Thermal and concentration analysis of two immiscible fluids flowing due to ciliary beating

Abstract

This article explores the flow properties with mass and heat transfer of multilayered flow of two immiscible fluids (Phan-Thien-Tanner and Jeffrey fluid models) flowing due to ciliary beating in a channel, which is beneficial in different applications related to bioengineering, biomedical sciences, and medical equipment. Ciliated epithelium in airways is covered with airway surface liquid, which is mainly composed of two different layers. The first one is the mucus layer (Phan-Thien-Tanner fluid), which is a non-Newtonian, viscoelastic fluid, and the second layer is the periciliary liquid layer, which is considered the Jeffery fluid model. The fluid is considered to be incompressible, and layers of fluid do not mix with each other. The fluid flow with mass and heat transfer is first modeled as a wave and then transformed into a fixed frame. Exact solutions for stresses, velocity, temperature, and concentration profiles are obtained by simple integration. The behavior of emerging factors is shown graphically (plotted in MATHEMATICA 13.0) in the results section. The key findings from the graphical results show that the middle layer of fluid has the greatest magnitude for velocity and temperature, while the outer layer has the greatest concentration profile. This analysis may be helpful in keeping the airways clear from inhaled pollutants like viruses and bacteria.

Keywords

• Ciliary flow
• PTT fluid model
• Jeffrey fluid model
• Exact solution
• Heat transfer
• Two layer flow