Showing papers on "Hartmann number published in 1973"
TL;DR: In this paper, an analysis of the fully-developed MHD free convective flow between two vertical, electrically conducting plates has been carried out, and the effects of the external circuit, heat sources and modified boundary conditions on the temperature at the non-perfect thermally conducting plates have been studied.
Abstract: An analysis of the fully-developed MHD free convective flow between two vertical, electrically conducting plates has been carried out. The effects of the external circuit, heat sources and modified boundary conditions on the temperature at the non-perfect thermally conducting plates have been studied. The nonlinear integro-differential equations, governing the flow, have been solved by perturbation method. Velocity and temperature profiles have been shown on graphs and the numerical values of other quantities are entered in tables. It is observed that the flow is stable at small values ofM, the Hartmann number, whereas at large values ofM, an increase inΦ
1 (the thermal conductance ratio) or λ (line heat source) leads to an instability of the flow. However, instability of the flow may be avoided by selecting the plates of high electrical conductivity.
12 citations
TL;DR: In this paper, the boundary layer equations of electrically conducting fluids over a semi-infinite horizontal flat plate due to the simultaneous action of buoyancy and applied vertical magnetic field are derived.
Abstract: The boundary layer equations of electrically conducting fluids over a semi-infinite horizontal flat plate due to the simultaneous action of buoyancy and applied vertical magnetic field are derived. The case when the surface temperature and the applied magnetic field are constant is studied in detail by Karman-Pohlhausen integral technique. Expressions for the shear stress and heat transfer at the plate are calculated for small Hartmann number and for any Prandtl number.
8 citations
TL;DR: In this article, the streaming flow of a weakly conducting viscous fluid past a nonconducting sphere in the presence of an aligned uniform magnetic field was investigated for low Hartmann numbers using a Galerkin method.
Abstract: The streaming flow of a weakly conducting viscous fluid past a nonconducting sphere in the presence of an aligned uniform magnetic field is investigated for low Hartmann numbers using a Galerkin method. If convection effects are neglected, it is found that eddies occur symmetrically fore and aft of the sphere when the Hartmann number exceeds 2.9.
4 citations
TL;DR: In this article, extremum principles for the rectilinear flow of a fluid in a pipe under the influence of a uniform magnetic field are established for the mass-flow rate which can be used to construct asymptotic formulae valid for large Hartmann numbers.
Abstract: Some extremum principles are established for the rectilinear flow of a fluid in a pipe under the influence of a uniform magnetic field. The pipe walls are composed of non-conducting and conducting segments. Bounds are deduced for the mass-flow rate which can be used to construct asymptotic formulae valid for large Hartmann numbers. Several illustrative examples are included.
3 citations
TL;DR: In this article, the authors deal with the following slow-flow problems in magnetohydrodynamics: (a) the flow in a rectangular cavity which is maintained by the uniform translation of the top wall with the magnetic field arbitrarily orientated.
2 citations
TL;DR: In this article, a numerical solution for the flow of an electrically conducting liquid in a duct of rectangular cross section whose walls in the direction at right angles to the applied magnetic field are nonconducting, whereas those parallel to the field are perfect conductors is given.
Abstract: A numerical solution is given for the problem of the flow of an electrically conducting liquid in a duct of rectangular cross section whose walls in the direction at right angles to the applied magnetic field are nonconducting, whereas those parallel to the field are perfect conductors It is assumed that all the quantities except the pressure are independent of the coordinate along the axis of the duct, that the applied magnetic field is homogeneous, and that the induced current is diverted into an external circuit The total current in the external circuit and the difference of the potentials of the conducting walls are found as functions of the external load, the Hartmann number, and the ratio of the lengths of the sides of the duct It should be noted that problems of this kind have already been considered on many occasions and by many different approximate methods The most complete bibliography on this question can be found in [1]
2 citations
TL;DR: In this paper, an analysis of a MHD composite slider bearing between two electrically conducting plates and in the presence of a magnetic field in the free space is carried out, and asymptotic solutions for the load capacity for a large Hartmann number M are derived and shown graphically.
