Stagnation point flows with heat and mass transfer

Abstract

In analyzing the features of fluid flow over an impermeable/rigid object, a point where the fluid particles attain the zero velocity i.e. come to rest at the object’s surface is known as stagnation point while the flow in the neighborhood of stagnation point is recognized as stagnation point flow. It is further categorized into two types (i) Orthogonal stagnation point (ii) Oblique stagnation point. When fluid particles are acting orthogonal or perpendicular to a rigid body surface then the resulting velocity becomes zero at a point. It is known as orthogonal stagnation point. Oblique stagnation point arises in the flow field when fluid particles are acting obliquely on a rigid body at an arbitrary angle of incidence. Such a point is the combination of orthogonal stagnation flow and shear flow parallel to the object. Stagnation flows may be characterized as inviscid or viscous, steady or unsteady, two-dimensional or three-dimensional, symmetric or asymmetric, normal or oblique, homogeneous or two immiscible fluids and forward or reverse. The behavior of stagnation point flow is very important in engineering and industrial phenomena. The flow over the tips of submarines, rockets, oilships and aircrafts are few examples of stagnation point flow. Another interesting example is the blood flow at a junction within an artery. Recently researchers and scientists are still interested to explore the characteristics of fluid flow in the presence of heat transfer. This is due to rapid advancements and developments in the technological and industrial processes. In fact the investigators are interested to enhance the efficiency of various machines by increasing the rate of heat transfer and quality of the final products with desired characteristics through rate of heating/cooling. The combined effects of heat and mass transfer are further significant in many natural, biological, industrial and geophysical processes. Such phenomena include designing of many chemical processing equipment, formation and dispersion of fog, distribution of temperature and moisture over agricultural fields, damaging of crops due to freezing, grooves of fluid trees, environmental pollution, drying of porous solids, packed bed catalytic reactors, geothermal reservoirs, enhanced oil recovery, thermal insulation and underground energy transport. Inspired by such practical applications, the present thesis is devoted to analyze the orthogonal stagnation point flows with heat and mass transfer. This thesis is structured as follows. Chapter one comprises literature survey of the previous published works and laws of the conservation of mass, linear momentum, energy and mass transport. Mathematical modeling and boundary layer equations of viscous, Casson, Maxwell and Jeffrey fluids are presented. Basic idea of homotopy analysis method is also included. Chapter two concentrates on the combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) in magnetohydrodynamic stagnation point flow due to a horizontal stretching cylinder. Heat and mass transfer are analyzed with heat generation/absorption and chemical reaction. Appropriate transformations are employed to convert the nonlinear partial differential equations into the ordinary differential equations. Convergent series solutions of the governing equations are obtained via homotopy analysis method (HAM). Impacts of various involved physical parameters on the velocity, temperature and concentration distributions are analyzed through graphs. Behaviors of various physical parameters on skin friction coefficient, Nusselt and Sherwood numbers are computed and discussed through numerical data. The outcomes of this chapter are published in Journal of Central South University 22 (2015) 707-716. Chapter three addresses the double stratified mixed convection stagnation point flow induced by an impermeable inclined stretching cylinder. Inclined magnetic field is applied to the electrically conducting fluid. Heat transfer characteristics are analyzed with viscous dissipation. Temperature and concentration at and away from the boundary are assumed variable. Convergent series solutions of momentum, energy and concentration equations are computed. Influences of various involved physical parameters on the velocity, temperature and concentration distributions are discussed graphically. Behaviors of skin friction coefficient, Nusselt and Sherwood numbers are presented numerically. Comparison of skin friction coefficient is also examined in the limiting