scholarly journals Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid

2021 ◽  
Author(s):  
Aqeel ur Rehman ◽  
Zaheer Abbas
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stable Solution ◽  
Mhd Flow ◽  
Least Square Method ◽  
Dual Solutions ◽  
Least Square ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Many boundary value problems (BVPs) have dual solutions in some cases containing one stable solution (upper branch) while other unstable (lower branch). In this paper, MHD flow and heat transfer past a shrinking sheet is studied for three distinct fluids: kerosene hybrid nanofluid, kerosene nanofluid, and kerosene nanofluid. The partial differential equations (PDEs) are turned into ordinary differential equations (ODEs) using an appropriate transformation and then dual solutions are obtained analytically by employing the Least Square method (LSM). Moreover, stability analysis is implemented on the time-dependent case by calculating the least eigenvalues using Matlab routine bvp4c. It is noticed that negative eigenvalue is related to unstable solution i.e., it provides initial progress of disturbance and positive eigenvalue is related to stable solution i.e., the disturbance in solution decline initially. The impacts of various parameters, skin friction coefficient, and local Nusselt number for dual solutions are presented graphically. It is also noted that the results obtained for hybrid nanofluids are better than ordinary nanofluids.

scholarly journals Dual Solutions and Stability Analysis of a Hybrid Nanofluid over a Stretching/Shrinking Sheet Executing MHD Flow

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 276 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
El-Sayed M. Sherif
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Temporal Stability ◽  
Mhd Flow ◽  
Numerical Results ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

In this paper, the unsteady magnetohydrodynamic (MHD) flow of hybrid nanofluid (HNF) composed of C u − A l 2 O 3 /water in the presence of a thermal radiation effect over the stretching/shrinking sheet is investigated. Using similarity transformation, the governing partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs), which are then solved by using a shooting method. In order to validate the obtained numerical results, the comparison of the results with the published literature is made numerically as well as graphically and is found in good agreements. In addition, the effects of many emerging physical governing parameters on the profiles of velocity, temperature, skin friction coefficient, and heat transfer rate are demonstrated graphically and are elucidated theoretically. Based on the numerical results, dual solutions exist in a specific range of magnetic, suction, and unsteadiness parameters. It was also found that the values of f ″ ( 0 ) rise in the first solution and reduce in the second solution when the solid volume fraction ϕ C u is increased. Finally, the temporal stability analysis of the solutions is conducted, and it is concluded that only the first solution is stable.

Simulation of time-dependent radiative heat motion over a stretching/shrinking sheet of hybrid Nanofluid: Stability analysis for dual solutions

2022 ◽  
pp. 239779142110690
Author(s):  
Seema Tinker ◽  
SR Mishra ◽  
PK Pattnaik ◽  
Ram Prakash Sharma
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Dual Solutions ◽  
The Other ◽  
Time Dependent ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Heat Transfer Characteristics ◽  
Suction Parameter ◽  
Transfer Characteristics

The heat transfer characteristics for the flow of a time-dependent hybrid nanofluid with thermal radiation and source/sink over a stretching/shrinking sheet are examined in the current investigation. We have transformed the governing equations of the presented study into the similarity equations utilizing similarity variables. However, a numerical solution is obtained by using in-build MATLAB code bvp5c. The mass and energy profiles for diverse values of thermophysical parameters are studied together with their physical quantities. It is observed that dual solutions exist, that is, one is upper, and the other is lower branch solution for a definite choice of the unsteadiness parameter. Also, stability analysis is executed to determine the long-term stability of dual solutions, indicating that out of the two, only one is stable and the other is unstable. It is revealed that comparatively, the first solution shows stability, while the second solution shows instability. There is a considerable influence of second-order slip on the problem’s respective flow and heat transfer characteristics. Further, major outcomes also show the dimensionless frictional stress and the magnitude of conventional heat transfer enhancement with growing suction parameter values.

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.

scholarly journals Influence of a Darcy-Forchheimer porous medium on the flow of a radiative magnetized rotating hybrid nanofluid over a shrinking surface

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sumera Dero ◽  
Hisamuddin Shaikh ◽  
Ghulam Hyder Talpur ◽  
Ilyas Khan ◽  
Sayer O. Alharbim ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Shooting Method ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Dual Solutions ◽  
Hybrid Nanofluid ◽  
Solution Stability ◽  
Shrinking Surface

AbstractIn this paper, the heat transfer properties in the three-dimensional (3D) magnetized with the Darcy-Forchheimer flow over a shrinking surface of the $$Cu + Al_{2} O_{3} /$$ C u + A l 2 O 3 / water hybrid nanofluid with radiation effect were studied. Valid linear similarity variables convert the partial differential equations (PDEs) into the ordinary differential equations (ODEs). With the help of the shootlib function in the Maple software, the generalized model in the form of ODEs is numerically solved by the shooting method. Shooting method can produce non-unique solutions when correct initial assumptions are suggested. The findings are found to have two solutions, thereby contributing to the introduction of a stability analysis that validates the attainability of first solution. Stability analysis is performed by employing if bvp4c method in MATLAB software. The results show limitless values of dual solutions at many calculated parameters allowing the turning points and essential values to not exist. Results reveal that the presence of dual solutions relies on the values of the porosity, coefficient of inertia, magnetic, and suction parameters for the specific values of the other applied parameters. Moreover, it has been noted that dual solutions exist in the ranges of $$F_{s} \le F_{sc}$$ F s ≤ F sc , $$M \ge M_{C}$$ M ≥ M C ,$$S \ge S_{C} ,$$ S ≥ S C , and $$K_{C} \le K$$ K C ≤ K whereas no solution exists in the ranges of $$F_{s} > F_{sc}$$ F s > F sc , $$M < M_{c}$$ M < M c , $$S < S_{c}$$ S < S c , and $$K_{C} > K$$ K C > K . Further, a reduction in the rate of heat transfer is noticed with a rise in the parameter of the copper solid volume fraction.

