Integral equation solution

Flow considered in integral equation solution for stagnation region. [Pg.519]

Integral Equation Solutions. As a consequence of the quasi-steady approximation for gas-phase transport processes, a rigorous simultaneous solution of the governing differential equations is not necessary. This mathematical simplification permits independent analytical solution of each of the ordinary and partial differential equations for selected boundary conditions. Matching of the remaining boundary condition can be accomplished by an iterative numerical analysis of the solutions to the governing differential equations. [Pg.32]

A method for obtaining integral equation solutions to Equations 2, 3, and 4 for the quasi-steady gas-phase temperature and weight fraction... [Pg.33]

Upon substituting these boundary conditions in Equation A-6 into Equation A-5, the integral equation solution is ... [Pg.48]

The integral equation solution resulting from the substitution of boundary conditions Equation A-10 into Equation A-5 is ... [Pg.49]

Mackie, R. L., Madden, T. R., and P. E. Wannamaker, 1993, Three-dimensional magnetotelluric modeling using difference equations - theory and comparisons to integral equation solutions Geophysics, 58, 215-226. [Pg.390]

Kelmanson, M. A. Boundary integral equation solution of viscous flows with free surfaces,... [Pg.379]

Mills PL, Dudukovic MP. Integral equation solution for the effectiveness factor of partially wetted catalysts. Ind. Eng. Chem. 1982 21 1. [Pg.129]

A second general technique for treating the angular distribution of the neutron flux is presented in Sec. 7.4. This is the method of integral equations. Solutions for the directed flux 0(r,Q) are derived on the basis of the one-velocity model for various media of infinite extent. The application of these solutions for the infinite medium to systems of finite size is demonstrated in the case of the homogeneous slab and sphere. [Pg.331]

Strength reduced the caleolsted for vater>like parameters by 30 percent or more and linear BNC integral equation solutions (33) gave similar results. This sort of quadrupole is however not appropriate for the water molecule as for tetrahedral symmetrv vanishes but a tetrahedral... [Pg.80]

Determine the stresses in a thick wall cylinder similar the one of Fig. 9.1 using the integral equation solution given by Eq. 9.58. Use the assumption of a step input in pressure as well as elastic response in bulk and Maxwellian in shear as in the earlier example. Compare your solution to that obtained using the correspondence principle. [Pg.325]

This, for the time being, completes the thin airfoil mathematical formulation. The small inclination limit assumed here is taken to explore the role of edge singularities and the nonuniqueness of an integral equation solution more general solutions not bearing this limitation are given in Chapter 5. At this point, we introduce nondimensional variables x, y and p(x,y) defined by... [Pg.46]

Integral equation solution. Fortunately, we do not need to understand the mechanics required to solve integral equations like Equation 3-23. Indeed, the general solution to the equation... [Pg.47]

Integral equation solution. This integral equation was encountered in Chapter 3, where we discussed shale flow modeling. The general solution to... [Pg.98]

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