A Switched Dynamical System Approach to the Flow and Heat Transfer of Immiscible Fluids

Abstract

This paper provides important insights into immiscible fluids models, which can exhibit complex nonlinear behavior due to variations in thickness, viscosity, thermal conductivity, and jump velocity fields across the interface surface. These characteristics will be used to model our problem as a switching dynamical system. The bifurcation tools for switching systems will be used to create a systematic computational analysis of the rise dynamics of the behavior of solutions influenced by the interface surface. This technique is applied to investigate the flow and heat transfer behavior of two immiscible fluids for a recently proposed model. The explicit formula for tracking the accurate behavior of the interface surface, which is used as a critical part of the bifurcation analysis, is provided. The results show that the existence of heteroclinic connections and switching stability of multiple equilibria are the primary causes of the formation of a novel class of trapping phenomena. The biological significance of our results on flow and heat transfer characteristics is discussed.