×

Theory of thermomicrofluids. (English) Zbl 0241.76012


MSC:

76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Eringen, A. C., Internat. J. Engrg. Sci., 2, 205 (1964)
[2] Eringen, A. C., J. Math. Mech., 16, 1 (1966)
[3] Eringen, A. C., (Huang, T. C.; Johnson, M. W., Developments in Mechanics, Vol. 3 (1967), Wiley: Wiley New York), Part 1
[4] Eringen, A. C., (Görtler, H., Proceedings of the Eleventh International Congress of Applied Mechanics (1966), Springer-Verlag: Springer-Verlag Berlin)
[5] Eringen, A. C., Internat. J. Engrg. Sci., 5, 191 (1967)
[6] Eringen, A. C., Internat. J. Engrg. Sci., 7, 115 (1969)
[7] Lee, J. D.; Eringen, A. C., Wave Propagation in Nematic Liquid Crystals, J. Chem. Phys., 54, 5027 (1971)
[8] Eringen, A. C.; Chang, T. S., (Recent Advances in Engineering Science, Vol. V (1970), Gordon & Breach: Gordon & Breach New York), Part II
[9] T. ArimanJ. Biomechanics; T. ArimanJ. Biomechanics · Zbl 0153.55703
[10] Hudimoto, B.; Tokuoka, T., Internat. J. Engrg. Sci., 7, 515 (1969)
[11] Allen, S. J.; Kline, K. A., Z. Angew. Math. Phys., 20, 145 (1969)
[12] Kaloni, P. N.; DeSilva, C. N., Phys. Fluids, 12, 994 (1969) · Zbl 0191.23501
[13] Eringen, A. C., (Kröner, E., Mechanics of Generalized Continua (1968), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0181.53802
[14] Stojanović, R., Mechanics of Polar Continua (1969), Intern. Center for Mechanical Sciences publications: Intern. Center for Mechanical Sciences publications Udine, Italy
[15] Allen, S. J.; DeSilva, C. N.; Kline, K. A., Errata, Phys. Fluids, 11, 1590 (1968)
[16] Kline, K. A.; Allen, S. J., Z. Angew. Math. Phys., 19, 898 (1968)
[17] Allen, S. J.; Kline, K. A., Z. Angew. Math. Phys., 19, 425 (1968)
[18] DeSilva, C. N.; Kline, K. A., Z. Angew. Math. Phys., 19, 128 (1968)
[19] Eringen, A. C.; Suhubi, E. S., Internat. J. Engrg. Sci., 2, 389 (1964)
[20] Eringen, A. C., Nonlinear Theory of Continuous Media (1962), McGraw-Hill: McGraw-Hill New York
[21] Allen, S. J.; DeSilva, C. N., J. Fluid Mech., 24, 801 (1966)
[22] This work and Refs. [2] and [3] were widely distributed (400 copies each) as ONR reports in 1964 and 1965, and [4] was presented at the 11th International Conference of Applied Mechanics at Munich, August 1964. Reference [3] was presented at the 9th Midwestern Conference of Applied Mechanics at the University of Wisconsin, August 1965.; This work and Refs. [2] and [3] were widely distributed (400 copies each) as ONR reports in 1964 and 1965, and [4] was presented at the 11th International Conference of Applied Mechanics at Munich, August 1964. Reference [3] was presented at the 9th Midwestern Conference of Applied Mechanics at the University of Wisconsin, August 1965.
[23] E. L. Aero and E. V. KuvshinskiiFiziko Tverdogo Tela2; E. L. Aero and E. V. KuvshinskiiFiziko Tverdogo Tela2
[24] Grad, H., J. Phys. Chem., 56, 1039 (1952)
[25] Dahler, J. S.; Scriven, E. E., (Proc. Roy. Soc. (London), A275 (1963)), 504
[26] Cosserat, E.; Cosserat, F., Théorie des Corps Déformable (1909), Herman: Herman Paris · JFM 40.0862.02
[27] Eringen, A. C., Internat. J. Engrg. Sci., 8, 819 (1970)
[28] The present \(ν_{ kl }b_{ kl }ν_{ lk }b_{ lk } \); The present \(ν_{ kl }b_{ kl }ν_{ lk }b_{ lk } \)
[29] These results for isothermal fluids were given in our previous work [2].; These results for isothermal fluids were given in our previous work [2].
[30] In an algebraic error in Ref. [2] we had slightly different forms for the second and fifth of these inequalities. Identical inequalities arise in micropolar elasticity for which, and for fluids, correct forms were given in our later work (cf. Refs. [31] and [6]). Incidentally, these works were distributed widely (400 copies) as ONR reports a year prior to their publication. Cowin [32] apparently did not notice these references and wrote an essay on our error in the second of these inequalities; however, he missed the fifth completely.; In an algebraic error in Ref. [2] we had slightly different forms for the second and fifth of these inequalities. Identical inequalities arise in micropolar elasticity for which, and for fluids, correct forms were given in our later work (cf. Refs. [31] and [6]). Incidentally, these works were distributed widely (400 copies) as ONR reports a year prior to their publication. Cowin [32] apparently did not notice these references and wrote an essay on our error in the second of these inequalities; however, he missed the fifth completely.
[31] Eringen, A. C., (Liebowitz, H., Fracture, Vol. II (1968), Academic Press: Academic Press New York)
[32] Cowin, S. C.; Pennington, C. J., Trans. Soc. Rheology, 13, 387 (1969)
[33] Kline, K. A.; Allen, S. J., Z. Angew. Math. Mech., 48, 435 (1968)
[34] This choice of constitutive variables is to be contrasted with that of Kline and Allen [33] wherein \(χ^k_{K\)
[35] Brenner, H., Rheology of Two-Phase Systems, Annual Review of Fluid Mechanics, Vol. 2 (1970)
[36] Skalak, R., (Fung; Perrone; Anliker, Biomechanics, Its Foundations and Objectives (1972), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ)
[37] Eringen, A. C., Continuum Foundation of Rheology-New Adventures, (Opening address, MS submitted May 1970 and presented at the International Symposium on Rheologically Complex Fluids. Opening address, MS submitted May 1970 and presented at the International Symposium on Rheologically Complex Fluids, Herceg-Novi, Yugoslavia (Sept. 8, 1970)), Publication of the Proceedings of this meeting is still pending · Zbl 0716.76012
[38] Heat Conducting Micropolar Fluids. Heat Conducting Micropolar Fluids, Rheol. Acta, 319 (1971), published recently · Zbl 0226.76003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.