Rates of mass transfer were measured at the inner surface of an annulus wrapped with a woven metallic screen under developing flow conditions using an electrochemical technique which involved measuring the limiting current of the cathodic reduction of potassium ferricyanide. Variables studied were screen characteristics, solution velocity, and physical properties of the solution. Mass-transfer rates based on the projected area of the annulus were found to increase by a factor ranging from 1.2 to 3 depending mainly on Re. The degree of mass-transfer enhancement was found to decrease with an increase in Re. Rates of mass transfer based on the true active area of the annulus and the screen were found to be smaller than the values at the smooth surface, the higher the Re the higher being the percentage decrease in the rate of mass transfer compared to the values at the smooth annulus. Practical implications of the present work in the design and operation of catalytic and electrochemical reactors used to conduct diffusion-controlled reactions have been highlighted.