scholarly journals Aligned Magnetic Field and Radiation Effects on Biomagnetic Fluid over an Unsteady Stretching Sheet with Various Slip Conditions

AppliedMath ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 37-62
Author(s):  
Anik Gomes ◽  
Jahangir Alam ◽  
Ghulam Murtaza ◽  
Tahmina Sultana ◽  
Efstratios E. Tzirtzilakis ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Slip Conditions ◽  
Unsteady Stretching Sheet ◽  
Biomagnetic Fluid ◽  
Aligned Magnetic Field

The aim of the present study is to analyze the effects of aligned magnetic field and radiation on biomagnetic fluid flow and heat transfer over an unsteady stretching sheet with various slip conditions. The magnetic field is assumed to be sufficiently strong enough to saturate the ferrofluid, and the variation of magnetization is approximated by a linear function of temperature difference. The governing boundary layer equations with boundary conditions are simplified by suitable transformations. Numerical solution is obtained by using the bvp4c function technique in MATLAB software. The numerical results are derived for the velocity, temperature, the skin friction coefficient, and the rate of heat transfer. The evaluated results are compared with analytical study documented in scientific literature. The present investigation illustrates that the fluid velocity is decreased with the increasing values of radiation parameter, magnetic parameter, and ferromagnetic interaction parameter, though is increased as the Prandtl number, Grashof number, permeable parameter and thermal slip parameter are increased. In this investigation, the suction/injection parameter had a good impact on the skin friction coefficient and the rate of heat transfer.

Boundary layer flow near stagnation-points on a vertical surface with slip in the presence of transverse magnetic field

2014 ◽  
Vol 24 (3) ◽  
pp. 643-653 ◽  
Author(s):  
Ibrahim Yakubu Seini ◽  
Daniel Oluwole Makinde
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Stagnation Point ◽  
Vertical Surface ◽  
Skin Friction Coefficient ◽  
Content Type ◽  
Layer Flow

Purpose – The purpose of this paper is to investigate the MHD boundary layer flow of viscous, incompressible and electrically conducting fluid near a stagnation-point on a vertical surface with slip. Design/methodology/approach – In the study, the temperature of the surface and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing differential equations are transformed into systems of ordinary differential equations and solved numerically by a shooting method. Findings – The effects of various parameters on the heat transfer characteristics are discussed. Graphical results are presented for the velocity and temperature profiles whilst the skin-friction coefficient and the rate of heat transfers near the surface are presented. It is observed that the presence of the magnetic field increases the skin-friction coefficient and the rate of heat transfer near the surface towards the stagnation-point. Originality/value – The presence of magnetic field increases the skin-friction coefficient and the rate of heat transfer near the surface towards the stagnation-point.

Flow and Heat Transfer in a Newtonian Nanoliquid due to a Curved Stretching Sheet

2017 ◽  
Vol 72 (9) ◽  
pp. 833-842 ◽  
Author(s):  
Pradeep Ganapathi Siddheshwar ◽  
Meenakshi Nerolu ◽  
Igor Pažanin
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Skin Friction Coefficient ◽  
Variable Coefficients

AbstractFlow of a Newtonian nanoliquid due to a curved stretching sheet and heat transfer in it is studied. The governing nonlinear partial differential equations are reduced to nonlinear ordinary differential equations with variable coefficients by using a similarity transformation. The flow characteristics are studied using plots of flow velocity components and the skin-friction coefficient as a function of suction-injection parameter, curvature, and volume fraction. Prescribed surface temperature and prescribed surface heat flux are considered for studying the temperature distribution in the flow. The thermophysical properties of 20 nanoliquids are considered in the investigation by modeling them through the use of phenomenological laws and mixture theory. The results of the corresponding problem involving a plane stretching sheet is obtained as a particular case of those obtained in the present paper. Skin friction coefficient and Nusselt number are evaluated and it is observed that skin friction coefficient decreases with concentration of nanoparticles in the absence as well as presence of suction where as Nusselt number increases with increase in concentration of nanoparticles in a dilute range.

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

2019 ◽  
Vol 29 (9) ◽  
pp. 3110-3127 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

PurposeThis paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation.Design/methodology/approachThe problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed.FindingsResults found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches.Originality/valueThe problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

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.

Effect of Vertical Baffle Installation on Forced Convective Heat Transfer in Channel Having a Backward Facing Step

2013 ◽  
Vol 388 ◽  
pp. 169-175 ◽  
Author(s):  
Amirhossein Heshmati ◽  
Hussein A. Mohammed ◽  
Mohammad Parsazadeh ◽  
Farshid Fathinia ◽  
Mazlan A. Wahid ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Convective Heat Transfer ◽  
Skin Friction ◽  
Convective Heat ◽  
Average Nusselt Number ◽  
Skin Friction Coefficient ◽  
Expansion Ratio ◽  
Forced Convective Heat Transfer

In this study, forced convective heat transfer is considered in channel over a backward facing step having a baffle on the top wall. Four different geometries with different expansion ratios and different type of baffles are numerically investigated. The study clearly shows that the geometry with expansion ratio 2 and solid baffle has the highest Nusselt number compared to other geometries. Considering both Nusselt number and skin friction coefficient for all four geometries clearly illustrated an increase in average Nusselt number by increasing the expansion ratio. This study clearly shows that mounting a slotted baffle at the top wall instead of a solid baffle caused a decline in average Nusselt number. It is also found that for geometry with expansion ratio of 3 and a slotted baffle on the top of the channel, skin friction coefficient in both bottom wall and step wall has its minimal compared to other geometries.

