Analytical modelling of cillia- driven prandtle fluid flow in a horizontal tube with viscous dissipation using homotopy perturbation method

This work analytically investigates the effects of viscous dissipation on cilia-induced Prandtl fluid flow in a horizontal tube. Approximate formulations for temperature and velocity profiles are obtained by solving the governing nonlinear equations using the Homotopy Perturbation Method (HPM). A comprehensive analysis is conducted on the influence of critical parameters such as the Prandtl number, viscosity ratio, and characteristics of ciliary motion. The impact of viscous dissipation on the thermal field is examined to understand its contribution to energy transfer. Graphs are employed to explore the effects of various stimulation parameters on heat and flow transfer. The structure of the equations is solved analytically, and graphical representations illustrate the pressure gradient, pressure rise, stream function, and velocity. Additionally, the analysis in ciliated tubes is effectively visualized through these graphs. The model enhances the realism of physiological and industrial transport simulations by emphasizing the significant effects of viscous dissipation on energy distribution and fluid velocity. A key innovation lies in incorporating viscous effects into a Prandtl fluid framework, which has often been neglected in previous studies. Near the tube walls, the fluid's peak temperature increases by approximately 15–25 % as ε rises (e.g., from 0.01 to 0.1). Thermal gradients become steeper and thermal boundary layers narrower at higher Prandtl numbers (e.g., from 5 to 20). The shear-thinning behavior becomes more pronounced as β increases (from 0.5 to 2.0), resulting in reduced effective viscosity. The graphical results validate HPM's accuracy and efficiency in modeling flow dynamics. With potential applications in biological systems such as the lungs and bile ducts, as well as in porous geological media, the findings offer valuable insights for applied mathematics and fluid mechanics.