**6. References**

484 Biomedical Science, Engineering and Technology

 **N=0 N=0.1 N=0.2 N=0.3**

The method here described can lead to very accurate solutions for the velocity field and related variables such as shear stress, rate of flow and pressure in a great variety of flows in tubes and channels. Symbolic software presently available, such Maple and MathCAD make it possible to obtain and compute higher order solutions that, in some cases, may have complex algebraic structures. The fact that for all cases here considered, ie cases where � � 3, � is much less than unity (cf table 2), leads to a regular perturbation scheme that in most cases requires terms up to second order to achieve enough accuracy. The cases when ��� and ��� deserve special mention. For ��� the shape factor (1) describes an excentric circle, and for ��� an ellipse. In this last instance � is not bounded and can take any finite value, which implies that the perturbation scheme would break down if ���. So that, in this particular case, the method is limited to elliptical cross-sections of axes ratio close to unity. The method can be expanded to many more complex flow geometries. This possibility is implicit in the more general shape factor (3), which makes it necessary to develop a compound perturbation scheme, in terms of more than one perturbation parameter. The structure of the shape factor (1) determines that the analysis, especially for � � 3� is more sensible to the perturbation parameter for � � �� ie close to the wall conduit. This requires a careful analysis of series convergency which should define the order of the higher order term considered. On the other hand, in the case of flow in straight tubes, in all cases studied, in a considerable region around the conduit axis, say for � � ���� the flow variables are independent of the boundary geometry and take the values of the

*N=0*

The authors acknowledge the financial support provided, at different stages of the work here presented, by FONDECYT-CONICYT and DICYT at the University of Santiago of

Fig. 21. Axial velocity profiles at x=2.25 for � � ��3 and *Re =*100.

**4. Conclusion** 

corresponding flow in round tubes.

**5. Acknowledgment** 

Chile.

Batchelor G. K. (2000). *An Introduction to Fluid Dynamics*. Cambridge University Press.

