Synergistic effects of channel divergence and Yeleswarapu mucus rheology on the hydrothermal transport via ciliary motion

This work analyzes the peristaltic transport of a Yeleswarapu viscoelastic fluid in a two-dimensional, divergent channel lined with ciliated walls. The non-Newtonian model captures both shear-dependent viscosity and elastic stresses, critical for simulating biological fluids. Flow in the low Reynolds number regime is examined by transforming the problem into a cilia-coordinated wave frame, where the long-wavelength approximation logically eliminates inertial terms, leaving a balance between viscoelastic, pressure, and viscous forces. A perturbation method solves the resulting coupled momentum and energy equations, isolating the contributions of fluid elasticity and shear-thinning to the hydrodynamic and thermal fields. The analysis specifically elucidates how the synergy between cilia-generated metachronal waves and the channel's diverging geometry modifies the axial pressure gradient, creating recirculation zones that augment both volumetric transport and thermal diffusion. The inclusion of viscous dissipation as an internal heat source critically couples the velocity and temperature fields. Results illustrate that channel divergence and fluid elasticity jointly enhance thermal exchange by altering the boundary layer structure and increasing the interfacial contact area. The perturbation solutions are validated against a direct numerical simulation performed using MATLAB's bvp4c, confirming the model's accuracy. These findings provide a mechanistic understanding for optimizing cilia-mimetic microfluidic devices, where controlling heat and mass transfer is essential for biochemical processing and diagnostic applications.