Oscillating flow of Jeffrey fluid in a rough circular microchannel with slip boundary condition

Abstract

By utilizing the perturbation method, approximate analytical solutions for velocity and volumetric flow rate are provided for oscillating flow of Jeffrey fluid in a rough circular microchannel with slip boundary condition. Meanwhile, the impact of relevant parameters on the flow is analyzed theoretically and graphically. A particular interest is given to the effect of slip length b¯ on velocity and volumetric flow rate at various angular Reynolds numbers Re. The key findings show that the velocity grows at low angular Reynolds number (Re=1) and reduces at high angular Reynolds number (Re=50) with increasing slip length b¯. As for the volumetric flow rate, it demonstrates a gradual growth pattern with slip length at Re=1. However, there is a slight initial rise followed by a decline as the slip length b¯ increases atRe=50. Moreover, an analysis is conducted on how wall roughness ε and wave numbers kaffect the volumetric flow rate across varying angular Reynolds numbers Re and slip lengths b¯. Observations reveal that larger values of parameters ε and k lead to reduced volumetric flow rates at Re=1, irrespective of the slip length. At Re=50, a decline in volumetric flow rate is induced by an increase in wall roughness ε for smaller slip lengths. Conversely, the inverse outcome holds when slip lengths are larger. Higher wave numbers k correlate with elevated volumetric flow rates, independent of the slip length. In light of the applications of oscillating flow and Jeffrey fluid in biomedical research, particularly in the study of human physiological systems such as blood flow, these findings are of significant importance.