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Theory of thermomicrofluids. (English) Zbl 0241.76012

MSC:
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
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[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, (), Part 1
[4] Eringen, A.C, ()
[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, (), Part II
[9] {\scT. Ariman}, On the analysis of blood flow, J. Biomechanics, to appear. · 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, ()
[14] Stojanović, R, Mechanics of polar continua, (1969), Intern. Center for Mechanical Sciences publications Udine, Italy
[15] Allen, S.J; DeSilva, C.N; Kline, K.A; Allen, S.J; DeSilva, C.N; Kline, K.A, Errata, Phys. fluids, 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; Eringen, A.C; Suhubi, E.S, Internat. J. engrg. sci., Internat. J. engrg. sci., 2, 389, (1964)
[20] Eringen, A.C, Nonlinear theory of continuous media, (1962), 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.
[23] {\scE. L. Aero and E. V. Kuvshinskii}, Fiziko Tverdogo Tela{\bf2}, 1399.
[24] Grad, H, J. phys. chem., 56, 1039, (1952)
[25] Dahler, J.S; Scriven, E.E, (), 504
[26] Cosserat, E; Cosserat, F, Théorie des corps Déformable, (1909), Herman Paris · JFM 40.0862.02
[27] Eringen, A.C, Internat. J. engrg. sci., 8, 819, (1970)
[28] The present νkl and bkl correspond, respectively, to νlk and blk of Ref. [1].
[29] 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.
[31] Eringen, A.C, ()
[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 χkK was used instead of ikl. From the axiom of neighborhood, this implies a kind of fluid with incomplete elastic structure. A complete elastic structure requires the additional inclusion of xkK and χK:Lk (see, for example, Refs. [4] and [5]). Since a dependence of χkK does not imply a dependence on ikl (although the converse is true), the constitutive theory here bears but an aritficial similarity to that in Ref. [33].
[35] Brenner, H, Rheology of two-phase systems, Annual review of fluid mechanics, Vol. 2, (1970)
[36] Skalak, R, ()
[37] Eringen, A.C, Continuum foundation of rheology-new adventures, (), Publication of the Proceedings of this meeting is still pending · Zbl 0716.76012
[38] Heat conducting micropolar fluids, Rheol. acta, 319, (1971), published recently · Zbl 0226.76003
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