Convective heat transfer past a continuously moving plate embedded in a non-Darcian porous medium in the presence of a magnetic field

2001 ◽  
Vol 79 (7) ◽  
pp. 1031-1038 ◽  
Author(s):  
E M Abo-Eldahab ◽  
M S El Gendy
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Moving Plate ◽  
Convection And Heat Transfer ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Convective Parameter ◽  
Inertia Parameter

In the present study, free-convection and heat-transfer behavior of an electrically conducting fluid is investigated near a stretching sheet embedded in a non-Darcian medium. The temperature of the stretching sheet is varied. The sheet is stretched linearly with variable velocity and temperature. Boundary-layer equations are derived. The resulting approximate nonlinear ordinary differential equations are solved numerically. Velocity and temperature profiles as well as the local Nusselt number and skin-friction coefficient are computed for various values of the magnetic field, the Prandtl number, the free convective parameter, and the inertia parameter. PACS No.: 44.30+v

scholarly journals Effect of Temperature-Dependent Variable Viscosity on Magnetohydrodynamic Natural Convection Flow along a Vertical Wavy Surface

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Nazma Parveen ◽  
Md. Abdul Alim
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Variable Viscosity ◽  
Skin Friction Coefficient ◽  
Effect Of Temperature ◽  
Convection Flow ◽  
Temperature Dependent ◽  
Natural Convection Flow

The effect of temperature dependent variable viscosity on magnetohydrodynamic (MHD) natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations are first transformed into a nondimensional form using suitable set of dimensionless variables. The resulting nonlinear system of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, the stream lines and the isotherms are shown graphically for a selection of parameters set consisting of viscosity parameter (), magnetic parameter (), and Prandtl number (Pr). Numerical results of the local skin friction coefficient and the rate of heat transfer for different values are also presented in tabular form.

On Two-Dimensional Laminar Hydromagnetic Fluid-Particle Flow Over a Surface in the Presence of a Gravity Field

2000 ◽  
Vol 123 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Analytical Solutions ◽  
Fluid Phase ◽  
Skin Friction Coefficient ◽  
Two Dimensional ◽  
Particle Phase ◽  
Phase Stresses ◽  
The Magnetic Field

A continuum two-phase fluid-particle model accounting for particle-phase stresses and a body force due to the presence of a magnetic field is developed and applied to the problem of two-dimensional laminar hydromagnetic flow of a particulate suspension over a horizontal surface in the presence of a gravity field. Analytical solutions for the velocity distributions and the skin-friction coefficients of both phases are reported. Two cases of wall hydrodynamic (velocity) conditions corresponding to stationary and oscillatory velocity distributions are considered. Numerical evaluations of the analytical solutions are performed and the results are reported graphically to elucidate special features of the solutions. The effects of the particle-phase stresses and the magnetic field are illustrated through representative results for the horizontal velocity profiles, fluid-phase displacement thickness, and the complete skin-friction coefficient for various combinations of the physical parameters. It is found that the presence of the magnetic field increases the fluid-phase skin-friction coefficient for various particulate volume fraction levels while the presence of the particle-phase viscous stresses reduces it for various particle-to-fluid density ratios.

Investigation of Flat-Plate Hypersonic, Turbulent Boundary Layers With Heat Transfer

1961 ◽  
Vol 28 (3) ◽  
pp. 323-329 ◽  
Author(s):  
Eva M. Winkler
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Mach Number ◽  
Flat Plate ◽  
Skin Friction ◽  
Boundary Layers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Reynolds Analogy

Naturally turbulent boundary layers on a cooled flat plate have been investigated at several distances from the leading edge of the plate at a Mach number of 5.2 for three rates of steady-state heat transfer to the surface. Measurements of Pitot and static pressures and of total and wall temperatures made it possible to compute velocity profiles, static-temperature profiles, and boundary-layer parameters without resorting to assumptions. The data demonstrate that the Reynolds analogy between skin friction and heat transfer is valid for all conditions of the present experiments. With increasing rate of heat transfer to the surface, the skin-friction coefficient was found to decrease, a phenomenon opposite to that predicted by theories and empirical relations. On the basis of the present data and other published results of compressible and incompressible turbulent boundary-layer skin friction, a simple relation was devised which describes closely the variation of the skin-friction coefficient with Mach number, heat-transfer rate, and momentum-thickness Reynolds number.

Effect of Inclined Magnetic Field and Heat Transfer in a Walter’s B Fluid over a Stretching Sheet with Elastic Deformation

2020 ◽  
Vol 48 ◽  
pp. 38-48 ◽  
Author(s):  
C. Ragavan ◽  
Muniradhnam ◽  
A.K. Abdul Hakeem ◽  
Manoj K. Nayak ◽  
Oluwole Daniel Makinde
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Viscous Dissipation ◽  
Elastic Deformation ◽  
Power Law ◽  
Stretching Sheet ◽  
Geometric Function ◽  
Flux Boundary Conditions ◽  
Walter’S B Fluid ◽  
Aligned Magnetic Field

This article deals with the heat transfer in a Walter’s liquid B fluid through a stretching sheet subject to elastic deformation. We have incorporated the combined effects of aligned magnetic field and viscous dissipation. The effect of viscous dissipation regulating the heat transfer is considered. In addition, prescribed power law surface temperature and prescribed power law surface heat flux boundary conditions are introduced. The transformed non-linear coupled governing equations are solved analytically using hyper geometric function. The effects of various embedded pertinent parameters on velocity and temperature profiles are well discussed with the aid of appropriate graphs and tables. Our results are verified with previously published results of some noteworthy researchers. It is found that the augmenting aligned magnetic field strength reduces the flow velocity and the related momentum boundary layer thickness.

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