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Investigation of velocity profile in time dependent boundary layer flow of a modified power-law fluid of fourth grade

Yurusoy M.

International Journal of Applied Mechanics and Engineering

2020

Vol. 25, no. 2

176--191

This paper deals with the investigation of time dependent boundary layer flow of a modified power-law fluid of fourth grade on a stretched surface with an injection or suction boundary condition. The fluid model is a mixture of fourth grade and power-law fluids in which the fluid may display shear thickening, shear thinning or normal stress textures. By using the scaling and translation transformations which is a type of Lie Group transformation, time dependent boundary layer equations are reduced into two alternative ordinary differential equations systems (ODEs) with boundary conditions. During this reduction, special Lie Group transformations are used for translation, scaling and combined transformation. Numerical solutions have been carried out for the ordinary differential equations for various fluids and boundary condition parameters. As a result of numerical analysis, it is observed that the boundary layer thickness decreases as the power-law index value increases. It was also observed that for the fourth-grade fluid parameter, as the parameter increases, the boundary layer thickness decreases while the velocity in the y direction increases.

Flows of Newtonian and power-law fluids in symmetrically corrugated cappilary fissures and tubes

Walicka A.

International Journal of Applied Mechanics and Engineering

2018

Vol. 23, no. 1

187--211

In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of Newtonian and power-law 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. wedge and cone, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. For the wedge and cone geometry the present results for the power-law fluid were compared with the results obtained by another method; this comparison indicates a good compatibility between both the results.