Unsteady MHD Rear Stagnation-Point Flow of a Hybrid Nanofluid with Heat Generation/Absorption Effect

2021 ◽  
Vol 87 (1) ◽  
pp. 41-51
Author(s):  
Nurul Amira Zainal ◽  
Kohilavani Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heat Generation ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Absorption Effect ◽  
Suction Parameter ◽  
The Impact ◽  
Rear Stagnation Point

The study of unsteady flow is essential in various engineering systems, for instance, the periodic fluid motion and start-up process. Therefore, this numerical study focuses on examining the unsteady magnetohydrodynamics (MHD) rear stagnation-point flow in Al2O3-Cu/H2O hybrid nanofluid past a permeable stretching/shrinking surface with the impact of heat generation/absorption. By choosing a suitable similarity transformation, partial differential equations are transformed into a system of nonlinear ordinary differential equations and solved using the bvp4c function in the MATLAB package. The effects of the solution domain’s operating parameters are analysed, and dual solutions are observable as the sheet shrinks. It is found that the addition of the suction parameter escalates the heat transfer efficiency. Eventually, the existence of the unsteadiness parameter and the heat generation/absorption effect significantly encourage heat transfer deterioration.

scholarly journals Stability Analysis of Unsteady MHD Rear Stagnation Point Flow of Hybrid Nanofluid

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2428
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heat Generation ◽  
Heat Transfer Performance ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Transfer Performance ◽  
Distribution Profile

Previous studies have reported that investigating the stagnation point flow is relevant in a variety of industrial and technological processes, including extrusion and the polymer industries. Hence, the present work aims to analyse the heat transfer performance of unsteady magnetohydrodynamics (MHD) in hybrid nanofluid and heat generation/absorption impact. The multivariable differential equations with partial derivatives are converted into a specific type of ordinary differential equations by using valid similarity transformations. The resulting mathematical model is clarified utilising the bvp4c function. The results of various control parameters were analysed, and it was discovered that increasing the nanoparticle concentration and magnetic field increases the coefficient of skin friction along the stretching/shrinking surface. The inclusion of the heat generation parameter displays an upward trend in the temperature distribution profile, consequently degrading the heat transfer performance. The findings are confirmed to have more than one solution, and this invariably leads to a stability analysis, which confirms the first solution’s feasibility.

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.

Effect of Porous Medium in Stagnation Point Flow of Ferrofluid Due to a Variable Convected Thicked Sheet

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Maria Imtiaz ◽  
Hira Nazar ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Nusselt Number ◽  
Differential Equations ◽  
Stagnation Point ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Heat Transfer Analysis ◽  
Series Solutions ◽  
The Impact

Abstract The focus of this paper is to study the effects of stagnation point flow and porous medium on ferrofluid flow over a variable thicked sheet. Heat transfer analysis is discussed by including thermal radiation. Suitable transformations are applied to convert partial differential equations to ordinary differential equations. Convergent results for series solutions are calculated. The impact of numerous parameters on velocity and temperature is displayed for series solutions. Graphical behavior for skin friction coefficient and Nusselt number is also analyzed. Numerical values of Nusselt number are tabulated depending upon various parameters

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.

Stagnation Point Flow through a Porous Medium towards a Radially Stretching Sheet in the Presence of Uniform Suction or Injection and Heat Generation

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Hazem Ali Attia ◽  
Karem Mahmoud Ewis ◽  
Mostafa A. M. Abdeen
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Stagnation Point Flow ◽  
Uniform Suction ◽  
Flow Through ◽  
Energy Equations

An analysis is made of the steady laminar axisymmetric stagnation point flow of an incompressible viscous fluid in a porous medium impinging on a permeable radially stretching sheet with heat generation or absorption. A uniform suction or blowing is applied normal to the plate which is maintained at a constant temperature. Similarity transformation is used to transform the governing partial differential equations to ordinary differential equations. The finite difference method and generalized Thomas algorithm are used to solve the governing nonlinear momentum and energy equations. The effects of the uniform suction/blowing velocity, the stretching parameter and the heat generation/absorption coefficient on both the flow field and heat transfer are presented and discussed. The results indicate that increasing the stretching parameter or the suction/blowing velocity decreases both the velocity and thermal boundary layer thicknesses. The effect of the stretching parameter on the velocity components is more apparent for suction than blowing while its effect on the temperature and rate of heat transfer at the wall is clearer in the case of blowing than suction.

