Computational Analysis for Non-linear Flow Problems with Activation Energy

Abstract

Mass transfer effects in fluid mixture are observed due to concentration variation of species in fluid. This variation occurs in a fluid when species moves from a higher concentration region to a lower concentration. Further the energy obtained by reactants before a chemical reaction can occur is referred to as activation energy. This is also called as a minimum required energy to initiate a reaction. Mass transfer phenomenon subject to activation energy is encountered in chemical and geothermal engineering, cooling of nuclear devices, mechanism comprised of (oil, water) suspension and food making. Significance of non-Newtonian fluids is observed through its extensive biological and industrial applications. These fluids are quite prevalent in engineering processes. Examples of such fluids may include plastic molding, polymers and paper making, soaps, cosmetics, foams, lubricant, in processed food and mixture of oil etc. Mathematically the flows of these materials cannot be studied by Navier Stokes equations. One constitutive relationship between shear stress and deformation rate for such fluids is not appropriate. Thus to overcome this issue, numerous models of non-Newtonian materials like differential, integral and rate types have been suggested in order to explain the rheological properties. Differential type fluid explores the characteristics of normal stress, shear thinning and shear thickening. Second grade/third grade and power law materials belonging to the subclasses of differential type models show normal stress/shear thinning and thickening properties. Relaxation and retardation times features are captured by rate type fluids. Rate type models include Jeffrey, Maxwell, Oldroyd, Burgers and generalized Newtonian models. In general the differential equations for non Newtonian fluids are higher than Navier-Stokes equations. The solutions thus require more boundary conditions. This thesis consists of seven chapters. Chapter one comprised some basic concepts which includes activation energy, nanofluid, thermal radiation, entropy, Darcy-Forchhemier flow, stratification and Cattaneo-Christov theory. Conservation laws and solution procedure are highlighted. Chapter two reports the double stratification and activation energy in flow of tangent hyperbolic fluid. Flow is induced by nonlinear stretching sheet of variable thickness. Heat flux by Cattaneo-Christov theory is implemented. Non-linear system is computed for the convergent solutions. The data of this chapter is published in International Journal of Numerical Methods for Heat & Fluid Flow. Chapter three focused on mixed convection flow of tangent hyperbolic liquid. Joule heating, double stratification, non-linear thermal radiation, Brownian motion and thermophoresis are present. Phenomenon of mass transfer is examined by activation energy along with binary chemical reaction. Computations of convergent solutions are carried out for the nonlinear mathematical system. Contents of this chapter are published in Scientia Iranica. Chapter four disclosed the effects of Joule heating and entropy generation minimization for steady flow of third grade nanomaterial. A significant perspective of this attempt is to address the influences of activation energy and chemical reaction. Modified Arrhenius function is utilized to investigate the activation energy. Convergent homotopic solutions of resulting non-linear system are developed. Data of this chapter is submitted for publication in International Communication in Heat and Mass transfer for publication. Chapter five addressed the entropy generation in flow of Walters-B nanomaterial. Energy equation consists of Ohmic heating, radiation and heat generation. Binary chemical reaction with modified Arrhenius energy is employed. The consequences of thermophoresis, Brownian motion and viscous dissipation are accounted. Convergent solutions by homotopy analysis technique are constructed. Data of this chapter is published in Scientia Iranica. Chapter six focused on consequences of activation energy for magneto nanoparticles considering zero mass flux condition. Fluid flow in porous space is analyzed by using Darcy-Forchheimer model. Additionally, the significance of thermal radiation is discussed. Aspects of thermophoresis and Brownian motion are observed. Influences of convective and zero mass flux conditions at boundary are examined. Systems of partial differential equations are reduced in to ordinary differential equations by employing transformation technique. Modeled system is solved numerically and the involved parameters outcomes discussed through graphs. Chapter seven reported the impact of entropy generation for steady flow of second grade nanomaterial with thermal radiation. Main theme of this formulation is to analyze the significance of activation energy and chemical reaction under assumed convective and zero mass flux conditions at boundary. Appropriate non dimensional variable have been employed to get ordinary differential system. Convergent series solution is derived by using homotopic technique. The solutions are explored with respect to pertinent variables. The contents of chapters six and seven are submitted for publication in International Communication in Heat and Mass transfer.