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  • 1
    Electronic Resource
    Electronic Resource
    Numerical solution of a singular integral equation appearing in magnetohydrodynamics (1984)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 35 (1984), S. 760-770 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Für den MHD Fluß durch ein rechteckiges Rohr mit gut leitenden Elektroden wurde die numerische Lösung für die Geschwindigkeit und das induzierte Feld ermittelt. Das Problem ließ sich auf eine singuläre Integralgleichung zurückführen, die numerisch gelöst wurde. Es hat sich herausgestellt, daß wenn die Hartmann-Zahl größer wird, das Geschwindigkeitsprofil eine Tendenz zur Abflachung zeigt und der Fluß durch den Querschnitt zurückgeht. Im Vergleich mit dem Einsatz von nicht leitenden Wänden wurde ebenfalls ein geringerer Fluß festgestellt. Für die Lösung der Integralgleichung, die Geschwindigkeit und das magnetische induzierte Feld sind graphische Darstellungen und Tabellen angegeben.
    Notes: Abstract The numerical solution for the velocity and induced magnetic field has been obtained for the MHD flow through a rectangular pipe with perfectly conducting electrodes. The problem reduces to the solution of a singular integral equation which has been solved numerically. It is found that as the Hartmann number is increased the velocity profile shows a flattening tendency and the flux through a section is reduced. Also as compared with the case of nonconducting walls the flux is found to be smaller. Graphs and tables are given for the solution of the integral equation and the velocity and induced magnetic field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945441
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Temperature distribution for MHD flow between coaxial cylinders with discontinuity in wall temperatures (1979)
    Springer
    Flow, turbulence and combustion 35 (1979), S. 67-83 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The temperature distribution in the MHD axial flow between two coaxial infinite cylinders under a transverse radial magnetic field has been found out when there is a discontinuity in the wall temperatures at a section of the channel. The numerical values of temperature distribution at large distances from the section have been worked out first for various Hartman numbers. To this is superimposed the perturbation introduced due to discontinuity. Near the region of discontinuity the approximate matching is done by using the finite difference method. Tables and graphs are given to depict the behaviour with various Hartman numbers. A relief of the temperature distribution is also given. It is found that the temperature shows a decreasing tendency with increasing Hartman number, a well-known characteristic of such type of problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00382655
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    One-dimensional mathematical modelling of enclosure fire dynamics (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Fire and Materials 12 (1988), S. 51-60 
    Details
    ISSN: 0308-0501
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a one-dimensional mathematical model of enclosure fire dynamics. The model is based on the fundamental equations of mass, momentum and energy and uses the top hat velocity and temperature profiles for the movement of plume gases. A computational algorithm is also developed to solve the set of transient model partial differential equations. In addition, the explicit equations have been derived for computing the steady state velocity and temperature profiles. These derivations are based on the assumption that the plume width follows the relationship given by Eqn (12). Further, these relationships help to identify a dimensionless parameter, Frs, known as source Froude number, which has a significant effect on the behaviour of the plume gases. It may be noted that this assumption is only applicable for the case of Frs = 1. The plume behaviour is studied with reference to three cases of source Froude numbers, i.e. Frs 〈 1, Frs = 1, Frs 〉 1.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fam.810120203
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  • 4
    Electronic Resource
    Electronic Resource
    Finite element method for unsteady MHD flow through pipes with arbitrary wall conductivity (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 291-302 
    Details
    ISSN: 0271-2091
    Keywords: Finite Elements ; MHD Flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element method is given to obtain the numerical solution of the coupled equations in velocity and magnetic field for unsteady MHD flow through a pipe having arbitrarily conducting walls. Pipes of rectangular, circular and triangular sections have been taken for illustration. Computations have been carried out for different Hartmann numbers and wall conductivity at various time levels. It is found that if the wall conductivity increases, the flux through a section decreases. The same is the effect of increasing the Hartmann number. It is also observed that the steady state is approached at a faster rate for larger Hartmann numbers or larger wall conductivity. Selected graphs are given showing the behaviour of velocity, induced magnetic field and flux across a section.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650040307
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  • 5
    Electronic Resource
    Electronic Resource
    Some numerical experiments on high accuracy fast direct finite difference method for elliptic problems (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 631-641 
    Details
    ISSN: 1069-8299
    Keywords: numerical analysis ; fast direct method ; elliptic problems ; finite difference methods ; eigenvalue problems ; harmonic ; biharmonic ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A high accuracy finite difference scheme has been developed for solving some elliptic problems which appear in engineering and applied sciences. These include Laplace, Poisson, Helmholtz and related equations. The second- and fourth-order problems dealing with vibration of membranes and plates have also been examined. Numerically, the problem reduces to a block tridiagonal system which can be solved by suitably modifying the fast direct method developed by Hockney. Comparison has been made with results obtained from some alternative numerical methods or analytical methods whenever available
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 6
    Electronic Resource
    Electronic Resource
    Boundary characteristic orthogonal polynomials in numerical approximation (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 1027-1043 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes a procedure to generate boundary characteristic orthogonal polynomials (BCOPs) over a domain in Rn. The method is based upon the Gram-Schmidt process of orthogonalization. The orthogonal polynomial sequence (OPS) is generated from a set of linearly independent functions which satisfy the given boundary conditions. The procedure is illustrated by taking several examples in R2, the most important case from the application point of view. Extensive numerical work has been carried out for simple domains like the circle, square and isosceles right-angled triangle. The following cases have been considered: (a) when the BCOPs vanish on the boundary; (b) when they and their normal derivatives vanish on the boundary; (c) when no conditions have been imposed on the boundary. The results for other geometries such as an ellipse, a parallelogram and an arbitrary triangle follow by some simple transformations. The procedure is also applicable to one-dimensional problems and can be easily extended to R3.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640101209
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Finite element method in magnetohydrodynamic channel flow problems (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1104-1111 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method has been applied to the steady-state fully developed magnetohydrodynamic channel flow of a conducting fluid in the presence of transverse magnetic field. Simple elements have been used to obtain the numerical values of velocity and induced magnetic field. To test the efficiency of the method, three different geometries, viz., rectangle, circle and triangle, are taken as the section of the pipe whose walls are non-conducting. Comparison is made with those cases in which exact solutions are available. Apart from giving good results, the FEM makes it possible to solve the problem for a pipe with arbitrary cross-section which was not possible by the other methods.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620180714
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    Paper (German National Licenses)
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