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  • Wiley-Blackwell  (3)
  • 1985-1989  (2)
  • 1970-1974  (1)
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  • 1
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Consider a solid heat conductor with a non-linear constitutive equation for the heat flux. If the material is anisotropic and inhomogeneous, the heat conduction equation to be satisfied by the temperature field θ(x, t) is, \documentclass{article}\pagestyle{empty}\begin{document}$$ \rho c\frac{{\partial \theta }}{{\partial t}} = {\rm div}({\rm L}(\theta,{\rm x})[{\rm grad}\theta]) + q $$\end{document} Here L(θ, x) [grad θ] is a vector-valued function of θ, x, grad θ which is linear in grad θ, In the present paper, the application of the finite element method to the solution of this class of problems is demonstrated. General discrete models are developed which enable approximate solutions to be obtained for arbitrary three-dimensional regions and the following boundary and initial conditions: (a) prescribed surface temperature, (b) prescribed heat flux at the surface and (c) linear heat transfer at the surface. Numerical examples involve a homogeneous solid with a dimensionless temperature-diffusivity curve of the form κ = κ0(l + σT). The resulting system of non-linear differential equations is integrated numerically.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: In a previous article (J. Fernández Rico, R. López and G. Ramírez, J. Comp. Chem., 9, 790 (1988)) we have proposed the calculation of molecular integrals involving STOs by means of some recurrence relations which use two sets (h and H) of overlap integrals (basic matrices). In the present paper, we derive explicit expressions of these integrals employing the two-range expansion of the 0s-function. This approach yields equations for the elements of the two basic matrices in terms of two further matrices, k(x,y) and i(x,y), and some auxiliary functions. Relations between the elements of these matrices and the functions are thoroughly explored and numerical tests are included for illustrating the behavior of the method.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We present a new algorithm for the calculation of two-center one-electron integrals with STOS based on two sets of recurrence relations. The first one enables us to calculate any of these integrals in terms of a few “basic integrals.” Furthermore, these basic integrals are written in terms of certain auxiliary functions which can be obtained through the second set of relations from only two starting values. We give also simple formulas for these starting quantities. Finally, the numerical stability, accuracy, and speed of the different steps of the algorithm are analyzed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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