Unsteady two-dimensional and axisymmetric mhd boundary-layer flows
TL;DR: In this article, the effects of surface mass transfer, Joule heating and viscous dissipation on the effect of magnetic field on the skin friction is analyzed. But the effect is more pronounced as compared to its effect on heat transfer.
Abstract: Nonsimilar solution of the unsteady laminar incompressible magneto-hydrodynamic boundary layer flow and heat transfer for an electrically conducting fluid over two-dimensional and axisymmetric bodies in the presence of an applied magnetic field has been obtained. The effects of surface mass transfer, Joule heating and viscous dissipation are included in the analysis. Numerical computation have been carried out for the flow over a circular cylinder and a sphere using an implicit finite difference scheme in combination with a quasi-linearization technique. It is observed that magnetic field and suction cause the location of vanishing skin friction to move downstream while, the effect of injection is just the opposite. The effect of magnetic field on the skin friction is more pronounced as compared to its effect on the heat transfer. On the other hand, the heat transfer is strongly affected by the viscous dissipation and the effect is more for larte times. However, heat transfer responds comparatively less to the fluctuations of the free stream than the skin friction.
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TL;DR: In this paper, contact conduction and contact resistance were investigated. But contact conuction with convection, phase change, and phase change was not one of the main issues in this paper.
Abstract: 2. Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1892 2.1. Contact conduction and contact resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1892 2.2. Micro/nanoscale thermal effects, laser pulse heating, and hyperbolic heat transport . . 1892 2.3. Composites, heterogeneous media and complex geometries . . . . . . . . . . . . . . . . . . . 1893 2.4. Conduction with convection, phase change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893 2.5. Analytical, numerical and experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893 2.6. Thermomechanical problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893 2.7. Miscellaneous and special applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893
53 citations
TL;DR: In this paper, the authors examined the unsteady magnetohydrodynamic (MHD) mixed convection flow over a sphere combined with variable fluid properties, and found that vanishing skin friction is prevented or at least delayed by enhancing the mixed convections in both the cases of steady and unstrainy fluid flow.
Abstract: This paper examines the unsteady magnetohydrodynamic (MHD) mixed convection flow over a sphere combined with variable fluid properties. An implicit finite difference scheme, together with the quasi-linearization, is used to find non-similar solutions for the governing equations. The vanishing skin friction is prevented or at least delayed by enhancing the mixed convection in both the cases of steady and unsteady fluid flow. Both skin friction and heat transfer coefficients are found to be increasing with an increase in time or MHD parameter.
13 citations
TL;DR: In this article, free convective magnetohydrodynamic flow from a spinning vertical cone to an orthotropic Darcian porous medium under a transverse magnetic field was studied and the non-dimensionalized two-point boundary value problem was solved numerically using the Keller Box implicit finite difference method.
Abstract: Free convective magnetohydrodynamic flow from a spinning vertical cone to an orthotropic Darcian porous medium under a transverse magnetic field is studied. The non-dimensionalized two-point boundary value problem is solved numerically using the Keller Box implicit finite difference method. The effects of spin parameter, orthotropic permeability functions, Prandtl number and hydromagnetic number on flow characteristics are presented graphically. Tangential velocity and swirl velocity are accentuated with increasing permeability owing to a corresponding decrease in porous media resistance. Temperatures are depressed with increasing permeability. Validation of the solutions is achieved with earlier studies. Applications of the study arise in electromagnetic spin coating materials processing.
11 citations
Abstract: Purpose
The purpose of this paper is to consider axisymmetric mixed convection flow of water over a sphere with variable viscosity and Prandtl number and an applied magnetic field.
Design/methodology/approach
The non-similar solutions have been obtained from the origin of the streamwise co-ordinate to the point of zero skin friction using quasilinearization technique with an implicit finite-difference scheme.
