Non-linear time-dependent flow models of third grade fluids: A conditional symmetry approach

Applications of Group Theoretical Methods to Non‐Newtonian Fluid Flow Models: Survey of Results

“…The one-parameter group, which transforms the PDE (48) and the boundary conditions (49), is of the form [1]…”

“…A revisit has been made by Aziz et al [49] for three flow problems [44,47,48] related to a third-grade fluid model and discussed earlier. A conditional symmetry approach was employed in [49] to construct some new exact solutions of these models. All possible nonclassical symmetry generators were calculated in [49] for these problems.…”

“…A conditional symmetry approach was employed in [49] to construct some new exact solutions of these models. All possible nonclassical symmetry generators were calculated in [49] for these problems. The concept of conditional/nonclassical symmetry was not previously used to find conditionally invariant solutions of non-Newtonian fluid flow problems.…”

“…This is the first time that a complete nonclassical symmetry analysis was performed to tackle a nonlinear problem dealing with the flow models of nonNewtonian fluids. For the flow model [44], the following nonclassical symmetry generators were found in [49] …”

“…Thus, infinitely many nonclassical symmetry generators were obtained for any arbitrary value of the function ( ). With the use of the nonclassical symmetries given in (231), the following new invariant solutions were obtained in [49] for the model [44] …”