Browsing by Subject "Creeping flow"

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    Lie group analysis of creeping flow of a second grade fluid
    (2001) Yürüsoy M.; Pakdemirli M.; Noyan Ö.F.
    The two-dimensional equations of motion for the slowly flowing second grade fluid are written in cartesian coordinates neglecting the inertial terms. By employing Lie group analysis, the symmetries of the equations are calculated. The Lie algebra consists of four finite parameter Lie group transformations, one being the scaling symmetry and the others being translations. Two different types of solutions are found using the symmetries. Using the translations in x and y coordinates, an exponential type of exact solution is constructed. For the scaling symmetry, the outcoming ordinary differential equations are more involved and only a series type of approximate solution is presented. Finally, some boundary value problems are discussed. © 2001 Elsevier Science Ltd.
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    Approximate symmetries of creeping flow equations of a second grade fluid
    (2004) Dolapçi I.T.; Pakdemirli M.
    Creeping flow equations of a second grade fluid are considered. Two current approximate symmetry methods and a modified new one are applied to the equations of motion. Approximate symmetries obtained by different methods and the exact symmetries are contrasted. Approximate solutions corresponding to the approximate symmetries are derived for each method. Symmetries and solutions are compared and advantages and disadvantages of each method are discussed in detail. © 2004 Elsevier Ltd. All rights reserved.