Heat and mass transfer analysis of peristaltic flow of Reiner-Rivlin fluid in a flexible curved channel

Abstract

This study investigates the peristaltic transport of a Reiner-Rivlin non-Newtonian fluid through a curved channel with compliant walls, incorporating heat and mass transfer effects. The main aim of the study is to provide the theoretical framework for applications with a peristaltic flow of complex fluid in different biological systems/biomedical equipment in a curved path. This theoretical framework is also applicable to the cardiovascular behavior and the designs of biomedical devices such as dialysis systems. The governing equations for momentum, energy, and concentration are formulated, and closed-form analytical solutions are obtained via a regular perturbation technique for small wavenumbers. Key findings reveal that curvature dramatically alters flow dynamics: velocity profiles transition from asymmetric (tilted toward the inner wall at low curvature) to symmetric (parabolic at high curvature), mimicking the geometric influence of blood vessels. The Reiner-Rivlin parameter approximately reduces 26 % of flow velocity compared to Newtonian fluids due to increased elastic solid-like behavior. As Reiner-Rivlin fluid has more shear thickening behavior, increasing the fluid parameter enhances the apparent viscosity, which leads to slower flow. The Soret effect drives concentration gradients approximately 38 %, with higher thermal diffusion promoting particle migration to cooler regions. Streamline patterns show that trapped bolus size diminishes with curvature, approaching straight-channel symmetry. These results provide critical insights into biological flows (e.g., gastrointestinal motility, vascular transport) and biomedical device design.