Some solutions for finitely conducting viscous MHD plane flows

Authors:
O. P. Chandna, C. E. Soteros and M. K. Swaminathan

Journal:
Quart. Appl. Math. **42** (1984), 143-158

MSC:
Primary 76W05; Secondary 58G99

DOI:
https://doi.org/10.1090/qam/745095

MathSciNet review:
745095

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References | Similar Articles | Additional Information

**[1]**Hannes Alfvén,*On the motion of a charge particle in a magnetic field*, Ark. Mat. Astr. Fys.**27A**(1941), no. 22, 20. MR**0011466****[2]**J. G. Kingston and R. F. Talbot,*The solutions to a class of magnetohydrodynamic flows with orthogonal magnetic and velocity field distributions*, Z. Angew. Math. Phys.**20**, 956-965 (1969)**[3]**John S. Waterhouse and John G. Kingston,*Plane magnetohydrodynamic flows with constantly inclined magnetic and velocity fields*, Z. Angew. Math. Phys.**24**(1973), 653–658 (English, with French summary). MR**0331970**, https://doi.org/10.1007/BF01588165**[4]**O. P. Chandna and V. I. Nath,*On the uniqueness of MHD aligned flows with given streamlines*, Canad. J. Phys.**5**, 661-665 (1972)**[5]**V. I. Nath and O. P. Chandna,*On plane viscous magnetohydrodynamic flows*, Quart. of Appl. Math.**31**, 351-362 (1973)**[6]**V. I. Nath and O. P. Chandna,*On plane viscous MHD flows:*II, Quart. of Appl. Math.**32**, 337-341 (1974)**[7]**O. P. Chandna and G. P. Mathur,*Steady viscous magnetohydrodynamic flow in two dimensions with orthogonal magnetic and velocity field distributions*, Tensor (N.S.)**28**(1974), 269–272. MR**0356678****[8]**H. Toews and O. P. Chandna,*Plane magnetofluiddynamic flows with constantly inclined magnetic and velocity fields*, Canad. J. Phys.**52**(1974), 753–758. MR**0408437****[9]**M. R. Garg and O. P. Chandna,*Viscous orthogonal MHD flows*, SIAM J. Appl. Math.**30**(1976), no. 3, 577–585. MR**0411343**, https://doi.org/10.1137/0130051**[10]**O. P. Chandna and M. R. Garg,*The flow of a viscous MHD fluid*, Quart. Appl. Math.**34**(1976/77), no. 3, 287–299. MR**0449175**, https://doi.org/10.1090/S0033-569X-1976-0449175-1**[11]**O. P. Chandna and H. Toews,*Plane constantly-inclined MHD flow with isometric geometry*, Quart. Appl. Math.**34**(1976/77), no. 4, 331–337. MR**0449174**, https://doi.org/10.1090/S0033-569X-1977-0449174-5**[12]**O. P. Chandna and M. R. Garg,*On steady plane magnetohydrodynamic flows with orthogonal magnetic and velocity fields*, Int. J. Engng. Sci.**17**, 251-257 (1979)**[13]**R. M. Barron, O. P. Chandna and M. R. Garg,*Solutions in viscous constantly-inclined magnetohydrodynamics*, Jap. J. of Appl. Phys.**20**, 167-173 (1981)**[14]**R. M. Barron and O. P. Chandna,*Hodograph transformations and solutions in constantly-inclined MHD plane flows*, J. Engng. Math.**15**, 211-220 (1981)**[15]**O. P. Chandna and R. M. Barron,*Plane constantly inclined magnetogasdynamic flows*, Int. J. Engng. Sci.**19**, 409-419 (1981)**[16]**W. F. Ames,*Nonlinear partial differential equations in engineering*, Academic Press, New York-London, 1965. MR**0210342****[17]**P. Smith,*Substitution principle for MHD flows*, J. Math. Mech.**12**, 505-520 (1963)**[18]**Shih-I Pai,*Magnetogasdynamics and plasma dynamics*, Springer-Verlag, Vienna; Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR**0137449****[19]**M. H. Martin,*The flow of a viscous fluid. I*, Arch. Rational Mech. Anal.**41**(1971), 266–286. MR**0342014**, https://doi.org/10.1007/BF00250530

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DOI:
https://doi.org/10.1090/qam/745095

Article copyright:
© Copyright 1984
American Mathematical Society