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.
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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.
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Jawad Raza, Azizah M. Rohni, Zurni Omar, M. Awais and A.Q. Baig
The purpose of this paper is to investigate some multiple solutions for carbon nanotubes (CNTs) in a porous channel with changing walls. Moreover, the intention of the study is to…
Abstract
Purpose
The purpose of this paper is to investigate some multiple solutions for carbon nanotubes (CNTs) in a porous channel with changing walls. Moreover, the intention of the study is to examine the physicochemical and rheological properties of titania and CNTs.
Design/methodology/approach
The mathematical modeling is performed for the laws of conservation of mass, momentum and energy profiles. Governing partial differential equations are transformed into ordinary differential equations by applying suitable similarity transformation and then solved numerically with the help of shooting technique.
Findings
The effects of different physical parameters on the rheology of nanofluids are discussed graphically and numerically, in order to make the analysis more interesting. The present study revealed that multiple solutions of nanofluids in a channel with changing walls are obtained only for the case of suction.
Originality/value
Some new branches of the solution for nanofluids in a channel with changing walls are obtained in this research, which has never been reported before. Combined effects of physicochemical and rheology of titania and carbon nanotubes are investigated briefly. The effects of physical parameters on velocity and temperature profile are examined in detail which is more realistic than real-world problem.
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Jawad Raza, Azizah M. Rohni and Zurni Omar
The purpose of this paper is to investigate different branches of the solution of micropolar fluid in a channel with permeable walls. Moreover, the intention of the study is to…
Abstract
Purpose
The purpose of this paper is to investigate different branches of the solution of micropolar fluid in a channel with permeable walls. Moreover, the intention of the study is to examine the effect of different physical parameters on fluid flow.
Design/methodology/approach
The mathematical modeling is performed on the basis of law of conservation of mass, momentum and angular momentum. The governing partial differential equations were transformed into ordinary differential equations by applying suitable similarity transformation. Afterwards, the set of nonlinear ordinary differential equations was solved numerically by a shooting method.
Findings
The study reveals that various branches of the solution of the proposed problem exist only in the case of strong suction.
Originality/value
The investigation of new branches of the solution of non-Newtonian micropolar fluid is relatively difficult as far as the single solution is concern. This study explores the new branches of the solution of a micropolar fluid in a channel with suction/injection. Simultaneous effect of suction Reynolds number and vortex viscosity parameter on velocity and micro-rotation profile is examined for different branches of solution in order to make the analysis more interesting.