, that of pulsating flow in a distensible tube is applicable to such flows. Nutrition of the arterial wall depends on the rate of diffusion of luminal plasma to and through the wall. This research is of importance in understanding the functioning of the cardiovascular system. It also finds application in the study of certain disorders of the artery. Another area of interest is in the study of diffusion controlled heterogeneous reactions in tubular reactors. The majority of the heterogeneous reactions and especially those of industrial importance are diffusion controlled. If pulsations bring about a change in the rate of diffusion as has been postulated, then a change in the rate of the diffusion controlled reaction will result. Two physical models are discussed in this paper. The first refers to flow in a rigid conduit with a periodic disturbance superimposed on a steady mean flow. The second case applies to flow in a distensible tube which is longitudinally constrained, and the steady flow is disturbed by a pulse wave progressing in the direction of flow.