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

Abstract

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 investigation 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.

Keywords

• Williamson fluid model
• Porosity
• Heat dissipation
• MHD
• Differential Transform method