scholarly journals Unsteady Stagnation Point Flow of Hybrid Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet with Velocity Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1649
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Velocity Slip ◽  
Slip Condition ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Unsteady stagnation point flow in hybrid nanofluid (Al2O3-Cu/H2O) past a convectively heated stretching/shrinking sheet is examined. Apart from the conventional surface of the no-slip condition, the velocity slip condition is considered in this study. By incorporating verified similarity transformations, the differential equations together with their partial derivatives are changed into ordinary differential equations. Throughout the MATLAB operating system, the simplified mathematical model is clarified by employing the bvp4c procedure. The above-proposed approach is capable of producing non-uniqueness solutions when adequate initial assumptions are provided. The findings revealed that the skin friction coefficient intensifies in conjunction with the local Nusselt number by adding up the nanoparticles volume fraction. The occurrence of velocity slip at the boundary reduces the coefficient of skin friction; however, an upward trend is exemplified in the rate of heat transfer. The results also signified that, unlike the parameter of velocity slip, the increment in the unsteady parameter conclusively increases the coefficient of skin friction, and an upsurge attribution in the heat transfer rate is observed resulting from the increment of Biot number. The findings are evidenced to have dual solutions, which inevitably contribute to stability analysis, hence validating the feasibility of the first solution.

scholarly journals Influence of heat generation/absorption and stagnation point on polystyrene–TiO2/H2O hybrid nanofluid flow

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sadaf Masood ◽  
Muhammad Farooq ◽  
Aisha Anjum
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Entropy Generation ◽  
Heat Generation ◽  
Velocity Ratio ◽  
Hybrid Nanofluid ◽  
Engineering System ◽  
Nanofluid Flow ◽  
Homotopy Analysis

AbstractThis article focuses on hybrid nanofluid flow induced by stretched surface. The present context covers stagnation point flow of a hybrid nanofluid with the effect of heat generation/absorption. Currently most famous class of nanofluids is Hybrid nanofluid. It contains polystyrene and titanium oxide as a nanoparticles and water as a base fluid. First time attributes of heat transfer are evaluated by utilizing polystyrene–TiO2/H2O hybrid nanofluid with heat generation/absorption. Partial differential equations are converted into ordinary differential equation by using appropriate transformations for heat and velocity. Homotopy analysis method is operated for solution of ordinary differential equations. Flow and heat are disclosed graphically for unlike parameters. Resistive force and heat transfer rate is deliberated mathematically and graphically. It is deduced that velocity field enhanced for velocity ratio parameter whereas temperature field grows for heat generation/absorption coefficient. To judge the production of any engineering system entropy generation is also calculated. It is noticed that entropy generation grows for Prandtl number and Eckert number while it shows opposite behavior for temperature difference parameter.

Off-centered stagnation point flow of an experimental-based hybrid nanofluid impinging to a spinning disk with low to high non-alignments

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Saeed Dinarvand ◽  
Alireza Mahdavi Nejad
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Thermophysical Properties ◽  
Transformation Method ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Spinning Disk

