A case study of heat transmission in a Williamson fluid flow through a ciliated porous channel: A semi-numerical approach

Williamson fluid with cilia motion helps to understand the non-Newtonian fluids' rheological characteristics and get better heat transmission rates. Thus, the current problem is intended to semi-numerically discuss the heat transmission in Williamson fluid flow through a ciliated channel under a Magnetic field and Porous Medium. Mathematical modeling of the intended problem complicates the PDE system in viscous dissipation. The complex system of PDEs is transformed from wave to fixed frame under the low Reynolds number and long wavelength approximation. Differential Transform Method (DTM) has been incorporated as an efficient semi -numerical technique to solve these dimensionless coupled nonlinear partial differential equations. The existence of a solution has been established with the DTM, and the outcomes of the boundary layer distribution are found in mathematical and graphical forms. The pertinent parameters are analyzed through graphs which are plotted by the software Mathematica. The current inves-tigation suggests that the conduction process escalates heat transfer through the molecules of the liquid. It is further noticed that enhancing the values of Darcy's parameter magnitude of the velocity profile rises due to an increase in the number of pores. Finally, the present study will provide significant applications in bioengineering, medical sciences, and medical equipment for the clearance of viscoelastic fluid from dust and viruses.

Automated summary

The aim of this study is to investigate the heat transmission in ciliated channels of Williamson fluid under a magnetic field and porous medium, in order to understand the rheological characteristics of non-Newtonian fluids and improve heat transfer rates. A mathematical model was developed for the problem and solved using the Differential Transform Method (DTM). The effects of various parameters on the boundary layer distribution were analyzed through mathematical and graphical representations. The study found that conduction process enhances heat transfer through the molecules of the liquid, and increasing the number of pores increases the magnitude of the velocity profile. The findings of this study have significant applications in bioengineering, medical sciences, and medical equipment for the clearance of viscoelastic fluid from dust and viruses.