Loading...
Please wait, while we are loading the content...
Group invariant solutions and conservation laws for jet flow models of non-Newtownian power-law fluids
| Content Provider | Semantic Scholar |
|---|---|
| Author | Magan, Avnish Bhowan |
| Copyright Year | 2014 |
| Abstract | The non-Newtonian incompressible power-law fluid in jet flow models is investigated. An important feature of the model is the definition of a suitable Reynolds number, and this is achieved using the standard definition of a Reynolds number and ascertaining the magnitude of the effective viscosity. The jets under examination are the two-dimensional free, liquid and wall jets. The two-dimensional free and wall jets satisfy a different partial differential equation to the two-dimensional liquid jet. Further, the jets are reformulated in terms of a third order partial differential equation for the stream function. The boundary conditions for each jet are unique, but more significantly these boundary conditions are homogeneous. Due to this homogeneity the conserved quantities are critical in the solution process. The conserved quantities for the two-dimensional free and liquid jet are constructed by first deriving the conservation laws using the multiplier approach. The conserved quantity for the two-dimensional free jet is also derived in terms of the stream function. For a Newtonian fluid with n = 1 the twodimensional wall jet gives a conservation law. However, this is not the case for the two-dimensional wall jet for a non-Newtonian power-law fluid. The various approaches that have been applied in an attempt to derive a conservation law for the two-dimensional wall jet for a power-law fluid with n 6= 1 are discussed. In conjunction with the attempt at obtaining conservation laws for the two-dimensional wall jet we present tenable reasons for its failure, and a feasible way forward. Similarity solutions for the two-dimensional free jet have been derived for both the velocity components as well as for the stream function. The associated Lie point symmetry approach is also presented for the stream function. A parametric solution has been obtained for shear thinning fluid free jets for 0 1. It is observed that for values of n > 1 in the range 1/2 < n <∞, the velocity profile extends over a finite range. For the two-dimensional liquid jet, along with a similarity solution the complete Lie point symmetries have been obtained. By associating the Lie point symmetry with the elementary conserved vector an invariant solution is found. A parametric solution for the two-dimensional liquid jet is derived for 1/2 < n < ∞. The solution does not exist for n = 1/2 and the range |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://wiredspace.wits.ac.za/jspui/bitstream/10539/14926/2/Avnish%20Bhowan%20Magan%20-%20masters%20final%20draft.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
