Numerical study for some nonlinear differential systems

Abstract

The study of nonlinear fluid flows (having complex geometries) has many applications in industrial engineering e.g. construction of, paper production, polymer sheet, glass fabric, hot rolling and petroleum production. Focus of present study is on mathematical modelling for boundary layer flow having different geometries in a non-Newtonian viscosity model. This study involves four models namely (Carreau, Carreau-Yasuda, Williamson and Maxwell models). Our main concern will be the analysis of non-Newtonian fluids within the boundary layer. For fluids with share-rate dependent viscosity the base flow has no longer analytic solutions for the Naiver Stoke equations. However, for a large value of Reynolds number the flow inside the boundary layer can be determined via a similarity solution. The solution of the modelled differential equations is computed by using moderate and well-known numerical technique name ly shooting method. The different governing physical parameter are utilized to control the motion of fluid. Skin friction coefficient, Nusselt number and Sherwood number are calculated in order to examine the flow behavior near the surface of the sheet, rotating surface and disk. A comparison has been made with the previous published literature in order to check the accuracy of the method. Conclusion is drawn based on entire study. This thesis comprises 9 chapters by including introduction as zero chapter. Research background and the objectives are stated at the end of this chapter. Chapter 1 is dedicated to investigating the effects of variable viscosity on MHO Carreau nanofluid flow along a nonlinear stretching surface in the presence of thermal stratified medium. Generalized Fourier's and Fick's laws are used in order to examine the heat and mass transport phenomena. Near the surface of the plate mass flux is assumed to be zero. The contents of this paper are published in the Journal of the Brazilian Society of Mechanical Sciences and Engineering. (2018) 40: 457. http5://doLorg/l0.l007/540430-018-1371-6. Chapter 2 is devoted to acquiring non-similar solutions for the behavior of slip conditions on steady MHO Carreau-Yasuda fluid flow over a rotating disk. In order to examine the heat transfer phenomena superior form of Fourier's law is used and the conductivity of the fluid is assumed to be changeable. The contents of this chapter are published in Journal of the Brazilian Society of Mechanical Sciences and Engineering, 412(2019):78. Chapter 3 deal with transient MHD Carreau-Yasuda nanofluid flow produced by impulsively started rotating disk in the occurrence of Darcy-Forchheimer and chemical reactive species considering conventional Fourier's and Fick's laws. The findings are accepted in Canadian journal of Physics, 97(2019) 670-677. Variable viscosity and inclined Lorentz force effects on Williamson nanofluid over a stretching sheet with variable thickness is addressed in chapter 4. Variable viscosity is assumed to vary as a linear function of temperature. The contents of chapter 4 are published in Results in Physics, 8(2018) 862-868. Chapter 5 is presented to elaborate the effects of temperature dependent viscosity and doubl e stratification is also assumed by taking Williamson fluid model. The contents of this chapter are published in International Journal of Heat and Mass Transfer, 126(2018) 941-948. Change in internal energy of thermal diffusion stagnation point Maxwell nanofluid flow along with solar radiation and thermal conductivity is discussed in chapter 6. After boundary layer approximation, the governing equations are achieved (namely Maxwell upper convected material derivative, thermal and concentration diffusions). The contents of this chapter are accepted in Chinese Journal of Chemical Engineering, (2019) doLorg/10.1016/j.cjche.2018.12.023. Chapter 7 is written to analysis the behavior of transformed internal energy change 111 magnetohydrodynamic Maxwell nanofluid flow over a stretching sheet along with Arrhenius activation energy and chemical reaction. The contents this chapter are accepted in European Physical Journal of Plus, (2019) 134: 198. doLorg/10.1140/epjp/i2019-12563-8. Chapter 8 addresses the heat and mass diffusion (Cattaeno-Christov model) upper convected Maxwell nanomaterials passed by a linear stretched surface (slip surface) near the stagnation point region. Improved form of Fourier's and Fick's laws are employed to investigate heat and mass diffusion phenomena. The contents of this chapter are accepted in Journal of the Brazilian Society of Mechanical Sciences and Engineering, (2019) 41: 138. doLorg/10.1007/s40430-019- 1620-3.