Analysis of Nonlinear Flow Problems with Heat Transfer

Abstract

Recently the researchers and scientists are interested to explore the characteristics of fluid flow in the presence of heat transfer. This is due to its rapid advancements and developments in the technological and industrial processes. In fact the investigators are interested to enhance the efficiency of various machnies by increasing the rate of heat transfer and quality of the final products with desired characcteristics through rate of cooling. The combined effects of heat and mass transfer are further significant in many natural, biological, geophysical and industrial processes. Such phenomena include designing of many chemical processing equipment, distribution of temperature and moisture over agricultural fields, formation and dispersion of fog, damaging of crops due to freezing, environmental pollution, grooves of fluid trees, drying of porous solids, geothermal reservoirs, packed bed catalytic reactors, enhanced oil recovery, underground energy transport and thermal insulation. Inspired by such practical applications, the present thesis is devoted to analyze the nonlinear flows problems with heat transfer. This thesis is structured as follows. Chapter one just includes basic concepts and fundamental equations. Chapter two addresses the magnetohydrodynamic (MHD) flow of Powell-Eyring nanomaterial bounded by a nonlinear stretching sheet. Novel features regarding thermophoresis and Brownian motion are taken into consideration. Powell-Eyring fluid is electrically conducted subject to non-uniform applied magnetic field. Assumptions of small magnetic Reynolds number and boundary layer approximation are employed in the mathematical development. Zero nanoparticles mass flux condition at the sheet is selected. Adequate transformations yield nonlinear ordinary differential systems. The developed nonlinear systems have been computed through the homotopic approach. Effects of different pertinent parameters on velocity, temperature and concentration fields are studied and analyzed. Further numerical data of skin friction and heat transfer rate is also tabulated and interpreted. The contents of this chapter have been published in “Results in Physics, 7 (2017) 535–543”. Chapter three investigates the magnetohydrodynamic (MHD) stagnation point flow of Jeffrey material towards a nonlinear stretching surface with variable thickness. Heat transfer characteristics are examined through the melting process, viscous dissipation and internal heat generation. A nonuniform applied magnetic field is considered. Boundarylayer and low magnetic Reynolds number approximations are employed in the problem formulation. Both the momentum and energy equations are converted into the non-linear ordinary differential system using appropriate transformations. Convergent solutions for resulting problems are computed. Behaviors of various parameters on velocity and temperature distributions are examined. Heat transfer rate is also computed and analyzed. These observations have been published in “International Journal of Thermal Sciences, 132 (2018) 344-354”. Chapter four extends the analysis of previous chapter for second grade nanofluid flow with mixed convection and internal heat generation. Novel features regarding Brownian motion and thermophoresis are present. Boundary-layer approximation is employed in the problem formulation. Momentum, energy and concentration equations are converted into the non-linear ordinary differential system through the appropriate transformations. Convergent solutions for resulting problem are computed. Temperature and concentration are investigated. The skin friction coefficient and heat and mass transfer rates are also analyzed. Our results indicate that the temperature and concentration distributions are enhanced for larger values of thermophoresis parameter. The contents of this chapter have been published in “Results in Physics, 7 (2017) 2821-2830”. Darcy-Forchheimer flow of viscous fluid caused by a curved stretching sheet have been discussed in chapter five. Flow for porous space is characterized by Darcy-Forchheimer relation. Concept of homogeneous and heterogeneous reactions is also utilized. Heat transfer for Cattaneo--Christov theory characterizing the feature of thermal relaxation is incorporated. Nonlinear differential systems are derived. Shooting algorithm is employed to construct the solutions for the resulting nonlinear system. The characteristics of various sundry parameters are discussed. Skin friction and local Nusselt number are numerically described. The conclusions have been published in “Results in Physics, 7 (2017) 2886-2892”. In chapter six, the work of chapter five is extended to viscous nanofluid flow due to a curved stretching surface. Convective heat and mass boundary conditions are discussed. Flow in porous medium is characterized by Darcy-Forchheimer relation. Attributes of Brownian diffusion and thermophoresis are incorporated. Boundary layer assumption is employed in the mathematical development. The system of ordinary differential equations is developed by mean of suitable variables. Shooting algorithm is employed to construct the numerical solutions of resulting nonlinear systems. The skin friction coefficient and local Nusselt and Sherwood numbers have been analyzed. These contents are accepted for publication in “International Journal of Numerical Methods for Heat and Fluid Flow”. In chapter seven, the work of chapter six is extended for magnetohydrodynamic (MHD) flow of micropolar fluid due to a curved stretching surface. Homogeneous-heterogeneous reactions are taken into consideration. Heat transfer process is explored through heat generation/absorption effects. Micropolar liquid is electrically conducted subject to uniform applied magnetic field. Small magnetic Reynolds number assumption is employed in the mathematical treatment. The reduction of partial differential system to nonlinear ordinary differential system has been made by employing suitable variables. The obtained nonlinear systems have been computed. The surface drag and couple stress coefficients and local Nusselt number are described by numerical data. The contents of this chapter have been published in “Journal of Molecular Liquids 240 (2017) 209–220”. Chapter eight extended the idea of chapter seven by considering magnetohydrodynamic (MHD) flow of Jeffrey nanomaterial due to a curved stretchable surface. Novel features regarding thermophoresis and Brownian motion are considered. Heat transfer process is explored through heat generation/absorption effects. Jeffrey liquid is electrically conducted subject to uniform applied magnetic field. Boundary layer and low magnetic Reynolds number assumptions are employed. The obtained nonlinear systems are solved. The characteristics of various sundry parameters are studied through plots and numerical data. Moreover the physical quantities such as skin friction coefficient and local Nusselt number are described by numerical data. These findings have been submitted for publication in “International Journal of Heat and Mass Transfer”. The objective of chapter nine is to provide a treatment of viscous fluid flow induced by nonlinear curved stretching sheet. Concept of homogeneous and heterogeneous reactions has been utilized. Heat transfer process is explored through convective heating mechanism. The obtained nonlinear system of equations has been computed and solutions are examined graphically. Surface drag force and local Nusselt number are numerically discussed. Such contents are submitted for publication in “Applied Mathematics and Mechanics”. Chapter ten provides a numerical simulation for boundary-layer flow of viscous fluid bounded by nonlinear curved stretchable surface. Convective conditions of heat and mass transfer are employed at the curved nonlinear stretchable surface. Heat generation/absorption and chemical reaction effects are accounted. Nonlinear ordinary differential systems are computed by shooting algorithm. The characteristics of various sundry parameters are explored. Further the skin friction coefficient and local Nusselt and Sherwood numbers are tabulated numerically. The contents of present chapter have been published in “Results in Physics, 7 (2017) 2601-2606”.