Findings
The effect of M is not notable on the temperature and heat transfer coefficient when λ is large. The skin friction coefficient and velocity profile are enhance with the increase of MHD parameter M when λ is small. Viscous dissipation has no significant on the skin friction coefficient under MHD effect. For M=1, the movement of the slot or slot suction or slot injection do not cause any effect on flow separation. The slot suction and the movement of the slot in downstream direction delay the point of zero skin friction for M=0.
Originality/value
The present results are original and new for water boundary-layer flow over sphere in mixed convection flow with MHD effect and non-uniform mass transfer. So this study would be useful in analysing the skin friction and heat transfer coefficient on sphere of mixed convection flow of water boundary layer with MHD effect.
11 citations
Cites background or result from "Unsteady two-dimensional and axisym..."
...7) with those of Sathyakrishna et al. (2001), where A1⁄4 0, λ1⁄4 0 and Ec1⁄4 0 2241 Non-uniform mass transfer...
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...Comparison of the skin friction coefficient for constant properties (Pr¼ 0.7) with those of Sathyakrishna et al. (2001), where A¼ 0, λ¼ 0 and Ec¼ 0 D ow nl oa de d by E K B D at a C en te r A t 1 2: 31 2 0 Se pt em be r 20 16 ( PT ) Figures 4 and 5 display the result of MHD parameter M on the skin…...
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...18 16 14 12 λ=50 λ=20 λ=10 λ=5 λ=2 λ=1 λ=0 Chen et al. (1977) present results 10 C f(R e) 1/ 2 8 6 4 2 0 0 10 20 30 40 50 φ, degrees 60 70 80 90 C f(R e) 1/ 2 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0 0.5 Sathyakrishna et al. (2001) M=0.0 M=0.5 M=1.0 present results 1 1.5 2 x Figure 3....
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...Sathyakrishna et al. (2001) found that the effect of magnetic field on the skin friction is more pronounced as compared to its effect on the heat transfer....
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...We have found that the results obtained by taking Pr¼ 0.7, M¼ 0, Ec¼ 0 and A¼ 0 are have excellent agreement with Chen and Mucoglu (1977) and the results obtained by taking Pr¼ 0.7, λ¼ 0, Ec¼ 0 and A¼ 0 are have excellent agreement with Sathyakrishna et al. (2001) (see Figures 2 and 3)....
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TL;DR: In this paper, the impact of roughness on nonlinear mixed convective nanofluid flow past a sphere is analyzed in the presence of nonlinear density variations, where the problem is modelled in the form of a nonlinear partial differential equations that are dimensional in nature.
Abstract: The impact of roughness on nonlinear mixed convective nanofluid flow past a sphere is analysed in the presence of nonlinear density variations. This study is found to be innovative as it investigates the effects of nanoparticles, nonlinearity and surface roughness on mixed convective flow past a sphere with three diffusive components. The problem is modelled in the form of nonlinear partial differential equations that are dimensional in nature. This set of equations is transformed to dimensionless form by applying non-similar transformations. The technique of Quasilinearization is employed to linearize the transformed set of equations and then the implicit finite difference scheme is used for further simulation to get the required numerical solutions. The graphical presentation of numerical results exhibit that the friction, heat, mass and nanoparticles mass transfer rates at the surface of sphere increase along with the fluid's velocity due to the roughness of the surface, while the fluid's temperature reduces, significantly. The steep jump in the fluid's velocity near the wall is observed due to the surface roughness. The present analysis reveals that separation of boundary layer can be delayed with the proper selection of roughness and mixed convection parameters. Also, the third diffusing component, namely, liquid oxygen influences the fluid flow significantly. That is, the introduction of liquid oxygen diffusion into the liquid hydrogen diffusion diminishes the species concentration boundary layer, while it increases the corresponding mass transfer rate.
10 citations
References
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Book•
01 Jan 1955
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.
17,321 citations
TL;DR: In this article, a solution method is described and applied for treating non-similar thermal boundary layers, where the solutions are locally autonomous and are found by solving quasi-ordinary differential equations of the similarity type.
