Stagnation point flows over a surface

Abstract

Heat transport over a stretching surface in the expanse of stagnation point flows have wide applications in fiber sheet manufacturing, glass production, polymers, paper production, metal spinning, continuous casting and many others. According to the opinion of researchers, various fluids are chemical engineering and biomedical sciences are in nature. One usually comes across the situations where the flow of non-Newtonian fluids occurs. These fluids have relevance particularly in cosmetic products, biological liquids, butter, toothpaste, certain oils, grease, shampoos etc. Such material cannot be described in general by the classical Newtonian's law of viscosity. Thus various mathematicians, engineers and computer scientists have devoted their attention to the modeling and simulation of such flows. At present, the non-Newtonian fluids are characterized under three cases namely the differential, the integral and the rate. Although numerous works have been reported for the differential type fluids but the rate type classes are not given proper attention. Especially, the boundary layer flows in rate type fluids are not much studied. Various investigators in the field examined the unidirectional flows of Maxwell and Oldroyd-B fluids. Besides these, the appealing feature of micropolar theory is that it can additionally predict the microrotation effects. Specifically, the micropolar fluid deals with the mathematical and behavior of various fluids such as liquid crystals, exotic lubricants, animal blood and ferroliquid etc. In view of the above mentioned discussion, this thesis is structured in the following forms. Chapter 2 deals with the incompressible and unsteady flow of viscous fluid. Mixed convection flow in the vicinity of stagnation-point flow near a stretching surface is analyzed in second chapter. Free stream velocity has occupied time-dependency. The conservation laws are reformed into ODEs after employing the appropriate transformations. Analytical technique(HAM) is used to solve the nonlinear problem. The numerical values of skin friction coefficient and local Nusselt number for various pertinent parameters are tabulated. It is noticed that the magnitude of skin friction coefficient decays with the increasing values of radiation parameter and mixed convection parameter. Such observations are published in "International Journal of Numerical Methods and Fluids, 68 (2012) 483-493". Chapter 3 addresses the mixed convection flow of viscous fluid towards stagnation point over a linearly stretching surface when fluid is magnetohydrodynamic (MHD). Series solutions are constructed for assisting and opposing flow cases. Moreover the effects of velocity and thermal slip parameters are scrutinized carefully. Physical parameters involving in governing problem are plotted. This research has been submitted for publication III the "Journal of Aerospace Engineering" , MHD stagnation-point flowof viscous fluid is discussed in chapter 3. The flow is generated by the linearly stretched surface. Suitable transformations are applied for partial differential equations to convert these in the coupled set of ordinary differential equations. The thermal radiation effect has been considered through the Rosseland approximation. Slip conditions are applied to model the problem. Influences of different physical parameters are obtained by graphical and tabular results. It is observed that skin friction coefficient becomes larger when Hartman number increases. The skin friction and local Nusselt number decrease for large values of velocity slip parameter. Such results are submitted in "Zeitschrift Naturforschung A". Chapter 4 exposes the solution of non-Newtonian fluid near the stagnation-point. Second grade incompressiblefluid invades on the wall orthogonally. The homotopy analysis method (HAM) is applied to solve nonlinear problems. The obtained convergent solutions have been equaled with numerical solutions. Admirable agreement is noticed between both solutions. These results are published in "Communications in Theoretical Physics, 57 (2012) 290-294" , Chapter 5 investigates two-dimensional mixed convection flow of Maxwell fluid. The phenomenon of variable thermal conductivity has been considered. The flow is considered near the region of stagnation-point. Analysis of heat transfer with thermal radiation and source/sink is also carried out. The solutions of transformed differential equations are obtained by homotopy analysis method. Discussion is provided for the velocity and temperature profiles. Convergence of series solution is examined. Results are compared with the previous limiting studies. This research is submitted in "International Journal of Heat and Mass Transfer". Chapter 6 provides the analysis of laminar flow for Maxwell fluid. Magnetic field effects for the stagnation-point flow near linear stretching sheet are also considered. Heat transfer with thermal radiation effect is addressed carefully. Convergence of the developed solutions is checked carefully. Appreciable change has been noticed for involved physical parameters for velocity and temperature. Comparison for local Nusselt number is presented with previous results in limiting case. Such observations are published in "Heat Transfer: Asian Research". The flow of an Oldroyd-B fluid with variable thermal conductivity is analyzed in chapter 7. The governing equations are modeled and then transformed into the ordinary differential equations. Deborah number and thermal radiation effects are attended in this chapter. It is found that the stretching parameter assists the velocity profile and resists the temperature profile. This work is submitted for pUblication in "Thermal Science". Chapter 8 examines the micropolar fluid near stagnation-point towards a stretching sheet. Attention is gIven to the behavior of various emergmg parameters VIa graphs. Numerical values of dimensionless skin friction coefficient and local Nusselt number are calculated. In limiting cases, appreciable agreement is made lmown with numerical solutions. Further, it is noted that temperature profile decreases by increasing microrotation parameter. The results of this problem are submitted in "International Journal of Numerical Methods for Heat and Fluid Flow".