Numerical study of non-Newtonian polymeric boundary layer flow and heat transfer from a permeable horizontal isothermal cylinder

In this article, we investigate the nonlinear steady state boundary layer flow and heat transfer of an incompressible Jeffery non-Newtonian fluid from a permeable horizontal isothermal cylinder. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit, finite-difference technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely with Deborah number (De), surface suction parameter (S), Prandtl number (Pr), ratio of relaxation to retardation times (λ) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. It is found that the velocity is reduced with increasing Deborah number whereas temperature is enhanced. Increasing λ enhances the velocity but reduces the temperature. The heat transfer rates is found to be depressed with increasing Deborah number, De, and enhanced with increasing λ. Local skin friction is found to be decreased with a rise in Deborah number whereas it is elevated with increasing values of relaxation to retardation time ratio (λ). Increasing suction decelerates the flow and cools the boundary layer i.e. reduces temperatures. With increasing tangential coordinate, the flow is also decelerated whereas the temperatures are enhanced. The simulation is relevant to polymer coating thermal processing. Polymeric enrobing flows are important in industrial manufacturing technology and process systems. Such flows are non-Newtonian. Motivated by such applications, we did the present problem

Mathematical models for heat and mass transfer in nanofluid flows.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.The behaviour and evolution of most physical phenomena is often best described using mathematical models in the form of systems of ordinary and partial differential equations. A typical example of such phenomena is the flow of a viscous impressible fluid which is described by the Navier-Stokes equations, first derived in the nineteenth century using physical approximations and the principles of mass and momentum conservation. The flow of fluids, and the growth of flow instabilities has been the subject of many investigations because fluids have wide uses in engineering and science, including as carriers of heat, solutes and aggregates. Conventional heat transfer fluids used in engineering applications include air, water and oil. However, each of these fluids has an inherently low thermal conductivity that severely limit heat exchange efficiency. Suspension of nanosized solid particles in traditional heat transfer fluids significantly increases the thermophysical properties of such fluids leading to better heat transfer performance. In this study we present theoretical models to investigate the flow of unsteady nanofluids, heat and mass transport in porous media. Different flow configurations are assumed including an inclined cylinder, a moving surface, a stretching cone and the flow of a polymer nanocomposite modeled as an Oldroyd-B fluid. The nanoparticles assumed include copper, silver and titanium dioxide with water as the base fluid. Most recent boundary-layer nanofluid flow studies assume that the nanoparticle volume fraction can be actively controlled at a bounding solid surface, similar to temperature controls. However, in practice, such controls present significant challenges, and may, in practice, not be possible. In this study the nanoparticle flux at the boundary surface is assumed to be zero. Unsteadiness in fluid flows leads to complex system of partial differential equations. These transport equations are often highly nonlinear and cannot be solved to find exact solutions that describe the evolution of the physical phenomena modeled. A large number of numerical or semi-numerical techniques exist in the literature for finding solutions of nonlinear systems of equations. Some of these methods may, however be subject to certain limitations including slow convergence rates and a small radius of convergence. In recent years, innovative linearization techniques used together with spectral methods have been suggested as suitable tools for solving systems of ordinary and partial differential equations. The techniques which include the spectral local linearization method, spectral relaxation method and the spectral quasiliearization method are used in this study to solve the transport equations, and to determine how the flow characteristics are impacted by changes in certain important physical and fluid parameters. The findings show that these methods give accurate solutions and that the speed of convergence of solutions is comparable with methods such as the Keller-box, Galerkin, and other finite difference or finite element methods. The study gives new insights, and result on the influence of certain events, such as internal heat generation, velocity slip, nanoparticle thermophoresis and random motion on the flow structure, heat and mass transfer rates and the fluid properties in the case of a nanofluid

Energy conversion under conjugate conduction, magneto-convection, diffusion and nonlinear radiation over a non-linearly stretching sheet with slip and multiple convective boundary conditions

