A new similarity solution with stability analysis for the three-dimensional boundary layer of hybrid nanofluids

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Najiyah Safwa Khashi'ie ◽  
Norihan M. Arifin ◽  
Ioan Pop ◽  
Roslinda Nazar ◽  
Ezad Hafidz Hafidzuddin
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Similarity Transformation ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Dimensional Boundary

Purpose The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties. Design/methodology/approach The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed. Findings The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only. Originality/value The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.

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

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Differential Equations ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Medium Effect ◽  
Hybrid Nanofluid ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Dimensional Flow

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 ϕ2 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-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.

The effect of vertical throughflow on the boundary layer flow of a nanofluid past a stretching/shrinking sheet

2017 ◽  
Vol 27 (9) ◽  
pp. 1910-1927 ◽  
Author(s):  
Ioan Pop ◽  
Kohilavani Naganthran ◽  
Roslinda Nazar ◽  
Anuar Ishak
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Vertical Throughflow ◽  
Layer Flow

Purpose The purpose of this paper is to study the effects of vertical throughflow on the boundary layer flow and heat transfer of a nanofluid driven by a permeable stretching/shrinking surface. Design/methodology/approach Similarity transformation is used to convert the system of boundary layer equations into a system of ordinary differential equations. The system of governing similarity equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. The generated numerical results are presented graphically and discussed based on some governing parameters. Findings It is found that dual solutions exist in both cases of stretching and shrinking sheet situations. Stability analysis is performed to determine which solution is stable and valid physically. Originality/value Dual solutions are found for positive and negative values of the moving parameter. A stability analysis has also been performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible.

scholarly journals Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 1077
Author(s):  
Muhammad Tamoor ◽  
Muhammad Kamran ◽  
Sadique Rehman ◽  
Aamir Farooq ◽  
Rewayat Khan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Convective Parameter ◽  
Momentum And Heat Transfer ◽  
Dimensional Boundary

In this study, a numerical approach was adopted in order to explore the analysis of magneto fluid in the presence of thermal radiation combined with mixed convective and slip conditions. Using the similarity transformation, the axisymmetric three-dimensional boundary layer equations were reduced to a self-similar form. The shooting technique, combined with the Range–Kutta–Fehlberg method, was used to solve the resulting coupled nonlinear momentum and heat transfer equations numerically. When physically interpreting the data, some important observations were made. The novelty of the present study lies in finding help to control the rate of heat transfer and fluid velocity in any industrial manufacturing processes (such as the cooling of metallic plates). The numerical results revealed that the Nusselt number decrease for larger Prandtl number, curvature, and convective parameters. At the same time, the skin friction coefficient was enhanced with an increase in both slip velocity and convective parameter. The effect of emerging physical parameters on velocity and temperature profiles for a nonlinear stretching cylinder has been thoroughly studied and analyzed using plotted graphs and tables.

Dual similarity solutions because of mixed convective flow of a double-nanoparticles hybrid nanofluid: critical points and stability analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ioan Pop ◽  
Mohammadreza Nademi Rostami ◽  
Saeed Dinarvand
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Flow Regime ◽  
Magnetic Parameter ◽  
Volume Fraction ◽  
Similarity Solutions ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Buoyancy Parameter ◽  
Mixed Convective Flow

Purpose The purpose of this article is to study the steady laminar magnetohydrodynamics mixed convection stagnation-point flow of an alumina-graphene/water hybrid nanofluid with spherical nanoparticles over a vertical permeable plate with focus on dual similarity solutions. Design/methodology/approach The single-phase hybrid nanofluid modeling is based on nanoparticles and base fluid masses instead of volume fraction of first and second nanoparticles as inputs. After substituting pertinent similarity variables into the basic partial differential equations governing on the problem, the authors obtain a complicated system of nondimensional ordinary differential equations, which has non-unique solution in a certain range of the buoyancy parameter. It is worth mentioning that, the stability analysis of the solutions is also presented and it is shown that always the first solutions are stable and physically realizable. Findings It is proved that the magnetic parameter and the wall permeability parameter widen the range of the buoyancy parameter for which the solution exists; however, the opposite trend is valid for second nanoparticle mass. Besides, mass suction at the surface of the plate as well as magnetic parameter leads to reduce both hydrodynamic and thermal boundary layer thicknesses. Moreover, the assisting flow regime always has higher values of similarity skin friction and Nusselt number relative to opposing flow regime. Originality/value A novel mass-based model of the hybridity in nanofluids has been used to study the foregoing problem with focus on dual similarity solutions. The results of this paper are completely original and, to the best of the authors’ knowledge, the numerical results of the present paper were never published by any researcher.

