Nonlinear Mathematical Models with Chemical Reaction

Abstract

It is commonly known as the many materials like melts, muds, emulsions, tomato paste, shampoos, soaps, molten plastics, condensed milk, apple sauces, sugar solution, food stuffs, polymeric liquids etc do not hold the Newtonian’s law of viscosity and therefore known as the non-Newtonian fluids. The non-Newtonian fluids are charactertized as three types namely, differential, rate and integral types. It is noted that the differential type fluids have been examined much in the literature compared with the rate type fluids. The rate type fluid models exhibit the characteristics of relaxation and retardation times which cannot be handled through differential type fluids. However these fluids are unable to predict shear thinning/thickening and normal stress effects. There are many chemical reacting system classification subject to species chemical reaction with bounded activation energy. Activation energy is an essential part in chemical reaction. Such models arise in geo-thermal, chemical engineering, mechanics of water and oil storage processes. The communication between mass transfer and chemical reaction are typically exceptionally compound and can identified in the creation and utilization of reactant classes for different duties both inside fluid and mass transmission. With these motivations in mind, the present thesis is organized as follows. Having all the above aspects in mind, in this thesis, we visualized the aspects of various type nonlinear fluids under different conditions and laws. The Fourier’s and Fick’s laws and their advanced forms are used for better modeling of heat and mass transport processes. The structure of this thesis is governed as follows. Literature review regarding previous published attempts, description of solution procedure and relations for conservation of mass, linear momentum and energy are given in chapter one. Chapter two addresses three-dimensional nanomaterial flow of Maxwell material over a stretchable moving sheet. The flow in rotating frame is generated by linear stretched sheet. Furthermore, nanofluid mechanism is addressed subject to thermophoresis and Brownian diffusions. Chemical reaction at a stretchable surface is accounted via modified Arrhenius energy. Boundary layer approximation is utilized. Suitable variables lead to strong nonlinear ODEs. Numerical approach is implemented for solution development. The velocity components, temperature and mass concentration are scrutinized. Computational iterations for mass and heat transfer rates are discussed through tabulated forms. The observations of this chapter have been published in Applied Nanoscience March (2019), DOI: 10.1007/S13204- 019-00998-3 . Purpose of Chapters three is to examine Darcy- Forchheimer in a rotating frame. Flow due to stretched sheet fills the porous space. Binary chemical reaction is entertained. Resulting system is numarically solved. The plots are arranged for rotational parameter, porosity parameter, coefficients of inertia, Prandtl number and Schmidt number. It is revealed that rotation on Velocity has opposite effects when compared with temperature and concentration distribution. Skin friction coefficient and local Nusselt and Sherwood numbers are numarically discussed. Motion of the fluid reduces for higher porosity parameter and inertia coefficient. The findings of this chapter have been published in International Journal of Method for Heat and Fluid Flow, Vol.29 No.3, pp 935-948.https://doi.org/10.1108/HFF-06-2018-0292. Chpter four is prepared to examine outcome of activation energy in rotating flow of an Oldroyd-B nano liquid.. Flow is generated due to stretched surface. Binary chemical reaction is studied. Brownian and thermophoresis effects are considered. The system of nonlinear ordinary differential equations are derived. Convergent series solutions are obtained by homotopy analysis method. The resulting expressions for velocities, temperature and concentration are computed for different embedded parameters. It is found that velocities have decreasing effect when rotation parameter is enhanced. Brownian and thermophoresis are increasing functions of temperature and concentration. The physical quantities are sketched and discussed numerically. Concentration and temperature fields show decreasing behavior via Brownian and thermophoresis parameters This material is published in International Journal of Method for Heat and Fluid Flow, July (2019), DOI.org/10.1108/HFF-12-2018-0755. Chapter five explores 3D incompressible steady MHD flow of Oldroyd-B material in a rotating frame. The flow is caused through linearly stretched sheet. Applied magnetic field is accounted. Cubic autocatalytic chemical reaction is considered at the surface. Convective conditions at the boundary are considered for heat transport. Flow problem is modeled with the help of boundary layer approximations. Homotopy method is utilized for the series solutions. Impacts of Materials of these three chapters have been Accepted in Indian Journal of Physics Main aim of chapter six is to to study the three-dimensional rotating mixed convective flow of nanomaterial. Chemical reaction associated with Arrhenius energy is also accounted. Flow is created through exponential stretchable sheet. Slip mechanisms to nanomaterial like Brownian and thermophoresis diffusions are considered. Moreover, heat transfer analysis is developed in existence of heat source/sink and radiative flux. Similarity transformations are implemented to develop the system of nonlinear ordinary ones. Numerical approach (Built-in-Shooting) has been utilized to handle the governing mathematical system. Graphically impacts of pertinent parameters on the velocity, mass concentration and temperature are deliberated. Local Nusselt number and Sherwood number are examined and analyzed. It is noticed that temperature field enhances versus radiation and heat source/sink parameter while it decays through higher Prandtl number. The outcomes of this chapter are published in Applied Nanoscience, March (2019), DOI: https//doi.org/10.1007/s1320 Chapter seven highlights to investigate three-dimensional steady rotating flow of rate type fluid (Maxwell fluid) over an exponential stretching surface. The Maxwell fluid saturates the porous space via Darcy-Forchheimer relation. Flow caused by the exponential stretchable surface of sheet. Chemical reaction along with Arrhenius energy is considered at the surface. Energy expression is modeled subject to heat source/sink and radiation flux. Appropriate transformations leads to ordinary ones. Homotopy method is implemented for the series solutions. Pertinent parameters are discussed graphically. Special consideration is given to the engineering quantities like Sherwood and Nusselt numbers and discussed numerically through tabular form. Temperature distribution enhances versus higher radiation and heat source/sink parameter while decays for larger Prandtl number. Furthermore velocity shows decreasing trend through larger porosity and Deborah number. The obtained results are published in Applied Nanoscience, March (2019), DOI:10.1007/s13204-019-01008-2 This chapter eight is prepared to explores the three-dimensional steady incompressible flow of Oldroyd-B fluid subject to stretchable surface. The flow of material induced through stretchable surface with Darcy-Forchheimer medium. Homogeneous-heterogeneous reactions are considered. Convective boundary conditions and heat source/sink effects are considered for the heat transport. Boundary layer concept is used in the development of flow problem. Series solutions are obtained of the nonlinear system through homotopy technique. Physical significance of pertinent parameters are discussed and plotted graphically. Heat transfer rate is discussed numerically. The outcomes of this chapter are published in Applied Nanoscience, April (2019) , DOI:10.1007/s13204-019-01037-x.