Energy conversion under conduction, convection, diffusion and radiation has been studied for MHD free convection heat transfer of a steady laminar boundary-layer flow past a moving permeable non-linearly extrusion stretching sheet. The nonlinear Rosseland thermal radiation flux model, velocity slip, thermal and mass convective boundary conditions are considered to obtain a model with fundamental applications to real world energy systems. The Navier slip, thermal and mass convective boundary conditions are taken into account. Similarity differential equations with corresponding boundary conditions for the flow problem, are derived, using a scaling group of transformation. The transformed model is shown to be controlled by magnetic field, conduction-convection, convection-diffusion, suction/injection, radiation-conduction, temperature ratio, Prandtl number, Lewis number, buoyancy ratio and velocity slip parameters. The transformed non-dimensional boundary value problem comprises a system of nonlinear ordinary differential equations and physically realistic boundary conditions, and is solved numerically using the efficient Runge-Kutta-Fehlberg fourth fifth order numerical method, available in Maple17 symbolic software. Validation of results is achieved with previous simulations available in the published literature. The obtained results are displayed both in graphical and tabular form to exhibit the effect of the controlling parameters on the dimensionless velocity, temperature and concentration distributions. The current study has applications in high temperature materials processing utilizing magnetohydrodynamics, improved performance of MHD energy generator wall flows and also magnetic-microscale fluid devices

A numerical study of entropy generation, heat and mass transfer in boundary layer flows.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.This study lies at the interface between mathematical modelling of fluid flows and numerical methods for differential equations. It is an investigation, through modelling techniques, of entropy generation in Newtonian and non-Newtonian fluid flows with special focus on nanofluids. We seek to enhance our current understanding of entropy generation mechanisms in fluid flows by investigating the impact of a range of physical and chemical parameters on entropy generation in fluid flows under different geometrical settings and various boundary conditions. We therefore seek to analyse and quantify the contribution of each source of irreversibilities on the total entropy generation. Nanofluids have gained increasing academic and practical importance with uses in many industrial and engineering applications. Entropy generation is also a key factor responsible for energy losses in thermal and engineering systems. Thus minimizing entropy generation is important in optimizing the thermodynamic performance of engineering systems. The entropy generation is analysed through modelling the flow of the fluids of interest using systems of differential equations with high nonlinearity. These equations provide an accurate mathematical description of the fluid flows with various boundary conditions and in different geometries. Due to the complexity of the systems, closed form solutions are not available, and so recent spectral schemes are used to solve the equations. The methods of interest are the spectral relaxation method, spectral quasilinearization method, spectral local linearization method and the bivariate spectral quasilinearization method. In using these methods, we also check and confirm various aspects such as the accuracy, convergence, computational burden and the ease of deployment of the method. The numerical solutions provide useful insights about the physical and chemical characteristics of nanofluids. Additionally, the numerical solutions give insights into the sources of irreversibilities that increases entropy generation and the disorder of the systems leading to energy loss and thermodynamic imperfection. In Chapters 2 and 3 we investigate entropy generation in unsteady fluid flows described by partial differential equations. The partial differential equations are reduced to ordinary differential equations and solved numerically using the spectral quasilinearization method and the bivariate spectral quasilinearization method. In the subsequent chapters we study entropy generation in steady fluid flows that are described using ordinary differential equations. The differential equations are solved numerically using the spectral quasilinearization and the spectral local linearization methods

Mhd Stagnation Point Flow of a Jeffrey Fluid Over a Stretching/Shrinking Sheet through Porous Medium

In this analysis the MHD stagnation point flow of Jeffrey fluid over a stretching/shrinking sheet through porous medium is studied. The governing partial differential equations are transformed into nonlinear ordinary differential equation using the similarity transformations and are solved shooting technique. The effects of governing parameters on the velocity, the temperature and the concentration while the skin friction coefficients, the rate of heat transfer are studied graphically. Keywords: MHD; Jeffrey fluid, stretching/shrinking sheet, Porous medium

Numerical study of radiative Maxwell viscoelastic magnetized flow from a stretching permeable sheet with the Cattaneo–Christov heat flux model

