Power-Law Fluid Flow in Diverse Converging-Diverging Geometries of Corrugated Channels

Gaining insights into the behavior of non-Newtonian fluids, including power-law fluids, within corrugated channels is essential for numerous industrial processes. In this paper, we introduce an analytical approach to establish the connection between pressure drop and flow rate in laminar flow conditions, specifically focusing on the flow of power-law fluids within 2D Planar converging-diverging corrugated channels. We explore five distinct converging-diverging geometries such as linear wedge, parabolic wedge, hyperbolic profile, hyperbolic cosine profile, and the sinusoidal converging-diverging channels. We derive analytically the pressure-flow rate relations using the lubrication approximation in these channels. For the validations, the derived expressions converges to the Newtonian flow physics when the viscosity is assumed constant. The versatility of this method allows its application to various fluid types and channel shapes within defined constraints, serving as a valuable framework for numerical integration when obtaining analytical expressions becomes challenging due to mathematical intricacies or practical considerations.