scholarly journals Influences of Slip Velocity and Induced Magnetic Field on MHD Stagnation-Point Flow and Heat Transfer of Casson Fluid over a Stretching Sheet

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Mohamed Abd El-Aziz ◽  
Ahmed A. Afify
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Slip Velocity ◽  
Casson Fluid ◽  
Integration Scheme ◽  
Physical Parameters ◽  
Induced Magnetic Field ◽  
Casson Fluid Model

The steady MHD boundary layer flow near the stagnation point over a stretching surface in the presence of the induced magnetic field, viscous dissipation, magnetic dissipation, slip velocity phenomenon, and heat generation/absorption effects has been investigated numerically. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. The governing partial differential equations using appropriate similarity transformations are reduced into a set of nonlinear ordinary differential equations, which are solved numerically using a shooting method with fourth-order Runge-Kutta integration scheme. Comparisons with the earlier results have been made and good agreements were found. Numerical results for the velocity, induced magnetic field, temperature profiles, skin friction coefficient, and Nusselt number are presented through graphs and tables for various values of physical parameters. Results predicted that the magnetic parameter with α<1 has the tendency to enhance the heat transfer rate, whereas the reverse trend is seen with α>1. It is also noticed that the rate of heat transfer is a decreasing function of the reciprocal of a magnetic Prandtl number, whereas the opposite phenomenon occurs with the magnitude of the friction factor.

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.

scholarly journals CASSON FLUID OF A STAGNATION-POINT FLOW (SPF) TOWARDS A VERTICAL SHRINKING/STRETCHING SHEET

2021 ◽  
Vol 5 (1) ◽  
pp. 16-26
Author(s):  
Winifred N. Mutuku ◽  
Anselm O. Oyem
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Fluid Model ◽  
Casson Fluid ◽  
Stagnation Point Flow ◽  
Integration Scheme ◽  
Shrinking Sheet ◽  
Electrically Conducting ◽  
Casson Fluid Model ◽  
Fluid Behaviour

This study presents a convectively heated hydromagnetic Stagnation-Point Flow (SPF) of an electrically conducting Casson fluid towards a vertically stretching/shrinking sheet. The Casson fluid model is used to characterize the non-Newtonian fluid behaviour and using similarity variables, the governing partial differential equations are transformed into coupled nonlinear ordinary differential equations. The dimensionless nonlinear equations are solved numerically by Runge-Kutta Fehlberg integration scheme with shooting technique. The effects of the thermophysical parameters on velocity and temperature profiles are presented graphically and discussed quantitatively. The result shows that the flow field velocity decreases with increase in magnetic field parameter and Casson fluid parameter .

scholarly journals Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1238 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Stagnation Point ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Three Solutions ◽  
Convective Boundary ◽  
Suction Parameter ◽  
Stretching Surfaces ◽  
The Impact

In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A > 0.1, and a single solution exists when λ1 > 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.

scholarly journals Slip Effects on Unsteady Oblique Stagnation Point Flow of Nanofluid in a View of Inclined Magnetic Field

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Rizwana Rizwana ◽  
Azad Hussain ◽  
S. Nadeem
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Stagnation Point ◽  
Flow Behavior ◽  
Casson Fluid ◽  
Stagnation Point Flow ◽  
Working Fluid ◽  
Petroleum Reservoir ◽  
Metallic Nanoparticle ◽  
The Impact

This study may be applicable in heavy power engine and cooling of a nuclear reactor, insulation for buildings, petroleum reservoir operations, and magnetic material processing solar energy collectors. In this manuscript, the slip results are evaluated for the non-Newtonian fluid on the oblique stagnation point flow of induced magnetic field over the oscillating surface. The valuation of heat flux is examined through the Fourier law of heat transfer. The metallic nanoparticle Copper Cu is within the base fluid, and water is utilized in the analysis. Nanofluids have benefits such as steadiness of the working fluid, decreasing blockage, clogs, decreasing prices, decreasing the friction coefficient, and decreasing the size of the heat transfer system. Similarity variables are utilized to convert the developed flow into higher nonlinear coupled ordinary differential equations (ODE) which are tackled numerically using a mathematical technique such as the bvp4c method in Maple and Matlab software. According to the present geometry, the flow behavior of the operating nanofluid has analyzed by stream lines. Disparities in velocity and temperature profile are demonstrated by graphs to describe the effects of controlling parameters. The Casson fluid parameter enhances the velocity of the fluid. The system heats up by the impact of Joule heating and dissipation.

