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Flows of Sisko Fluid Through Symmetrically Curved Capillary Fissures and Tubes

Walicka A., Jurczak P., Falicki J.

Machine Dynamics Research

2018

Vol. 42, No. 3

27--54

This paper presents a general analytical method for deriving mathematical relationships between pressure losses and the volumetric ﬂow rate for laminar ﬂows of a Sisko ﬂuid. In this paper, only the laminar ﬂow of Sisko type ﬂuids is considered. It was demonstrated that the method can be used to ﬁnd solutions for other pseudoplastic ﬂuids and for different hapes of fissures and tubes. It can also be a good basis for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. As an example, the following cases of convergent-divergent or divergent-convergent ﬁssures and tubes, namely: parabolic, hyperbolic, hyperbolic cosine and cosine curve were considered. For each example, the formulae for pressure losses, volumetric ﬂow rate and ﬂow velocity were obtained. The most general forms of these formulas can be obtained by introducing hindrance factors.

Flows of DeHaven fluid in symmetrically curved capillary fissures and tubes

Walicka A., Falicki J., Jurczak P.

International Journal of Applied Mechanics and Engineering

2018

Vol. 23, no. 2

521--550

In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of DeHaven type fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. variable cross-section, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. Each example is concluded with a presentation of the formulae for the velocity flow on the outer surface of a thin porous layer. Upon introduction of hindrance factors, these formulae may be presented in the most general forms.