SIMILARITY ANALYSIS OF BOUNDARY LAYER EQUATIONS OF A CLASS OF NON-NEWTONIAN FLUIDS

Abstract A similarity analysis of three-dimensional boundary layer equations of a class of non-Newtonian fluids in which the stress is an arbitrary function of rates of strain is made. It is shown that under scaling transformation, for an arbitrary stress function, only 90° of wedge flow leads to similarity solutions, whereas for a specific more restricted form, similarity solutions exist for arbitrary wedge angles. In the case of spiral group transformation, no similarity solutions exist if we force the stress function to remain arbitrary after the transformation, whereas for a specific more restricted form, similarity solutions exist for arbitrary wedge angles. For both transformations, similarity equations for power-law and Newtonian fluids are presented as special cases of the analysis. Finally the conditions for invariance and the form of the stress function for a two-dimensional case are also presented.

[1]  Ganjam K. Rajeswari,et al.  Flow of a particular class of non-Newtonian visco-elastic and visco-inelastic fluids near a stagnation point , 1962 .

[2]  A. G. Hansen,et al.  Similarity Solutions of Laminar, Incompressible Boundary Layer Equations of Non-Newtonian Fluids , 1968 .

[3]  D. W. Beard,et al.  Elastico-viscous boundary-layer flows I. Two-dimensional flow near a stagnation point , 1964, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  A. Acrivos,et al.  Momentum and heat transfer in laminar boundary-layer flows of non-Newtonian fluids past external surfaces , 1960 .

[5]  Mehmet Pakdemirli,et al.  Boundary layer flow of power-law fluids past arbitrary profiles , 1993 .

[6]  M. Pakdemirli.  Conventional and multiple deck boundary layer approach to second and third grade fluids , 1994 .

[7]  Vijay K. Garg,et al.  Flow of a non-Newtonian fluid past a wedge , 1991 .

[8]  A. G. Hansen,et al.  Similarity solutions of a class of laminar three-dimensional boundary layer equations of power law fluids , 1967 .

[9]  Mehmet Pakdemirli,et al.  THE BOUNDARY LAYER EQUATIONS OF THIRD-GRADE FLUIDS , 1992 .

[10]  Abinash Chandra Srivastava,et al.  The flow of a non-Newtonian liquid near a stagnation point , 1958 .

[11]  W. R. Schowalter.  The application of boundary‐layer theory to power‐law pseudoplastic fluids: Similar solutions , 1960 .

[12]  E. Suhubi,et al.  Similarity solutions of boundary layer equations for second order fluids , 1992 .

[13]  K. Rajagopal,et al.  An existence theorem for the flow of a non-newtonian fluid past an infinite porous plate , 1986 .

[14]  Erdoğan S. Şuhubi,et al.  Boundary layer theory for second order fluids , 1992 .

[15]  M. G. Timol,et al.  Similarity solutions of three-dimensional boundary layer equations of non-Newtonian fluids , 1986 .

[16]  Kumbakonam R. Rajagopal,et al.  ON A BOUNDARY LAYER THEORY FOR NON-NEWTONIAN FLUIDS , 1980 .