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

Challenges and progress on the modelling of entropy generation in porous media: a review

Depending upon the ultimate design, the use of porous media in thermal and chemical systems can provide significant operational advantages, including helping to maintain a uniform temperature distribution, increasing the heat transfer rate, controlling reaction rates, and improving heat flux absorption. For this reason, numerous experimental and numerical investigations have been performed on thermal and chemical systems that utilize various types of porous materials. Recently, previous thermal analyses of porous materials embedded in channels or cavities have been re-evaluated using a local thermal non-equilibrium (LTNE) modelling technique. Consequently, the second law analyses of these systems using the LTNE method have been a point of focus in a number of more recent investigations. This has resulted in a series of investigations in various porous systems, and comparisons of the results obtained from traditional local thermal equilibrium (LTE) and the more recent LTNE modelling approach. Moreover, the rapid development and deployment of micro-manufacturing techniques have resulted in an increase in manufacturing flexibility that has made the use of these materials much easier for many micro-thermal and chemical system applications, including emerging energy-related fields such as micro-reactors, micro-combustors, solar thermal collectors and many others. The result is a renewed interest in the thermal performance and the exergetic analysis of these porous thermochemical systems. This current investigation reviews the recent developments of the second law investigations and analyses in thermal and chemical problems in porous media. The effects of various parameters on the entropy generation in these systems are discussed, with particular attention given to the influence of local thermodynamic equilibrium and non-equilibrium upon the second law performance of these systems. This discussion is then followed by a review of the mathematical methods that have been used for simulations. Finally, conclusions and recommendations regarding the unexplored systems and the areas in the greatest need of further investigations are summarized

Analytical modeling of MHD flow over a permeable rotating disk in the presence of soret and dufour effects: Entropy analysis.

The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation in special cases. The entropy generation equation is derived as a function of velocity, temperature and concentration gradients. Effects of flow physical parameters including magnetic interaction parameter, suction parameter, Prandtl number, Schmidt number, Soret and Dufour number on the fluid velocity, temperature and concentration distributions as well as entropy generation number are analysed and discussed in detail. Results show that increasing the Soret number or decreasing the Dufour number tends to decrease the temperature distribution while the concentration distribution is enhanced. The averaged entropy generation number increases with increasing magnetic interaction parameter, suction parameter, Prandtl number, and Schmidt number

Power Balance in Aerodynamic Flows

A control volume analysis of the compressible viscous flow about an aircraft is performed,including integrated propulsors and flow control systems. In contrast to most past analyses which have focused on forces and momentum flow, in particular thrust and drag, the present analysis focuses on mechanical power and kinetic energy flow. The result is a clear identification and quantification of all the power sources, power sinks, and their interactions which are present in any aerodynamic flow. The formulation does not require any separate definitions of thrust and drag, and hence it is especially useful for analysis and optimization of aerodynamic configurations which have tightly integrated propulsion and boundary layer control systems

Transient analysis of Casson fluid thermo-convection from a vertical cylinder embedded in a porous medium : entropy generation and thermal energy transfer visualization

Thermal transport in porous media has stimulated substantial interest in engineering sciences due to increasing applications in filtration systems, porous bearings, porous layer insulation, biomechanics, geomechanics etc. Motivated by such applications, in this article a numerical investigation of entropy generation effects on the heat and momentum transfer in unsteady laminar incompressible boundary layer flow of a Casson viscoplastic fluid over a uniformly heated vertical cylinder embedded in a porous medium is presented. Darcy’s law is employed to simulate bulk drag effects at low Reynolds number for an isotropic, homogenous porous medium. Heat line visualization is also included. The mathematical model is derived and normalized using appropriate transformation variables. The resulting time-dependent non-linear coupled partial differential conservation equations with associated boundary conditions are solved with an efficient unconditionally stable implicit finite difference Crank Nicolson scheme. The time histories of average values of momentum and heat transport coefficients, entropy generation and Bejan number, as well as the steady-state flow variables are computed for several values of non-dimensional parameters arising in the flow equations. The results indicate that entropy generation parameter and Bejan number are both elevated with increasing values of Casson fluid parameter, Darcy number, group parameter and Grashof number. To analyze the heat transfer process in a two-dimensional domain, plotting heat lines provides an excellent approach in addition to streamlines and isotherms. The dimensionless heat function values are shown to correlate closely with the overall rate of heat transfer. Bejan’s heat flow visualization implies that the heat function contours are compact in the neighbourhood of the leading edge of the boundary layer on the hot cylindrical wall. It is observed that as the Darcy number increases, the deviations of heat lines from the hot wall are reduced. Furthermore the deviations of flow variables from the hot wall for a Casson fluid are significant compared with those computed for a Newtonian fluid and this has important implications in industrial thermal materials processing operations

