Numerical Simulation of Slip Influence on the Flow of a MHD Williamson Fluid Over a Vertical Convective Surface

2018 ◽  
Vol 7 (4) ◽  
pp. 309-321 ◽  
Author(s):  
CH. Amanulla ◽  
N. Nagendra ◽  
M. Suryanarayana Reddy
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Skin Friction ◽  
Conductive Polymer ◽  
Skin Friction Coefficient ◽  
Polymer Materials ◽  
Radial Magnetic Field ◽  
Similarity Transformations ◽  
Keller Box Method

Abstract An analysis of this paper is examined, two-dimensional, laminar with heat transfer on natural convective flow in an electro-conductive polymer on the external surface of a vertical plate under radial magnetic field and slip effects is considered. The coupled governing partial differential equations are transformed to ordinary differential equations by using non-similarity transformations. The obtained ordinary differential equations are solved numerically by a well-known method named as Keller Box Method (KBM). The computed results for the velocity and temperature profiles as well as heat transfer and skin-friction coefficient have been depicted and discussed in detail through graphs for various parametric conditions. Increasing thermal slip strongly decreases skin friction and Nusselt number. Skin friction is also depressed with increasing magnetic body force parameter. Increasing momentum slip is observed to decrease skin friction. The model is relevant to the simulation of magnetic polymer materials processing.

scholarly journals Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet in a micropolar fluid

2013 ◽  
Vol 17 (2) ◽  
pp. 525-532
Author(s):  
Nor Yacob ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Leading Edge ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Keller Box Method ◽  
Flow And Heat Transfer ◽  
The Magnetic Field

An analysis is carried out for the steady two-dimensional mixed convection flow adjacent to a stretching vertical sheet immersed in an incompressible electrically conducting micropolar fluid. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the leading edge. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically using a finite difference scheme known as the Keller box method. The effects of magnetic and material parameters on the flow and heat transfer characteristics are discussed. It is found that the magnetic field reduces both the skin friction coefficient and the heat transfer rate at the surface for any given K and ?. Conversely, both of them increase as the material parameter increases for fixed values of M and ?.

scholarly journals Flow and Heat Transfer at a Nonlinearly Shrinking Porous Sheet:The Case of Asymptotically Large Powerlaw Shrinking Rates

2013 ◽  
Vol 18 (3) ◽  
pp. 779-791 ◽  
Author(s):  
K.V. Prasad ◽  
K. Vajravelu ◽  
I. Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Temperature Fields ◽  
Shrinking Sheet ◽  
Arbitrary Power ◽  
Keller Box Method ◽  
Flow And Heat Transfer

Abstract The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.

scholarly journals Stagnation-point flow past a shrinking sheet in a nanofluid

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Roslinda Nazar ◽  
Mihaela Jaradat ◽  
Norihan Arifin ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Nonlinear System ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

AbstractIn this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It was found that nanoparticles of low thermal conductivity, TiO2, have better enhancement on heat transfer compared to nanoparticles Al2O3 and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.

scholarly journals Unsteady Transport Phenomena of Hybrid Al2O3-Cu/H2O Nanofluid Past a Shrinking Slender Cylinder

2021 ◽  
Vol 50 (12) ◽  
pp. 3753-3764
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Theoretical Investigations ◽  
Suitable Form ◽  
Layer Flow

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

Radiative and Viscous Ohmic Dissipation on MHD Tangent Hyperbolic Fluid over a Convectively Heated Sheet in a Suspension of Dust Particles

2018 ◽  
Vol 16 ◽  
pp. 177-190 ◽  
Author(s):  
S.U. Mamatha ◽  
Chakravarthula S.K. Raju ◽  
Mahesha ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ohmic Heating ◽  
Skin Friction Coefficient ◽  
Dust Particles ◽  
Stretching Surface ◽  
Ohmic Dissipation ◽  
Transfer Rates ◽  
Similarity Transformations ◽  
Tangent Hyperbolic Fluid

The present study deals with steady incompressible magneto hydrodynamic hyperbolic tangent fluid flow induced by a convectively heated stretching surface with the suspension of dust particles, Darcy-Forchheimer, thermal radiation, viscous dissipation and Ohmic heating. Similarity transformations were used to convert partial differential equations (PDEs) to a system of nonlinear ordinary differential equations (NODEs) which are solved numerically by Runge-Kutta Fehlberg method. The effect of pertinent parameters on velocity and temperature profiles of both fluid and dust phase within the boundary layer has been studied by considering various values of controlling parameters. Additionally, the skin friction coefficient and reduced heat transfer coefficient have been examined for various values of the governing parameters. It is found that Hartmann number and Forchheimer parameter reduce friction factor and heat transfer rates.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Ferrofluids