1 citations
TL;DR: In this article, a similarity transformation is given, which reduces the partial, nonlinear differential equations describing a compressible, polytropic plasma flow across an azimuthal magnetic field in a duct with plane inclined walls to an ordinary non-linear differential equation of second order.
Abstract: A similarity transformation is given, which reduces the partial, nonlinear differential equations describing a compressible, polytropic plasma flow across an azimuthal magnetic field in a duct with plane inclined walls to an ordinary nonlinear differential equation of second order. The latter is solved rigorously in terms of a hyperelliptic integral. The form of the plasma flow fields in pure outflows (diffuser) is discussed analytically in dependence of the Reynolds (R) and Hartmann (H) numbers and the polytropic coefficient (γ) for given duct angles θ0 . The realizable Mach numbers are shown to be eigenvalues of the nonlinear boundary-value problem, M=MX{R, H, γ, θ0). The flow solutions are different in type for Hartmann numbers H 1) below and 2) above a critical Hartmann number Hc defined by Hc2= [2(γ - 1)/(γ +1)]R+ [2 γ/(γ +1)]2. Some of the eigenvalues Mx are calculated and the associated velocity profiles are represented graphically for prescribed flow parameters.
1 citations
01 Dec 1973
TL;DR: In this article, an exact solution for the problem of the flow of a conducting dusty gas occupying a semi-infinite space in the presence of a transverse magnet field was derived by Laplace transform technique.
Abstract: An exact solution is derived by Laplace-transform technique for the problem of the flow of a conducting dusty gas occupying a semi-infinite space in the presence of a transverse magnet field. It is assumed that the flow is independent of the distance parallel to the plate and that the mass concentration of dust is small. Formulas are derived in terms of a constant external impulsive velocity field for the velocity profiles of both the dust and the conducting gas only for values of Hartmann number greater than or equal to unity. For these values of the Hartmann number the skin friction is also obtained.
TL;DR: In this article, the convective instability of a layer of conducting liquid carrying a current and lying in a magnetic field perpendicular to the current was considered, and the problem of nonconductive approximation in a linear setting was solved.
Abstract: The convective instability of a layer of conducting liquid carrying a current and lying in a magnetic field perpendicular to the current is considered. The problem of the nonconductive approximation in a linear setting is solved. The relationships between the Rayleigh number and the Hartmann number (determining the neutral stability) are derived.
TL;DR: In this article, the stability of plane-parallel flows of a viscous, electrically conducting fluid in a transverse magnetic field is studied. But the results obtained agree with the calculations of Lock and Kakutani and are at variance with the results of Pavlov.
Abstract: We study within the framework of linear theory the stability of plane-parallel flows of a viscous, electrically conducting fluid in a transverse magnetic field. The magnetic Reynolds numbers are assumed small. The critical Reynolds number as a function of the Hartmann number is obtained over the entire range of variation of the latter. The small perturbation spectrum is studied in detail on the example of Hartmann flow. Neutral curves are constructed for symmetric and antisymmetric disturbances. The destablizing effect of a magnetic field is studied in the case of modified Couette flow. The results obtained agree with the calculations of Lock and Kakutani (where they meet) and are at variance with the results of Pavlov.
TL;DR: In this paper, the stability of the interface between viscous conducting media in the presence of a current and a magnetic field for a magnetic Reynolds number much smaller than unity was considered.
Abstract: The paper considers the stability of the interface between viscous conducting media in the presence of a current and a magnetic field for a magnetic Reynolds number much smaller than unity. In order to obtain the dispersion relationships, a method is used that is based on the variational principle. It is shown that the method indicated yields good results when the magnetic field is considered. The dependence of the maximum growth rate of the instability on the defining parameters is presented. The problem of the stability of a fluid layer situated between solid walls for linearly distributed conductivity and density is likewise solved. The stabilizing effect of the Hartmann number on the stability is shown.