Effect of temperature-dependent viscosity on entropy generation in transient viscoelastic polymeric fluid flow from an isothermal vertical plate

A numerical investigation of the viscosity variation effect upon entropy generation in time-dependent viscoelastic polymeric fluid flow and natural convection from a semi-infinite vertical plate is described. The Reiner-Rivlin second order differential model is utilized which can predict normal stress differences in dilute polymers. The conservation equations for heat, momentum and mass are normalized with appropriate transformations and the resulting unsteady nonlinear coupled partial differential equations are elucidated with the well-organized unconditionally stable implicit Crank-Nicolson finite difference method subject to suitable initial and boundary conditions. Average values of wall shear stress and Nusselt number, second-grade fluid flow variables conferred for distinct values of physical parameters. Numerical solutions are presented to examine the entropy generation and Bejan number along with their contours. The outcomes show that entropy generation parameter and Bejan number both increase with increasing values of group parameter and Grashof number. The present study finds applications in geothermal engineering, petroleum recovery, oil extraction and thermal insulation, etc

Transient natural convection induced by the absorption of concentrated solar radiation in high temperature molten salts

Solar-thermal energy systems that involve the deposition of radiation in absorbing high temperature molten salts to harness the entire solar spectrum and achieve high efficiencies and low Levelised Cost Of Energy (LCOE) are of considerable interest for power generation. From a design stand point, to achieve a competitive solar power generation devices, it is imperative to have an accurate knowledge of the inherent physical processes of such a fluid system. Thus under high temperature conditions, detailed understanding of the heat transfer and fluid flow characteristics in an irradiated fluid is considered. The work investigates the spectral dependent heat transfer and fluid dynamics in a thermal storage concept which uniquely combines a volumetric receiver and a single tank thermal store. The Thermal Energy Storage (TES) is protypical of a small scale concept concentrated solar plant. Advances in computing power, has seen Computational Fluid Dynamics(CFD) consolidated as a powerful tool employed by researchers and engineers to simulate real world behaviour and complex phenomena to a certain degree of accuracy with low effort in time, personnel and resources. This thesis is focused on the development of a realistic numerical model capable of predicting the local volumetric absorption of solar radiation in a fluid layer which provides an improved understanding of the hydrodynamic and thermal conditions in an enclosed fluid layer. Computational Fluid Dynamics is used to simulate the transient heat transfer and fluid flow determined by a combined influence of volumetric absorption and natural convection in a high temperature fluid filled enclosure. The enclosure is studied for the specific case in which a high temperature salt is first heated by direct volumetric absorption of the incident solar radiation and secondly by natural convection from a absorber plate located at the bottom of the enclosure whose sole purpose is to absorb all non-absorbed radiation reaching the lower surface. The current models considers the depth dependence absorption of solar radiation based on (i) a solar weighted absorption coe cient (assumed constant over all wavelengths) and (ii) spectral absorption coe cient characterised by wavelength band based on a standard solar spectrum reference. A commercially available CFD Package based on Finite Element Method (FEM), COMSOL Multiphysics is used to discretise and solve the Navier Stokes and energy equation under transients heating conditions for a non Boussinesq condition by accounting for the temperature variable properties of molten salts. A time-dependent and Backward Differentiation Formula (BDF) solver using implicit time-stepping methods is combined with refined mesh to solve the non-linear PDE. Validity of the numerical tool has been conducted, by comparing results from published results found in literature with corresponding numerical results. The mesh element optimum sizes and time steps used conform to those obtained in validation models. Simulations have been conducted for a daily charging period of three hours as used in conjunction with a solar system. The effects of bottom absorber plate, flux Rayleigh number, aspect ratio, variable Air Mass and inclination angle have also been investigated. Numerical results are presented in terms of surface plots, temperature contours, and velocity contours and streamlines which show the thermal field distribution and flow structures, for volumetric absorption of thermal radiation coupled with natural convection. Performance criteria are based on quantification of the level of thermal stratification using the MIX number, the dimensionless exergy and capture efficiency. Three dimensionality effects were studied by considering three dimensional simulation for the same problem. The results show that the present method and models are capable of capturing the main features of the flow and the overall performance of these turbulence models in terms of predicting time-averaged quantities. Results obtained indicate a nonlinear temperature profile consisting of two distinct layers: a surface layer and a bottom layer. The numerical results reveal natural convection in the cavity follows an initial stage, a transitional stage and a quasi-steady stage. Results indicate that volumetric absorption of solar radiation, when coupled to natural convection has a direct influence on the thermal field through the disparities in absorption and emission phenomena. The isotherms and streamlines show that the natural convective heat transfer and flow are quite different from those obtained in differentially heat enclosures. Thus the heat transfer mechanism destroys a symmetry of the system that relates clockwise and counter clockwise flows. Temperature and flow field are found to be greatly influenced by the aspect ratio (H/D) of the store and the flux Rayleigh number. It is found that the predicted heat transfer from the lower surface in the cavity is increased when the simulation is extended from two to three dimensional. Results obtained indicated that increasing the aspect ratio, Air Mass and inclination angle all result in increasing levels of thermal stratification. Natural convection from the lower absorber surface is found to increase with increasing flux Rayleigh number

