Mixed Convection Flows of Nonlinear Fluids

Abstract

The boundary layer flows over a moving surface have vital importance due to their ever increasing usage in the industries. In such industrial processes, the kinematics of stretching and heat transfer through rate of cooling have substantial impact in the improvement of final product of better quality. No doubt, the thermal buoyancy force arising due to cooling or heating of a moving surface may alter significantly the flow and thermal fields and thereby the heat transfer behavior in the manufacturing process. In several practical applications, the order of magnitudes of buoyancy and viscous forces are comparable for moderate flow velocities and large surface temperature differences and convective heat transfer process is thus called as mixed convection. The buoyancy forces due to temperature and concentration differences are significant in mixed convection thermal and concentration diffusions. In fact the buoyancy forces causing a pressure gradient in the boundary layer modify the velocity, temperature and concentration distributions and consequently the rate of heat and mass transfer between the surface and fluid. Specifically the mixed convection flows are encountered in industrial processes like solar central receivers exposed to the wind currents, nuclear reactors called during emergency shutdown, electronic devices cooled by fans and heat exchangers etc. The mixed convection flows with heat and mass transfer are relevant to energy related engineering problems that include both metal and polymer sheets. Mostly, the fluids in industrial processes are non-Newtonian. Certain oils, paints, blood at low shear rate, shampoos, cosmetic products body fluids, pasta, ice cream, ice, mud etc are few examples of nonNewtonian fluids. Keeping all the aforementioned facts in mind, the present thesis is structured as follows.

Chapter one covers literature survey and laws of conservation of mass, linear momentum and energy. Boundary layer equations of second grade, Maxwell, Oldroyd-B and thixotropic fluids are presented. Basic idea of homotopy analysis method is also given. Chapter two deliberates the mixed convection boundary layer flow of thixotropic fluid with thermophoresis over a stretched sheet. Fluid is electrically conducting in the presence of constant applied magnetic field. Heat and mass transfer effects are considered in the presence of Joule heating and thermal radiation. Series solutions are obtained to analyze the velocity, temperature and concentration fields. Numerical values of local Nusselt and Sherwood numbers for different values of emerging parameters are computed and analyzed. A comparative study with the previous solutions in a limiting sense is made. The leading results of this problem are published in “Journal of Thermophysics and Heat Transfer 27 (2013) 733-740”. Three-dimensional mixed convection flow of second grade fluid over an exponentially stretching surface are studied in chapter three. Convective boundary conditions are utilized for the heat transfer analysis. Analysis is carried out in the presence of thermal radiation. The series solutions are established through a newly developed method recognized as ii

the homotopy analysis method. The convergent analysis of velocity components and temperature are derived. Graphs are plotted and analyzed for interesting physical parameters. A systematic study is performed to analyze the impacts of the significant parameters on the velocity and temperature, the skin friction coefficients and the local Nusselt number. The contents of this chapter are published in “Plos One 9 (2014) e90038”. Chapter four reports the heat and mass transfer effects in three-dimensional mixed convection flow of viscoelastic fluid with internal heat source/sink and chemical reaction. An exponential stretching surface is employed for flow generation. Magnetic field normal to the direction of flow is taken under consideration. Convective conditions at boundary surface are also encountered. An analytical approach homotopy analysis method is used to develop the solution expressions of the problem. Impacts of different controlling parameters such as stretching ratio parameter, Hartman number, internal heat source/sink, chemical reaction, mixed convection, concentration buoyancy parameter and Biot numbers on the velocity, temperature and concentration profiles are analyzed graphically. The local Nusselt number and Sherwood numbers are sketched and examined. The results of present chapter are accepted for publication in “Computational Mathematics and Mathematical Physics”. Chapter 5 provides the three-dimensional mixed convection flow of viscoelastic fluid over a stretching surface in presence of thermophoresis. Soret and Dufour effects are also taken into account. Series solutions are constructed. Dimensionless velocity, temperature and concentration distributions are shown graphically for different values of involved parameters. Numerical values of local Nusselt and Sherwood numbers are computed and analyzed. The contents of this chapter are submitted for possible publication in “International Journal of Nonlinear Sciences and Numerical Simulation”. Three-dimensional flow of Maxwell fluid over a stretching surface is addressed in chapter six. Analysis is prepared in presence of concentration and thermal buoyancy effects. Convective boundary conditions for heat and mass transfer are explored. Series solutions of the resulting problem are established. Results are displayed to examine the influence of physical parameters on the velocity, temperature and concentration fields. Main observations of this chapter are published in “Journal of Central South University 22 (2015) 717−726”. Chapter seven is prepared to examine the heat and mass transfer effects in three-dimensional flow of Maxwell