Abstract: A solution method is described and applied for treating non-similar thermal boundary layers. The solutions are locally autonomous (that is, independent of information from other streamwise locations) and are found by solving quasi-ordinary differential equations of the similarity type. All non-similar terms appearing in the conservation equations are retained without approximation, and only in derived subsidiary equations are terms selectively neglected. The accuracy of the results can be appraised from comparisons internal to the method itself. Thermal boundary-layer non-similarity arising both from velocity-field, non-similarity and from streamwise variations of surface temperature are analyzed. Numerical results for the surface heat transfer and for the boundary-layer temperature distribution are presented for various physical situations.
308 citations
TL;DR: In this article, a new solution method for nonsimilarity boundary layers, applicable locally and independently of information from other stream wise positions, is described and implemented, which is of the same type as those encountered in the treatment of similarity boundary layers.
Abstract: A new solution method for nonsimilarity boundary layers, applicable locally and independently of information from other stream wise positions, is described and implemented. The governing equations generated by the local nonsimilarity solution method are of the same type as those encountered in the treatment of similarity boundary layers. In addition to its local applicability, the utility of the new method is enhanced by its simplicity and directness, both in concept and in actual computations. Several nonsimilar velocity boundarylayer problems are solved herein with a view to illustrating the method, the participating nonsimilarities stemming from the freestream velocity distribution, surface mass transfer, and transverse curvature. On the basis of comparisons with available published information as well as of comparisons internal to the method itself, it may be concluded that the local nonsimilarity method provides results of high accuracy at all streamwise locations, except those near a point of separation.
243 citations
153 citations
"Unsteady two-dimensional and axisym..." refers methods in this paper
...The system of partial differential equations (1) and (2) along with boundary conditions (3) and initial conditions (5) using either the relations (10) and (11) or (13) and (14) has been solved using an implicit finite difference scheme in combination with a quasi-linearization technique [ 14 ]....
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TL;DR: In this paper, the work of Goldstein and Stewartson has been extended to include suction through a porous surface and the stream function xjrl is expanded in a series of the type = 2 ^ 3 £ 6 4 (f) + 2 H *In g[F,(f +fiF, (f)] + 0 *In©, r = 0 where £ = x, y =yl/2*x and (jq, y x) are non-dimensional distances measured from the separation point.
Abstract: Numerical solutions of the laminar boundary-layer equation for the mainstream velocity U = t/0(l — ^x) without suction have been obtained by Hartree and Leigh, and the solutions have suggested that a singularity is present at the separation point. Assuming the existence of this singularity, Goldstein developed an asymptotic solution in the upstream neighbourhood of separation, but his solution required that a certain integral condition must be satisfied. Stewartson extended this asymptotic solution so as to be independent of any integral condition. Jones and Leigh have compared the numerical and asymptotic solutions and have found satisfactory agreement between them. In part I of this paper the work of Goldstein and Stewartson has been extended to include suction through a porous surface. The stream function xjrl is expanded in a series of the type = 2 ^ 3 £ 6 4 (f) + 2 H *In g[F,(f) +fiF,(f)] + 0(*“ In©, r = 0 where £ = x , y =yl/2*x and (jq, y x) are non-dimensional distances measured from the separation point. Analytical solutions for the functions f r(v) = 0, 1, ...,5 ) have been obtained and the solutions for r = 0, 1, ..., 4 reduce to those given by Goldstein in the case of zero suction. The solution for f^yj) without suction was confirmed by comparison with the numerical work of Jones, and corrections were made to his values for two constants. The solution for without suction was next considered so as to show that Goldstein’s condition is not satisfied. This condition required the vanishing of a certain integral estimated by Jones at ( — 4 + 4)
133 citations
"Unsteady two-dimensional and axisym..." refers methods in this paper
...The foregoing numerical method eliminates the difficulties encountered by many investigators [1]-[ 8 ] at the starting point of the streamwise co-ordinate (~ or x) and near the point of zero skin friction....
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