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On the creeping flow of the second-order fluid. (English) Zbl 0568.76015

This interesting short note investigates the Giesekus-Tanner theorem[cf. H. Giesekus, Rheol. Acta 4, 59 ff (1963) and R. I. Tanner, Phys. Fluids 9, 1246 ff (1966)]. Concerning creeping flow of second-order incompressible fluids. It addresses itself to two specific question and answers them by providing two concrete examples, namely (a) second-order fluid solution where no Newtonian creeping flow solution exists, (b) three-dimensional creeping flow solution not satisfying second-order fluid equation. The conclusions are expressed by three theorems.

There remains some minor criticism of the note, for example, boundary conditions (II) need to be corrected if the author insists to use vectorial form, the equation numbered (5) seems to be missing as also Fig. 2 (cf. page no. 244).

Reviewer: N.C.Sacheti
MSC:
76A10Viscoelastic fluids