ETD Collection

Permanent URI for this collectionhttps://wiredspace.wits.ac.za/handle/10539/104


Please note: Digitised content is made available at the best possible quality range, taking into consideration file size and the condition of the original item. These restrictions may sometimes affect the quality of the final published item. For queries regarding content of ETD collection please contact IR specialists by email : IR specialists or Tel : 011 717 4652 / 1954

Follow the link below for important information about Electronic Theses and Dissertations (ETD)

Library Guide about ETD

Browse

Subject: search.filters.subject.Non-Newtonian fluids.

Search Results

Now showing 1 - 4 of 4
  • No Thumbnail Available
    Item
    Group theoretical and compatibility approaches to some nonlinear PDEs arising in the study of non-Newtonian fluid mechanics
    (2015-05-06) Aziz, Taha
    This thesis is primarily concerned with the analysis of some nonlinear problems arising in the study of non-Newtonian fluid mechanics by employing group theoretic and compatibility approaches. It is well known now that many manufacturing processes in industry involve non-Newtonian fluids. Examples of such fluids include polymer solutions and melts, paints, blood, ketchup, pharmaceuticals and many others. The mathematical and physical behaviour of non-Newtonian fluids is intermediate between that of purely viscous fluid and that of a perfectly elastic solid. These fluids cannot be described by the classical Navier–Stokes theory. Striking manifestations of non-Newtonian fluids have been observed experimentally such as the Weissenberg or rod-climbing effect, extrudate swell or vortex growth in a contraction flow. Due to diverse physical structure of non-Newtonian fluids, many constitutive equations have been developed mainly under the classification of differential type, rate type and integral type. Amongst the many non-Newtonian fluid models, the fluids of differential type have received much attention in order to explain features such as normal stress effects, rod climbing, shear thinning and shear thickening. Most physical phenomena dealing with the study of non-Newtonian fluids are modelled in the form of nonlinear partial differential equations (PDEs). It is easier to solve a linear problem due to its extensive study as well due to
  • No Thumbnail Available
    Item
    Group invariant solutions for the unsteady magnetohydrodynamic flow of a fourth grade fluid in a porous medium
    (2014-07-18) Carrim, Abdul Hamid
    The e ects of non-Newtonian uids are investigated by means of two appropri- ate models studying a third and fourth grade uid respectively. The geometry of both these models is described by the unsteady unidirectional ow of an in-compressible uid over an in nite at rigid plate within a porous medium. The uid is electrically conducting in the presence of a uniform applied magnetic eld that occurs in the normal direction to the ow. The classical Lie symmetry approach is undertaken in order to construct group invariant solutions to the governing higher-order non-linear partial dif-ferential equations. A three-dimensional Lie algebra is acquired for both uid ow problems. In each case, the invariant solution corresponding to the non-travelling wave type is considered to be the most signi cant solution for the uid ow model under investigation since it directly incorporates the magnetic eld term. A numerical solution to the governing partial di erential equation is produced and a comparison is made with the results obtained from the analytical ap-proach. Finally, a graphical analysis is carried out with the purpose of observing the e ects of the emerging physical parameters. In particular, a study is carried out to examine the in uences of the magnetic eld parameter and the non-Newtonian fluid parameters.
  • No Thumbnail Available
    Item
    Group invariant solutions and conservation laws for jet flow models of non-Newtownian power-law fluids
    (2014-07-18) Magan, Avnish Bhowan
    The non-Newtonian incompressible power-law uid in jet ow models is investigated. An important feature of the model is the de nition of a suitable Reynolds number, and this is achieved using the standard de nition of a Reynolds number and ascertaining the magnitude of the e ective viscosity. The jets under examination are the two-dimensional free, liquid and wall jets. The two-dimensional free and wall jets satisfy a di erent partial di erential equation to the two-dimensional liquid jet. Further, the jets are reformulated in terms of a third order partial di erential equation for the stream function. The boundary conditions for each jet are unique, but more signi - cantly 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 rst 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 uid 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 uid. 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 uid 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 uid free jets for 0 < n < 1 and shear thickening uid free jets for n > 1. It is observed that for values of n > 1 in the range 1=2 < n < 1, the velocity pro le extends over a nite 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 < 1. The solution does not exist for n = 1=2 and the range 0 < n < 1=2 requires further investigation.
  • No Thumbnail Available
    Item
    Investigation of Stokes' second problem for non-Newtonian fluids
    (2014-06-12) Rikhotso, Deals Shaun
    The motion of an incompressible fluid caused by the oscillation of a plane at plate of in nite length is termed Stokes' second problem. We assume zero velocity normal to the plate and thus simpli ed Navier-Stokes equations. For the unsteady Stokes' second problem, solutions may be obtained by using Laplace transforms, perturbation techniques, homotopy, di erential transform method or Adomian decomposition method. Stokes' second problem is discussed for second-grade and Oldroyd-B non-Newtonian fluids. This dissertation summarizes previously published work.