Jawad Raza, Sumera Dero, Liaquat Ali Lund and Zurni Omar
The purpose of study is to examine the dual nature of the branches for the problem of Darcy–Forchheimer porous medium flow of rotating nanofluid on a linearly stretching/shrinking…
Abstract
Purpose
The purpose of study is to examine the dual nature of the branches for the problem of Darcy–Forchheimer porous medium flow of rotating nanofluid on a linearly stretching/shrinking surface under the field of magnetic influence. The dual nature of the branches confronts the uniqueness and existence theorem, moreover, mathematically it is a great achievement. For engineering purposes, this study applied a linear stability test on the multiple branches to determine which solution is physically reliable (stable).
Design/methodology/approach
Nanofluid model has been developed with the help of Buongiorno model. The partial differential equations in space coordinates for the law of conservation of mass, momentum and energy have been transformed into ordinary differential equations by introducing the similarity variables. Two numerical techniques, namely, the shooting method in Maple software and the three-stage Lobatto IIIA method in Matlab software, have been used to find multiple branches and to accomplish stability analysis, respectively.
Findings
The parametric investigation has been executed to find the multiple branches and explore the effects on skin friction, Sherwood number, Nusselt number, concentration and temperature profiles. The findings exhibited the presence of dual branches only in the case of a shrinking sheet.
Originality/value
The originality of work is a determination of multiple branches and the performance of the stability analysis of the branches. It has also been confirmed that such a study has not yet been considered in the previous literature.
Details
Keywords
Liaquat Ali Lund, Zurni Omar and Ilyas Khan
The purpose of this study is to find the multiple branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid perfusing a porous medium over the…
Abstract
Purpose
The purpose of this study is to find the multiple branches of the three-dimensional flow of Cu-Al2 O3/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
Originality/value
Dual branches of the three-dimensional flow of Cu-Al2 O3/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.