scholarly journals Unsteady Three-Dimensional MHD Non-Axisymmetric Homann Stagnation Point Flow of a Hybrid Nanofluid with Stability Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 784 ◽  
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Industrial Sector ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid

The hybrid nanofluid under the influence of magnetohydrodynamics (MHD) is a new interest in the industrial sector due to its applications, such as in solar water heating and scraped surface heat exchangers. Thus, the present study accentuates the analysis of an unsteady three-dimensional MHD non-axisymmetric Homann stagnation point flow of a hybrid Al2O3-Cu/H2O nanofluid with stability analysis. By employing suitable similarity transformations, the governing mathematical model in the form of the partial differential equations are simplified into a system of ordinary differential equations. The simplified mathematical model is then solved numerically by the Matlab solver bvp4c function. This solving approach was proficient in generating more than one solution when good initial guesses were provided. The numerical results presented significant influences on the rate of heat transfer and fluid flow characteristics of a hybrid nanofluid. The rate of heat transfer and the trend of the skin friction coefficient improve with the increment of the nanoparticles’ concentration and the magnetic parameter; however, they deteriorate when the unsteadiness parameter increases. In contrast, the ratio of the escalation of the ambient fluid strain rate to the plate was able to adjourn the boundary layer separation. The dual solutions (first and second solutions) are obtainable when the surface of the sheet shrunk. A stability analysis is carried out to justify the stability of the dual solutions, and hence the first solution is seen as physically reliable and stable, while the second solution is unstable.

Three-Dimensional Boundary-Layer Flow About an Ablating Slender Cone

1969 ◽  
Vol 91 (4) ◽  
pp. 632-648 ◽  
Author(s):  
T. K. Fannelop ◽  
P. C. Smith
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Cone Angle ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Boundary Layer Equations ◽  
Transverse Curvature ◽  
Dimensional Boundary ◽  
Layer Flow

A theoretical analysis is presented for three-dimensional laminar boundary-layer flow about slender conical vehicles including the effect of transverse surface curvature. The boundary-layer equations are solved by standard finite difference techniques. Numerical results are presented for hypersonic flow about a slender blunted cone. The influences of Reynolds number, cone angle, and mass transfer are studied for both symmetric flight and at angle-of-attack. The effects of transverse curvature are substantial at the low Reynolds numbers considered and are enhanced by blowing. The crossflow wall shear is largely unaffected by transverse curvature although the peak velocity is reduced. A simplified “channel flow” analogy is suggested for the crossflow near the wall.

Impact of Entropy Generation on Stagnation-Point Flow of Sutterby Nanofluid: A Numerical Analysis

2016 ◽  
Vol 71 (9) ◽  
pp. 837-848 ◽  
Author(s):  
Ehtsham Azhar ◽  
Z. Iqbal ◽  
E.N. Maraj
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Entropy Generation ◽  
Computational Analysis ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Physical Parameters ◽  
Stretching Plate

AbstractThe present article dicusses the computational analysis of entropy generation for the stagnation-point flow of Sutterby nanofluid over a linear stretching plate. The Sutterby fluid is chosen to study the effect for three major classes of non-Newtonian fluids, i.e. pseudoplastic, Newtonian, and dilatant. The effects of pertinent physical parameters are examined under the approximation of boundary layer. The system of coupled nonlinear partial differential equations is simplified by incorporating suitable similarity transformation into a system of non-linear-coupled ordinary differential equations. Entropy generation analysis is conducted numerically, and the results are displayed through graphs and tables. Significant findings are listed in the closing remarks.

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