Purpose The purpose of this study is to model and solve numerically the three-dimensional off-centered stagnation point flow and heat transfer of magnesium oxide–silver/water hybrid nanofluid impinging to a spinning disk. Design/methodology/approach The applied effective thermophysical properties of hybrid nanofluid including thermal conductivity and dynamics viscosity are according to the reported experimental relations that would be expanded by a mass-based algorithm. The single phase formulations coupled with experimental-based hybrid nanofluid model is implemented to derive the governing partial differential equations which are then transferred to a set of dimensionless ordinary differential equations (ODEs) with the use of the similarity transformation method. Afterward, the reduced ODEs are solved numerically by bvp4c function from MATLAB that is a trustworthy and efficient code according to three-stage Lobatto IIIa formula. Findings The effect of spinning parameter and nanoparticles masses (mMgO, mAg) on the hydrodynamics and thermal boundary layers behavior and also the quantities of engineering interest are presented in tabular and graphical forms. The recent work demonstrates that the analysis of flow and heat transfer becomes more complicated when there is a non-alignment between the impinging flow and the disk axes. From computational results demonstrate that, the radial and azimuthal velocities are, respectively, the increasing and decreasing functions of the disk spinning parameter. Further, for the greater values of the spinning parameter, an overshoot of the radial velocity owing to the centrifugal forces of the spinning disk is observed. Besides, the quantities of engineering interest gently enhance with first and second nanoparticle masses, while comparing their absolute values illustrates the fact that the effect of second nanoparticle mass (mAg) is greater. Further, it is inferred that the second nanoparticle’s mass enhancement results in the amplification of the heat transfer; although, the high skin friction and the relevant shear stress should be controlled. Originality/value The combination of experimental thermophysical properties with theoretical modeling of the problem can be the novelty of the present work. It is evident that the experimental relations of effective thermophysical properties can be trustable and flexible in the theoretical/mathematical modeling of hybrid nanofluids flows. Besides, to the best of the authors’ knowledge, no one has ever attempted to study the present problem through a mass-based model for hybrid nanofluid.

Radiation effect on three-dimensional stagnation point flow involving copper-aqueous titania hybrid nanofluid induced by a non-Fourier heat flux over a horizontal plane surface

2021 ◽  
Author(s):  
Umair Khan ◽  
Aurang Zaib ◽  
Anuar Ishak ◽  
S. Abu Bakar ◽  
El-Sayed M. Sherif ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Stagnation Point ◽  
Horizontal Plane ◽  
Radiation Effect ◽  
Plane Surface ◽  
Relaxation Parameter ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid

Abstract This research numerically investigates 3D stagnation-point flow (SPF) past a horizontal plane surface conveying copper-aqueous titania hybrid nanofluid induced by non-Fourier heat flux (NFHF) that utilized in heat transfer processes. A Tiwari-Das model is engaged to examine the fluid flow dynamics and the heat transfer features of the hybrid nanofluid with thermal radiation effect. With aid of similarity variables, the leading nonlinear system involving partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs). This set of dimensionless coupled ODEs is then tackled through the bvp4c solver in MATLAB. For hybrid nanofluid, the graphical findings of the pertaining parameters as well as the saddle/nodal indicative parameter are disclosed and explained with the assist of figures and tables. The results illustrate that the rise of hybrid nanoparticles declines the motion of the fluids in both axes of coordinates ( and directions), while the temperature enhances. In addition, the temperature distribution declines due to relaxation parameter but uplifts due to radiation. Also, the thermal relaxation parameter reduces the temperature. Moreover, the present solution displays an excellent agreement with earlier published works in the limited cases of normal fluid and nanofluid.

scholarly journals Unsteady MHD Mixed Convection Flow in Hybrid Nanofluid at Three-Dimensional Stagnation Point

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 549
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Mixed Convection ◽  
Skin Friction ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid

There has been significant interest in exploring a stagnation point flow due to its numerous potential uses in engineering applications such as cooling of nuclear reactors. Hence, this study proposed a numerical analysis on the unsteady magnetohydrodynamic (MHD) mixed convection at three-dimensional stagnation point flow in Al2O3–Cu/H2O hybrid nanofluid over a permeable sheet. The ordinary differential equations are accomplished by simplifying the governing partial differential equations through suitable similarity transformation. The numerical computation is established by the MATLAB system software using the bvp4c technique. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The influence of certain functioning parameters is inspected, and notable results exposed that the rate of heat transfer is exaggerated along with the skin friction coefficient while the suction/injection and magnetic parameters are intensified. The results also signified that the rise in the volume fraction of the nanoparticle and the decline of the unsteadiness parameter demonstrates a downward attribution towards the heat transfer performance and skin friction coefficient. Conclusively, the observations are confirmed to have multiple solutions, which eventually contribute to an investigation of the analysis of the solution stability, thereby justifying the viability of the first solution.

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