Investigation of Non-Axisymmetric Homann Stagnation-point Flow of Viscoelastic Nanofluid

Abstract

Non-Newtonian fluids (polymeric liquids) have remarkable significance in nearly every field, industry and technology. Their study is of eclectic interest for many researcher, engineers and mathematicians. They form an extensive range of products scilicet molten polymers, paints, thermoplastics, starch suspension, and so forth, that do not obey Newton's law of viscosity. Before-mentioned fluids obey the power-law model, which explains that stress functions nonlinearly with the deformation rate. The constitutive equations with the corresponding stress tensor are determined to model their viscoelastic conduct. Moreover, the investigation of flows in the stagnation zone is another fascinating area of study in fluid mechanics. This is because of the superfluous pressure and heat transport in the stagnation region, it is reckoned amongst the intriguing intricacies and has multiple applications as well. The present study highlights the modification of Homann's problem for the viscoelastic fluids adjacent to the stagnation region over a cylindrical disk with a time-independent free stream. By superposing periodic radial and azimuthal velocity terms onto Homann's external potential flow, the potential flow field in the cylindrical coordinates system is attained. This directs us to a distinct class of asymmetric flow near the stagnation-point, which solely depends upon shear-to-strain rate ratio. Furthermore, the impression of non-axisymmetry and magnetohydrodynamic (MHD) on Walter’s B liquid and Jeffrey fluid flow is inspected. Additionally, to highlight the nanofluid conduct, we employed the Buongiorno model. The outcomes of the pertinent parameters on the boundary layer are also scrutinized. The conservation laws are remodeled by a similarity transformation. A collocation method, specifically bvp4c is employed to numerically compute the solutions. A comparison is made between the numerical and their asymptotic outcomes for large values of shear-to-strain rate ratio. The outcomes of viscoelasticity and magnetic field on the skin friction and displacement thicknesses are also determined by perturbative expansion. This thesis is comprised of three Chapters. Chapter 1 addresses the conservation laws, definitions, and stress tensors related to the non-Newtonian fluids discussed in the succeeding chapters, literature survey, and the procedure to determine the solution for the problems. Chapter 2 explores the non-axisymmetric Homann flow of Walter's B nanofluid model along with non-linear Rosseland thermal radiation. Chapter 3 includes the study of Jeffrey's nanofluid in the stagnation-region with an electrically conducting flow. For both the problems, it is concluded that when the shear-to-strain-rate ratio approaches infinity, the coefficient of skin friction along x-direction reaches its asymptotic behavior; however, along y-direction it shows contrary results. Further conclusions are jotted down at the end of chapters 2 and 3.