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**Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid.**
*(English)*
Zbl 1063.76108

Summary: This paper deals with some steady unidirectional flows of Oldroyd 8-constant magnetohydrodynamic (MHD) fluid in bounded domains. The fluid is electrically conducting in the presence of a uniform magnetic field. Three nonlinear flows are produced by the motion of a boundary or by sudden application of a constant pressure gradient or by the motion of a boundary and pressure gradient. The governing nonlinear differential equations are solved analytically using homotopy analysis method (HAM). Expressions for the velocity distribution are given. It is noted that for steady flow the solutions are strongly dependent on the non-Newtonian and magnetic parameters. The MHD solutions for a Newtonian fluid, as well as those corresponding to the Oldroyd 3 and 6-constant fluids, a Maxwell fluid and a second-grade one, appear as limiting cases of our solutions. Finally, a physical interpretation of the results is given with the help of several graphs.