scholarly journals Double Solutions and Stability Analysis of Micropolar Hybrid Nanofluid with Thermal Radiation Impact on Unsteady Stagnation Point Flow

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 276
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Thermal Radiation ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Stable Solution ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Micropolar Nanofluid

The mathematical modeling of unsteady flow of micropolar Cu–Al2O3/water nanofluid driven by a deformable sheet in stagnation region with thermal radiation effect has been explored numerically. To achieve the system of nonlinear ordinary differential equations (ODEs), we have employed some appropriate transformations and solved it numerically using MATLAB software (built-in solver called bvp4c). Influences of relevant parameters on fluid flow and heat transfer characteristic are discussed and presented in graphs. The findings expose that double solutions appear in shrinking sheet case in which eventually contributes to the analysis of stability. The stability analysis therefore confirms that merely the first solution is a stable solution. Addition of nanometer-sized particle (Cu) has been found to significantly strengthen the heat transfer rate of micropolar nanofluid. When the copper nanoparticle volume fraction increased from 0 to 0.01 (1%) in micropolar nanofluid, the heat transfer rate increased roughly to an average of 17.725%. The result also revealed that an upsurge in the unsteady and radiation parameters have been noticed to enhance the local Nusselt number of micropolar hybrid nanofluid. Meanwhile, the occurrence of material parameter conclusively decreases it.

MHD flow and heat transfer over a permeable stretching/shrinking sheet in a hybrid nanofluid with a convective boundary condition

2019 ◽  
Vol 29 (9) ◽  
pp. 3012-3038 ◽  
Author(s):  
Emad H. Aly ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Mhd Flow ◽  
Convective Boundary Condition ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Convective Boundary ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this study is to present both effective analytic and numerical solutions to MHD flow and heat transfer past a permeable stretching/shrinking sheet in a hybrid nanofluid with suction/injection and convective boundary conditions. Water (base fluid) nanoparticles of alumina and copper were considered as a hybrid nanofluid. Design/methodology/approach Proper-similarity variables were applied to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. Exact analytical solutions were then presented for the dimensionless stream and temperature functions. Further, the authors introduce a very nice analytic and numerical solutions for both small and large values of the magnetic parameter. Findings It was found that no/unique/two equal/dual physical solutions exist for the investigated boundary value problem. The physically realizable practice of these solutions depends on the range of the governing parameters. For a stretching/shrinking sheet, it was deduced that a hybrid nanofluid works as a cooler on increasing some of the investigated parameters. Moreover, in the case of a shrinking sheet, the first solutions of hybrid nanofluid are stable and physically realizable rather than the nanofluid, while those of the second solutions are not for both hybrid nanofluid and nanofluid. Originality/value The present results for the hybrid nanofluids are new and original, as they successfully extend (generalize) the problems previously considered by different authors for the case of nanofluids.

scholarly journals MHD stagnation-point flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid with induced magnetic field

2019 ◽  
Vol 30 (3) ◽  
pp. 1345-1364 ◽  
Author(s):  
Mohamad Mustaqim Junoh ◽  
Fadzilah Md Ali ◽  
Norihan Md Arifin ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Induced Magnetic Field ◽  
Content Type

Purpose The purpose of this paper is to investigate the steady magnetohydrodynamics (MHD) boundary layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid past a stretching/shrinking sheet with the effect of induced magnetic field. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations via the similarity transformations before they are solved numerically using the “bvp4c” function in MATLAB. Findings It is found that there exist non-unique solutions, namely, dual solutions for a certain range of the stretching/shrinking parameters. The results from the stability analysis showed that the first solution (upper branch) is stable and valid physically, while the second solution (lower branch) is unstable. Practical implications This problem is important in the heat transfer field such as electronic cooling, engine cooling, generator cooling, welding, nuclear system cooling, lubrication, thermal storage, solar heating, cooling and heating in buildings, biomedical, drug reduction, heat pipe, space aircrafts and ships with better efficiency than that of nanofluids applicability. The results obtained are very useful for researchers to determine which solution is physically stable, whereby, mathematically more than one solution exist. Originality/value The present results are new and original for the problem of MHD stagnation-point flow over a stretching/shrinking sheet in a hybrid nanofluid, with the effect of induced magnetic field.

Cross flow and heat transfer past a permeable stretching/shrinking sheet in a hybrid nanofluid

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Amin Jafarimoghaddam ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Cross Flow ◽  
Porous Wall ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Lower Branch ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Branch Solution

Purpose The purpose of this paper is to study the laminar boundary layer cross flow and heat transfer on a rotational stagnation-point flow over either a stretching or shrinking porous wall submerged in hybrid nanofluids. The involved boundary layers are of stream-wise type with stretching/shrinking process along the surface. Design/methodology/approach Using appropriate similarity variables the partial differential equations are reduced to ordinary (similarity) differential equations. The reduced system of equations is solved analytically (by high-order perturbed field propagation for small to moderate stretching/shrinking parameter and low-order perturbation for large stretching/shrinking parameter) and numerically using the function bvp4c from MATLAB for different values of the governing parameters. Findings It was found that the basic similarity equations admit dual (upper and lower branch) solutions for both stretching/shrinking surfaces. Moreover, performing a linear stability analysis, it was confirmed that the upper branch solution is realistic (physically realizable), while the lower branch solution is not physically realizable in practice. These dual solutions will be studied in the present paper. Originality/value The authors believe that all numerical results are new and original and have not been published before for the present problem.

Sign in / Sign up

Export Citation Format

Share Document