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Nurfazila Rasli ◽  
Norshafira Ramli
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Magnetohydrodynamic Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

In this research, the problem of magnetohydrodynamic flow and heat transfer over an exponentially stretching/shrinking sheet in ferrofluids is presented. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying suitable similarity transformations. These equations are then solved numerically using the shooting method for some pertinent parameters. For this research, the water-based ferrofluid is considered with three types of ferroparticles: magnetite, cobalt ferrite, and manganese-zinc ferrite. The numerical solutions on the skin friction coefficient, Nusselt number, velocity and temperature profiles influenced by the magnetic parameter, wall mass transfer parameter, stretching/shrinking parameter, and volume fraction of solid ferroparticle are graphically displayed and discussed in more details. The existences of dual solutions are noticeable for the stretching/shrinking case in a specific range of limit. For the first solution, an increasing number in magnetic and suction will also give an increment of skin friction coefficient and Nusselt number over stretching/shrinking sheet. For the skin friction coefficient only, it is showed a decreasing pattern after the intersection. Besides, the presence of ferroparticles in the fluids causes a high number of the fluid’s thermal conductivity and heat transfer rate.

Melting heat transfer in boundary layer stagnation-point flow of a nanofluid towards a stretching–shrinking sheet

2014 ◽  
Vol 92 (12) ◽  
pp. 1703-1708 ◽  
Author(s):  
Kishore Kumar Ch. ◽  
Shankar Bandari
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Fourth Order Method

The present analysis deals with the study of two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow of a nanofluid towards a melting stretching sheet. Using similarity transformations, the governing differential equations were transformed into coupled, nonlinear ordinary differential equations, which were then solved numerically by using the Runge–Kutta fourth-order method along with the shooting technique for two types of nanoparticles namely copper (Cu) and silver (Ag) in the water-based fluid with Prandtl number Pr = 6.2, the skin friction coefficient, the local Nusselt number, the velocity and the temperature profiles are presented graphically and discussed.

Two-Phase Flow of Fluid-Particle Interaction over a Stretching Sheet in the Presence of Magnetic Field

2019 ◽  
Vol 20 (6) ◽  
pp. 651-659
Author(s):  
J. Hasnain ◽  
Z. Abbas ◽  
M. Sajid
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Perturbation Technique ◽  
Particle Interaction ◽  
Skin Friction Coefficient ◽  
Second Grade ◽  
Two Phase ◽  
Similarity Transformations ◽  
Keller Box Method ◽  
Layer Flow

AbstractThis article presents a theoretical study of magnetohydrodynamic boundary layer flow of a dusty viscoelastic fluid over a porous stretching sheet. The basic steady equations of the viscoelastic second grade fluid and dust phases are in the form of partial differential equations. A set of coupled nonlinear ordinary differential equations is obtained by using suitable similarity transformations. The approximate first order solutions of the resulting equations are obtained using the perturbation technique. The results are also verified with the well-known finite difference technique known as Keller box method. The physical insight of the involved parameters on the velocity of both fluid and dust phases and the skin-friction coefficient is shown through graphs and tables and discussed in detail. The study shows that an increased effective viscosity increases the velocity of both fluid and particle phase.

Radiative MHD Stagnation-Point Flow with Heat Transfer Past a Permeable Stretching/Shrinking Sheet in a Porous Medium

2017 ◽  
Vol 11 ◽  
pp. 110-128
Author(s):  
Shoeb R. Sayyed ◽  
B.B. Singh ◽  
Nasreen Bano
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Nonlinear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Energy Equations

In the present study, an analytical analysis has been carried out to investigate the MHD stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in a porous medium in the presence of thermal radiation. Similarity transformations have been employed to simplify the momentum and energy equations into coupled nonlinear ordinary differential equations. The resulting nonlinear ordinary differential equations are then solved analytically through BVPh 2.0 Mathematica package based on homotopy analysis method (HAM). Effects of various parameters such as Prandtl number, permeability parameter, magnetic parameter, suction/blowing parameter, stretching/shrinking parameter, radiation parameter and wall temperature exponent on velocity and/or temperature profiles are explored and discussed graphically. Our results have been compared with the available literature and have been found in excellent agreement. This study may have applications in metallurgy industry and aerodynamic extrusion of plastic sheet.

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.

Sign in / Sign up

Export Citation Format

Share Document