Summary
A theorem concerning the stability of a particular non-Newtonian fluid has been proved by Genesky1). In the present paper, we have taken a more general non-Newtonian fluid characterized by the relation\(T = - pI + \alpha _1 A_1 + \alpha _2 A_2 + \alpha _3 A_{1^2 } \) and it has been proved that the stability criterion for this fluid does not change. Further by takingα 2 = 0 we find that the existance of a point of inflection in the velocity profile of a steady one-dimensional basic flow is a necessary condition for the growth of a super-imposed two-dimensional disturbance. This is of interest that even in some special types of non-Newtonian flow, the existence of a point of inflection can be associated with the instability.
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Reference
Genesky, S. M., Quart, appl. Math.18 (1960) 245.
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Kapur, J.N., Goel, S. A stability theorem for general non-Newtonian fluid. Appl. sci. Res. 11, 304–310 (1963). https://doi.org/10.1007/BF03184989
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DOI: https://doi.org/10.1007/BF03184989