Combined heat and mass transfer and thermodynamic irreversibilities in the stagnation-point flow of Casson rheological fluid over a cylinder with catalytic reactions and inside a porous medium under local thermal nonequilibrium

The transport of heat and mass from the surface of a cylinder coated with a catalyst and subject to an impinging flow of a Casson rheological fluid is investigated. The cylinder features circumferentially non-uniform transpiration and is embedded inside a homogeneous porous medium. The non-equilibrium thermodynamics of the problem, including Soret and Dufour effects and local thermal non-equilibrium in the porous medium, are considered. Through the introduction of similarity variables, the governing equations are reduced to a set of non-linear ordinary differential equations which are subsequently solved numerically. This results in the prediction of hydrodynamic, temperature, concentration and entropy generation fields, as well as local and average Nusselt, Sherwood and Bejan numbers. It is shown that, for low values of the Casson parameter and thus strong non-Newtonian behaviour, the porous system has a significant tendency towards maintaining local thermal equilibrium. Furthermore, the results show a major reduction in the average Nusselt number during the transition from Newtonian to non-Newtonian fluid, while the reduction in the Sherwood number is less pronounced. It is also demonstrated that flow, thermal and mass transfer irreversibilities are significantly affected by the fluid’s strengthened non-Newtonian characteristics. The physical reasons for these behaviours are discussed by exploring the influence of the Casson parameter and other pertinent factors upon the thickness of thermal and concentration boundary layers. It is noted that this study is the first systematic investigation of the stagnation-point flow of Casson fluid in cylindrical porous media

MHD flow in a vertical channel under the effect of temperature dependent physical parameters

Mixed convective flow in a vertical channel filled with electrically conducting viscous fluid with isothermal wall conditions is investigated for variable properties. The combined effects of temperature dependent viscosity and temperature dependent thermal conductivity are analyzed. The solutions are obtained both analytically by perturbation method and numerically by Runge–Kutta method with shooting technique. The dimensionless governing parameters affecting velocity and temperature fields are variable viscosity parameter (−0.5 ≤ bν ≤ 0.5), variable thermal conductivity parameter (−0.5 ≤ bk ≤ 0.5), Hartmann number (1 ≤ M ≤ 3), applied electric field parameter (E0 = ±1, 0), wall temperature ratio parameter (−2 ≤ m ≤ 2) and buoyancy parameter (0 < N ≤ 1.5). For some limiting cases, the obtained results are validated by comparing with those available from the existing literature. Correlations for skin friction and Nusselt number in terms of governing parameters are developed

Blade row interaction in radial turbomachines

A computational study has been performed to investigate the effects of blade row interaction on the performance of radial turbomachines, which was motivated by the need to improve our understanding of the blade row interaction phenomena for further improvement in the performance. High-speed centrifugal compressor stages with three settings of radial gap are configured and simulated using a three-dimensional Navier-Stokes flow method in order to investigate the impact of blade row interaction on stage efficiency. The performance predictions show that the efficiency deteriorates if the gap between blade rows is reduced to intensify blade row interaction, which is in contradiction to the general trend for stage axial compressors, hi the compressors tested, the wake chopping by diffuser vanes, which usually benefits efficiency in axial compressor stages, causes unfavourable wake compression through the diffuser passages to deteriorate the efficiency. Similarly, hydraulic turbine stages with three settings of radial gap are simulated numerically. A new three-dimensional Navier-Stokes flow method based upon the dual-time stepping technique combined with the pseudo-compressibility method has been developed for hydraulic flow simulations. This method is validated extensively with several test cases where analytical and experimental data are available, including a centrifugal pump case with blade row interaction. Some numerical tests are conducted to examine the dependency of the flow solutions on several numerical parameters, which serve to justify the sensitivity of the solutions. Then, the method is applied to performance predictions of the hydraulic turbine stages. The numerical performance predictions for the turbines show that, by reducing the radial gap, the loss generation in the nozzle increases, which has a decisive influence on stage efficiency. The blade surface boundary layer loss and wake flow mixing loss, enhanced with a higher level of flow velocity around blading and the potential flow disturbances, are responsible for the observed trend