Darcy-Forchheimer porous medium effect on rotating hybrid nanofluid on a linear shrinking/stretching sheet

Purpose - The purpose of this study is to find the multiple branches of the three-dimensional flow of Cu-Al-2 O-3/water rotating hybrid nanofluid perfusing a porous medium over the stretching/shrinking surface. The extended model of Darcy due to Forchheimer and Brinkman has been considered to make the hybrid nanofluid model over the pores by considering the porosity and permeability effects. Design/methodology/approach - The Tiwari and Das model with the thermophysical properties of spherical particles for efficient dynamic viscosity of the nanoparticle is used. The linear similarity transformations are applied to convert the partial differential equations into ordinary differential equations (ODEs). The system of governing ODEs is solved by using the three-stage Lobatto IIIa scheme in MATLAB for evolving parameters. Findings - The system of governing ODEs produces dual branches. A unique stable branch is identified with help of stability analysis. The reduced heat transfer rate has been shown to increase with the reduced phi(2) in both branches. Further, results revealed that the presence of multiple branches depends on the ranges of porosity, suction and stretching/shrinking parameters for the particular value of the rotating parameter. Originality/value - Dual branches of the three-dimensional flow of Cu-Al-2 O-3/water rotating hybrid nanofluid have been found. Therefore, stability analysis of the branches is also conducted to know which branch is appropriate for the practical applications. To the best of the authors' knowledge, this research is novel and there is no previously published work relevant to the present study.

Automated summary

The study aims to explore the multiple branches of three-dimensional flow of Cu-Al-2 O-3/water rotating hybrid nanofluid in a porous medium over a stretching/shrinking surface. It utilizes an extended model of Darcy incorporating Forchheimer and Brinkman effects, with Tiwari and Das model for dynamic viscosity. The research reveals dual branches in the system of governing ODEs, with stability analysis identifying a stable branch showing increased heat transfer rate with reduced phi(2), depending on porosity, suction, and stretching/shrinking parameters.