Muco-ciliary flow with thermal and concentration analysis of Powell-Eyring fluid in the human airways

Abstract The thermal and concentration analysis of muco-ciliary transport in the human airways is important from a physiological perspective. This paper proposes a mathematical model of muco-ciliary two-layered fluid flow in a finite two-dimensional channel. The two-layered model is used because the human airways epithelium cell has both the periciliary liquid layer (PCL) and the airway ciliary layer (ACL). The Powell-Eyring fluidis used as an analogy for the viscoelastic mucus found in the airways. The formulated system of nonlinearpartial differential equations (PDEs) is first simplified by making use of low Reynolds number and longwavelength assumptions. The Adomian decomposition method is then used to solve the subsequent simplified system of nonlinear PDEs. The analysis focuses on the effects of important emerging parameters of interest on velocity, temperature, and concentration of ACL and PCL through graphs. The analysis also highlights the effects of relaxation time, viscous dissipation, and the rate of thermal diffusion. The results of this investigation showed that the suggested two-layered muco-ciliary model provides a better description ofmucus transport in the airways. The pressure gradient at the airways’ entrance shows a significant impacton the passage of mucus through the airways.