Analysis of non-Newtonian fluids is now recognized very well for its several engineering and industrial applications. Motivation of researchers in these materials is through food products (mayonnaise, milk, apple sauce, ketchup, chocolates in liquefies form, yogurt, alcoholic beverages, ice creams etc.), biological material (vaccines, syrups, blood, synovial fluid etc.), chemical material (cosmetics, shampoos, tooth pastes, pharmaceutical chemicals, grease, paints, oil reservoirs etc.). Such materials do not obey the Newton''s law of viscosity. Rheological features of all the non-Newtonian materials are not concluded by one constitutive relation. Therefore numerous models of such fluids have been recommended for the discussion about their diverse characteristics. The non-Newtonian fluids at present are argued through three main classifications i.e., (i) Rate type (ii) Differential type and (iii) Integral type. In addition the features of such materials passing towards a stationary/moving surface have key importance in paper production and glass fiber, polymer and metal extrusion mechanisms, rubber sheets and drawing of plastics, cooling of metallic surfaces and crystal growth. The analysis of heat transfer aspects through a cooling rate is crucial to achieving the best quality product. Features of heat transfer is based through involvement of various mechanisms i.e., thermal radiation, heat generation/absorption, Fourier''s law of heat conduction, convection and Newtonian conditions. Having all such aspects in mind, the modeling for flows of non-Newtonian fluids through different physical conditions is made. Solutions and analysis are carried out by utilizing homotopy analysis technique. Finally the structure of the thesis is governed as follows. Chapter one consists of literature review of relevant published works. Expressions for Jeffrey, Walter-B, thixotropic and third grade fluids are included. Basic concept of homotopy analysis method is also presented. Chapter two addresses the mixed convection flow of Jeffrey material by an inclined impermeable stretching cylinder. Feature of heat transport are examined via thermal radiation and non-uniform heat source/sink. Convective conditions for heat and mas transfer are imposed. Implementation of appropriate transformation leads to partial differential systems into ordinary ones. Resulting systems are driven through homotopic technique. Aspects of sundry physical variables on the flow field are discussed graphically. Numerical values are constructed for the behavior of distinct variables versus coefficient of skin friction, local Nusselt and Sherwood numbers. The contents of this chapter are published in Plos One 12 (2017) e0175584. Chapter three explains the nonlinear convective flow of magneto Jeffrey nanomaterial. Nonlinear radially stretching surface bounds the fluid. Double-diffusive convection and radiation are considered. Physical significance of Brownian movement and thermophoresis are explained. Mathematical problems are computed for convergent series solutions. Discussion is made for fluid flow, thermal and nanoparticle concentration fields. Surface drag force and rate of heat and mass transport are calculated and exhibited for different estimations of physical variables. The outcomes of this chapter are published in Results in Physics 7 (2017) 2341-2351. Chapter four describes nonlinear mixed convection in magnetohydrodynamic flow of Jeffrey nanomaterial. Fluid flow is bounds by a nonlinear variable thickness surface. Formulation and analysis are based through elaboration of nonlinear thermal radiation, heat generation/absorption and first order chemical reaction. Recent suggested condition of vanishing mass flux at surface is utilized. Implementation of appropriate transformation lead to ordinary differential systems. Significance of various parameters on physical quantities is explained graphically. Computations of surface drag force and heat transfer rate are explained. The results of this chapter are published in International Journal of Mechanical Sciences 134 (2017) 306-314. Chapter five is prepared for stagnation point flow of magneto Walter-B nanomaterial through a stretched sheet with Newtonian conditions. Thermal radiation and first order chemical reaction are developed in the energy and concentration equations. Homotopy technique yield convergence series solutions. Outcomes of distinct variables versus dimensionless velocity, temperature and nanoparticle concentration are explored through graphs. Coefficient of skin friction and local Nusselt and Sherwood numbers are discussed. Material of this chapter is published in Nuclear