Rigorous constructive solution to monodimensional poiseuille and thermal creep flows
Tóm tắt
A rigorous constructive method is discussed for solving the linear integral equations which govern either the Poiseuille flow and the thermal creep flow of a rarefied gas between parallel plates. In both cases numerical results are presented for the nondimensionalized mass flow rate, and for certain quantities which are closely related to the mass and slip velocities. Critical comparison with previous results is made wherever possible.
Tài liệu tham khảo
Abramowitz M. andStegun I. A., Ed.:Handbook of Mathematical Functions, Dover, New York, 1965.
Cercignani C.,Mathematical Methods in the Kinetic Theory, Plenum, New York, 1969.
Williams M. M.,Mathematical Methods in Particle Transport Theory, Butterworths, London, 1971.
Loyalka S. K.,The Physics of Fluids,17, 1053 (1974).
Boffi V. C. andMolinari V. G.,Heterogeneous Methods in Neutron Transport Theory, C.N.E.N. Report-RT/FI (68) 30, Rome, 1968. Meccanica,5, 177 (1970).
Asaoka T., J. Nucl. Energy 22, 99 (1968); Nucl. Sci. Engng. 34, 122 (1968).
Carlvik J., Nucl. Sci. Engng. 31, 295 (1968).
Mikhlin S. G.,Linear Integral Equations, Hindustan Publishing Corp. Dehli, 1960.
It is to be remarked, in fact, that for the eveng(x)'s of Eqs. (3a) and (3b) — which belong toL 2(I) — the corresponding\(\tilde g\)(ω)'s in Eq. (12) are even and belong just toL 2(− ∞, ∞), whereas for the double norm |||\(\tilde K\)||| of the kernel\(\tilde K(\omega ,\eta ) = \frac{{\tilde T - 1(\omega )}}{{\sqrt \pi }} \cdot \tilde p_n (\omega - \eta )\) of Eq. (12) it can be shown that\(|||\tilde K|||< \sqrt {\frac{{8a}}{{3\sqrt \pi }}< \infty } \).
Watson G. N.,The Theory of Bessel Functions, 2nd Edition, Cambridge, At the University Press, 1958.
Erdely A., Ed.:Table of Integral Transforms, Vol. 1, Mc Graw-Hill, New York, 1954.
Cupini E., Dematteis A., Premuda F. andTrombetti R.,Numerical Application of a New Approach to the Solution of the Neutron Transport Equation, C.N.E.N. Report - RT/FI (69) 45, Rome, 1969.
Erdely A., Ed.Higher Transcendental Functions, Vol. II, Mc Graw-Hill, New York, 1953.
Cercignani C. inProceedings of the 3rd Symposium on Rarefied Gas Dynamics, Paris, 1962, edited by Laurmann, Academic Press, New York, 1963.