MHD mixed convection stagnation-point flow of a viscoelastic fluid towards a stretching sheet in a porous medium with heat generation and radiation

2015 ◽  
Vol 93 (5) ◽  
pp. 532-541 ◽  
Author(s):  
M. Modather M. Abdou ◽  
E. Roshdy EL-Zahar ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscoelastic Fluid ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Heat Transfer Characteristics

An analysis was carried out to study the effect of thermal radiation on magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid near the stagnation point of a vertical stretching sheet in a porous medium with internal heat generation–absorption. The flow is generated because of linear stretching of the sheet and influenced by the uniform magnetic field that is applied horizontally in the flow region. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically using an accurate implicit finite difference scheme. A comparison of the obtained results with previously published numerical results is done and the results are found to be in good agreement. The effects of the viscoelastic fluid parameter, magnetic field parameter, nonuniform heat source–sink, and the thermal radiation parameter on the heat transfer characteristics are presented graphically and discussed. The values of the skin friction coefficient and the local Nusselt number are tabulated for both cases of assisting and opposing flows.

scholarly journals Heat Transfer Reaction on a Viscous Dissipative Free Convective Radiating Stream over a Permeable Laminate within Presence of Induced Magnetic Field

2020 ◽  
Vol 9 (3) ◽  
pp. 2057-2062
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Partial Differential Equations ◽  
Magnetic Flux ◽  
Differential Equations ◽  
Heat Source ◽  
Transfer Reaction ◽  
Induced Magnetic Field ◽  
Fundamental Point ◽  
Physical Features

The fundamental point of the paper is to inspect the heat transfer consequence on a viscous dissipative unconfined convective Radiating stream over a permeable shield in the existence of induced- magnetic flux. Consistent magnetic field of force will be applied vertically towards the plate which is electrically non-conducting. Partial differential equations which are non linear coupled worked out by Galerkin technique, the consequence of Radiation with Heat source parameter and other physical features on velocity, temperature along with induced-magnetic field are explained by graphs.

scholarly journals Magnetohydrodynamics Stagnation-Point Flow of a Nanofluid Past a Stretching/Shrinking Sheet with Induced Magnetic Field: A Revised Model

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1078 ◽  
Author(s):  
Mohamad Mustaqim Junoh ◽  
Fadzilah Md Ali ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Governing Equations ◽  
Induced Magnetic Field ◽  
The Stability ◽  
Stretching Or Shrinking Sheet

The revised Buongiorno’s nanofluid model with the effect of induced magnetic field on steady magnetohydrodynamics (MHD) stagnation-point flow of nanofluid over a stretching or shrinking sheet is investigated. The effects of zero mass flux and suction are taken into account. A similarity transformation with symmetry variables are introduced in order to alter from the governing nonlinear partial differential equations into a nonlinear ordinary differential equations. These governing equations are numerically solved using the bvp4c function in Matlab solver, a very adequate finite difference method. The influences of considered parameters ( P r , M, χ , L e , N b , N t , S, and λ ) on velocity, induced magnetic, temperature, and concentration profiles together with the reduced skin friction and heat transfer rate are discussed. Results from these criterion exposed the existence of dual solutions when magnetic field and suction are applied for a specific range of λ . The stability of the solutions obtained is carried out by performing a stability analysis.

scholarly journals The Inclined Factors of Magnetic Field and Shrinking Sheet in Casson Fluid Flow, Heat and Mass Transfer

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 373
Author(s):  
Shahanaz Parvin ◽  
Siti Suzilliana Putri Mohamed Isa ◽  
Norihan Md Arifin ◽  
Fadzilah Md Ali
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Fluid Model ◽  
Casson Fluid ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Flow Heat

The development of the mathematical modeling of Casson fluid flow and heat and mass transfer is presented in this paper. The model is subjected to the following physical parameters: shrinking parameter, mixed convection, concentration buoyancy ratio parameter, Soret number, and Dufour number. This model is also subjected to the inclined magnetic field and shrinking sheet at a certain angle projected from the y- and x-axes, respectively. The MATLAB bvp4c program is the main mathematical program that was used to obtain the final numerical solutions for the reduced ordinary differential equations (ODEs). These ODEs originate from the governing partial differential equations (PDEs), where the transformation can be achieved by applying similarity transformations. The MATLAB bvp4c program was also implemented to develop stability analysis, where this calculation was executed to recognize the most stable numerical solution. Numerical graphics were made for the skin friction coefficient, local Nusselt number, local Sherwood number, velocity profile, temperature profile, and concentration profile for certain values of the physical parameters. It is found that all the governed parameters affected the variations of the Casson fluid flow, heat transfer, mass transfer, and the profiles of velocity, temperature, and concentration. In addition, a stable solution can be applied to predict the impact of physical parameters on the actual fluid model by using a mathematical fluid model.

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