Heat transfer analysis in immiscible fluids flow

Immiscible fluids (liquid–liquid interface) are essential in various industrial and biomedical applications, including petroleum industry, chemical engineering, microfluidics, and biomedical engineering. Interfacial (liquid–liquid) dynamics play a crucial role in governing the flow characteristics, flow separation, heat transfer, etc. The interfacial dynamics with peristaltic pumping was investigated by Brasseur et al. [J. Fluid Mech. 174, 495–519 (1987)]. This model is extended with heat transfer analysis, which is not yet investigated, would explore the various thermophysical aspects in biophysical transport phenomena. In this study, a mathematical model is formulated to examine the heat transfer in two-layered immiscible fluids flowing under peristalsis. The viscosities of both the liquids are considered different in core and peripheral layers. Analytical solutions are derived using the low Reynolds number and long wavelength approximations. The present study investigates the dynamics of interface between immiscible fluids, fluids velocity, wall shear stress, pressure distribution, Nusselt number, isotherms, entropy generation, and streamline patterns with highlighting how viscosity ratio and thermal effects influence the fluid particle trajectories in core layer. The results reveal that the backward flow enhances in the peripheral region while reduces in core layer with higher viscosity ratio. The Grashof number and heat source parameter shift the interface downward, affecting both the velocity and temperature distributions within the core and peripheral regions. Moreover, an increase in the viscosity ratio, and Grashof number leads to rise in entropy generation. These findings offer valuable insights for improving the thermal systems for biomedical diagnoses and multiphase flow systems.