Engineering and Technology 49 (2017) 1636-1644. The objective of Chapter six is to analyze the nonlinear convection of Walter-B fluid in a variable thickness sheet subject to non-uniform magnetic field. Physical significance of heat transfer is based via nonlinear radiation and heat generation/absorption. Brownian motion and thermophoresis characterize nanomaterial. The derived nonlinear systems have been computed through homotopic scheme. Graph are sketched to see the aspects of pertinent variables versus fluid flow, thermal and concentration fields. Definitions of surface drag force and rate of heat transfer are examined numerically. The outcomes of this chapter are published in International Journal of Heat and Mass Transfer 110 (2017) 506-514. Chapter seven addresses the nonlinear convection in the stagnant point flow of thixotropic material subject to Cattaneo-Christov heat flux. Fluid flow is induced by a stretching sheet. Energy expression formulation is based by taking revised Fourier heat flux. Fluid is with variable thermal conductivity. The derived nonlinear systems are solved. Intervals of convergence are identified. Velocity and temperature are described for various variables. Numerical data for skin friction coefficient is presented. The observations of this chapter are published in Neural Computing and Applications DOI 10.1007/s00521-017-3001-0. Chapter eight models the magnetohydrodynamic nonlinear convective flow of thixotropic nanomaterial towards a stretched surface. Thermal radiation, heat generation/absorption and chemical reaction are further considered. Brownian movement and thermophoresis aspects are also retained. Newtonian heat and mas conditions in formulation are adopted. The transformed ordinary differential systems have been examined through homotopic technique. Graph are plotted to see the behavior of physical variables. Expressions of skin friction and Nusselt and Sherwood numbers are calculated through numerical values. The contents of this chapter are published in Results in Physics 7 (2017) 2124-2133. Chapter nine elaborates the nonlinear convective flow of thixotropic magneto nanomaterial. Fluid flow is induced by nonlinear stretching sheet of variable thickness. Aspects of heat transfer are discussed via nonlinear radiation and heat generation/absorption. Formulation of convective condition and zero mass flux at surface are taken. Features of Brownian movement and thermophoresis are utilized in concentration system. Homotopy procedure yields convergence series solutions. Physical description of fluid flow, thermal field, concentration field, skin friction coefficient and local Nusselt number is arranged. The results of this chapter are published in Physica B: Condensed Matter 537 (2018) 267-276. Chapter ten discusses the flow of electrically conducting third grade material towards a nonlinear stretching surface. Chemical reaction and viscous dissipation are accounted. Nonlinear thermal radiation and Joule heating are further considered. Convective conditions via heat and mass transfer is made. Homotopic technique is used to solve nonlinear systems. Convergence of derived solutions is discussed. Graph are plotted to see the behavior of physical variables. Surface drag force and rates of heat and mass transfer are scrutinized by numerical values. The contents of this chapter are submitted to Plos One. Chapter eleven investigates MHD flow of third grade material towards a nonlinear stretching surface subject to a stagnation point is modeled. Energy expression is developed through involvement of variable thermal conductivity. Double stratification effects are present. Transformation method is employed yields nonlinear differential equations. Series solutions are derived. Fluid flow, thermal and concentration fields are discussed. Skin friction coefficient and local Nusselt and Sherwood numbers are tabulated and analyzed. Material of this chapter is published in Results in Physics 8 (2018) 819-828. Chapter twelve reports the salient features of nonlinear mixed convection and chemical reactive flow of magneto third grade nanomaterial towards a stretchable surface via variable thickness. Nonlinear thermal radiation and heat generation/absorption are considered. The sheet moves with nonlinear velocity. Sheet is convectively heated. Nanoparticle concentration is analyzed in presence of zero mass flux condition. Graphical description for physical quantities are described. Aspects of involved parameters against skin friction coefficient and local Nusselt number are structured. The contents of this chapter are published in Results in Physics 7 (2017) 2752-2761." xml:lang="en_US