In this article, the Cattaneo-Christov heat flux model is implemented to study non-Fourier heat and mass transfer in the magnetohydrodynamic (MHD) flow of an upper convected Maxwell (UCM) fluid over a permeable stretching sheet under a transverse constant magnetic field. Thermal radiation and chemical reaction effects are also considered. The nonlinear partial differential conservation equations for mass, momentum, energy and species conservation are transformed with appropriate similarity variables into a system of coupled, highly nonlinear ordinary differential equations with appropriate boundary conditions. Numerical solutions have been presented for the influence of elasticity parameter (), magnetic parameter (M2), suction/injection parameter (λ), Prandtl number (Pr), conduction-radiation parameter (Rd), sheet stretching parameter (A), Schmidt number (Sc), chemical reaction parameter (γ_c), modified Deborah number with respect to relaxation time of heat flux (i.e. non-Fourier Deborah number) on velocity components, temperature and concentration profiles using the successive Taylor series linearization method (STSLM) utilizing Chebyshev interpolating polynomials and Gauss-Lobatto collocation. The effects of selected parameters on skin friction coefficient, Nusselt number and Sherwood number are also presented with the help of tables. Verification of the STSLM solutions is achieved with existing published results demonstrating close agreement. Further validation of skin friction coefficient, Nusselt number and Sherwood number values computed with STSLM is included using Mathematica software shooting quadrature

Study of Transport of Nanoparticles with Power Law fluid Model for Blood Rheology in Capillaries

The present paper deals with a mathematical model for blood flow through an axially symmetric blood capillary with peripheral layer and slip at the wall. The longitudinal transport of nanoparticles in blood vessels has been analyzed with blood as a power law fluid in a central core region of suspension of all the erythrocytes and a Newtonian fluid in a peripheral layer of plasma. In present analysis, the capillary walls are impermeable and not absorbent for the nanoparticles. The expressions for velocity profile, flow rate, mean velocity and concentration of the solute have been obtained and results have been discussed through graphs

Analysis of Various Complex Flows of Micropolar Fluids in the Slip Flow Regime

Four mathematical models have been developed to study the slip flow of micropolar fluids over a stretching/shrinking sheet under the influence of slip and the Newtonian heating conditions at the boundary. The optimal homotopy analysis method is applied for the solutions of these models. The results obtained from this study are useful in liquid crystals, polymeric suspensions, polishing artificial heart valves and internal cavities

Effects of Variable Viscosity on Power-Law Fluids over a Permeable Moving Surface with Slip Velocity in the Presence of Heat Generation and Suction

In this paper, a numerical investigation on the effects of variable viscosity, slip velocity and heat generation or absorption on power-law fluids with heat and mass transfer over a moving permeable surface is carried out. The transformation of the governing boundary layer equations into ordinary differential equations has been performed by applying similarity transformations. The transformed governing equations are numerically solved by using MATLAB BVP solver bvp4c. The obtained results are presented graphically and discussed for various values of the viscosity parameter, the slip parameter, the heat generation or absorption parameter, the Eckert number and Lewis number. The result shows that, the variable viscosity parameter , it is confirmed that the local skin-friction coefficient decreases while heat and mass transfer rates increases. The heat and mass transfer rates increases rapidly on increasing the Prandtl number. The rate of mass transfer is rapidly increased when the Lewis number increased

Computational Fluid Dynamics 2020

This book presents a collection of works published in a recent Special Issue (SI) entitled “Computational Fluid Dynamics”. These works address the development and validation of existent numerical solvers for fluid flow problems and their related applications. They present complex nonlinear, non-Newtonian fluid flow problems that are (in some cases) coupled with heat transfer, phase change, nanofluidic, and magnetohydrodynamics (MHD) phenomena. The applications are wide and range from aerodynamic drag and pressure waves to geometrical blade modification on aerodynamics characteristics of high-pressure gas turbines, hydromagnetic flow arising in porous regions, optimal design of isothermal sloshing vessels to evaluation of (hybrid) nanofluid properties, their control using MHD, and their effect on different modes of heat transfer. Recent advances in numerical, theoretical, and experimental methodologies, as well as new physics, new methodological developments, and their limitations are presented within the current book. Among others, in the presented works, special attention is paid to validating and improving the accuracy of the presented methodologies. This book brings together a collection of inter/multidisciplinary works on many engineering applications in a coherent manner