The ciliated flow of water-based graphene oxide and copper nanoparticles (GO-Cu/H₂O) in a complex permeable tube with entropy generation phenomenon

In recent years, thermal enhancement using the suspension of hybrid nanofluid has become useful to improve the heat transportation phenomenon in various engineering and industrial processes. The current investigation presents the thermal impacts of hybrid nanofluid with applications of ciliated motion through a cylindrical tube. The concentration of graphene oxide and copper nanoparticles is used in current formulations. Additionally, the physical influences of porosity parameters on the rheology and the heat analysis are examined. The rheological equations are modeled using cylindrical polar coordinates in the laboratory frame. The problem is simplified using two distinct assumptions: the lubrication theory and the long-wavelength estimate. The solutions of rheological equations are attained analytically using the integration technique. The obtained expressions for velocity profile, pressure gradient, temperature profile, and entropy production are described through graphs for numerous embedded parameters. The boundary layer (BL) occurrences are predicted in the axial velocity under higher porosity impacts. The transportation of the hybrid fluid is controlled with the help of the ciliated length. The present research is useful in the chemical processes of thermo-fluidic micro-pumps and devices of nanomaterials.