Effects of surface roughness on a couple stress fluid flow through corrugated tube

Fluid flow in micro-channels has been considered as one of the important research areas in the field of continuum mechanics due to its vast applications in biological sciences such as blood flow in arteries and capillaries. The channel walls of such fluid flows may exhibit some degree of roughness which influences the flow field functions such as rate of flow and fluid velocity. These flow problems can be modeled as couple stress fluid flows in axially corrugated pipes. This paper investigates the effect of surface roughness on the rate of flow and mean velocity of a couple stress fluid flow through a sinusoidal corrugated tube. The fluid motion is assumed to be steady and the Stokesian assumption of low Reynolds number is applied. Both longitudinal corrugations and transverse corrugations across the cross-section of the tube are studied. The boundary perturbation technique is employed to obtain the solution in each case. The total rate of flow and the mean velocity are obtained analytically in terms of the perturbation parameter up to order two. The results are represented graphically for different values of the couple stress viscosity coefficient, perturbation parameter and wave number of the corrugations. It is observed from the numerical results that the rate of flow decreases monotonically with the increase in the wave number for the case of longitudinal corrugations. For transverse corrugations, it is noticed that the wave number has a slight effect on the rate of flow. In addition, it is observed that the increase in the couple stress viscosity parameter results in a decrease in the flow rate for both cases. Finally, if the couple stress viscosity parameter is taken zero the case of classical viscous fluid flow is recovered.