Heat transfer analysis of Phan Thien Tanner peristaltic-ciliary fluid flow at distinct sagittal cross-sections in a narrow heated tube

Abstract

Analysing how heat transfer affects the transportation of embryos in the human female fallopian tube is a significant physiological concern. This theoretical analysis accords with the peristaltic-ciliary flow of Phan Thien Tanner (PTT) fluid in a finite heated narrow tube. The analysis focuses on the effects of geometric and PTT fluid model parameters, variations in geometry by encompassing five distinct sagittal cross-sections, and heat transfer dynamics. The subsequent formulated set of linear partial differential equations is simplified using the long wavelength and smaller Reynolds number assumptions and then solved for exact analytic solutions. Metachronal wave parameter ϵ, Brinkmann number Br, amplitude ratio ϕ, pressure gradient at the tube entrance ξ, elongation parameter ep, and Weissenberg number We emerged as geometric and PTT fluid model parameters. At all selected sagittal cross-sections, axial velocity and temperature decrease as ξ, ep, and We increase. The impacts of ϵ and ϕ on axial velocity and temperature are diverse at selected sagittal cross-sections. The increase in Br and viscous dissipation leads to a rise in temperature, while an increase in thermal diffusion rate results in a drop in temperature. The analysis reveals that the effects of the amplitudes of sinusoidal and metachronal waves on temperature and axial velocity vary at different sagittal cross-sections of the fallopian tube, necessitating the consideration of multiple sagittal cross-sections for accurate evaluation.