8 research outputs found
Stabilized finite element methods for natural and forced convection-radiation heat transfer
Thermal radiation in forced and natural convection can be an important mode of heat transfer
in high temperature chambers, such as industrial furnaces and boilers, even under non-soot
conditions. Growing concern with high temperature processes has emphasized the need for an
evaluation of the eect of radiative heat transfer. Nevertheless, the modelling of radiation is
often neglected in combustion analysis, mainly because it involves tedious mathematics, which
increase the computation time, and also because of the lack of detailed information on the
optical properties of the participating media and surfaces. Ignoring radiative transfer may
introduce signicant errors in the overall predictions. The most accurate procedures available
for computing radiation transfer in furnaces are the Zonal and Monte Carlo methods. However,
these methods are not widely applied in comprehensive combustion calculations due to
their large computational time and storage requirements. Also, the equations of the radiation
transfer are in non-dierential form, a signicant inconvenience when solved in conjunction
with the dierential equations of
ow and combustion. For this reason, numerous investigations
are currently being carried out worldwide to assess computationally ecient methods. In
addition ecient modelling of forced and natural convection-radiation would help to simulate
and understand heat transfer appearing in various engineering applications, especially in the
case of the heat treatment of high-alloy steel or glass by a continuously heating process inside
industrial furnaces, ovens or even smaller applications like microwaves. This thesis deals with
the design of such methods and shows that a class of simplied approximations provides advantages
that should be utilized in treating radiative transfer problems with or without
ow
convection. Much of the current work on modelling energy transport in high-temperature
gas furnaces or chemically reacting
ows, uses computational
uid dynamics (CFD) codes.
Therefore, the models for solving the radiative transfer equations must be compatible with the
numerical methods employed to solve the transport equations. The Zonal and Monte Carlo
methods for solving the radiative transfer problem are incompatible with the mathematical
formulations used in CFD codes, and require prohibitive computational times for spatial resolution
desired. The main objectives of this thesis is then to understand and better model the
heat treatment at the same time in the furnace/oven chamber and within the workpieces under
specied furnace geometry, thermal schedule, parts loading design, initial operation conditions,
and performance requirements. Nowadays, there is a strong need either for appropriate fast
and accurate algorithms for the mixed and natural convection-radiation or for reduced models
which still incorporate its main radiative transfer physics. During the last decade, a lot of
research was focused on the derivation of approximate models allowing for an accurate description
of the important physical phenomena at reasonable numerical costs. Hence, a whole
hierarchy of approximative equations is available, ranging from half-space moment approximations
over full-space moment systems to the diusion-type simplied PN approximations.
The latter were developed and extensively tested for various radiative transfer problems, where
they proved to be suciently accurate. Although they were derived in the asymptotic regime for a large optical thickness of the material, these approximations yield encouraging even
results in the optically thin regime. The main advantage of considering simplied PN approximations
is the fact that the integro-dierential radiative transfer equation is transformed
into a set of elliptic equations independent of the angular direction which are easy to solve.
The simplied PN models are proposed in this thesis for modelling radiative heat transfer for
both forced and natural convection-radiation applications. There exists a variety of computational
methods available in the literature for solving coupled convection-radiation problems.
For instance, applied to convection-dominated
ows, Eulerian methods incorporate some upstream
weighting in their formulations to stabilize the numerical procedure. The most popular
Eulerian methods, in nite element framework, are the streamline upwind Petrov-Galerkin,
Galerkin/least-squares and Taylor-Galerkin methods. All these Eulerian methods are easy to
formulate and implement. However, time truncation errors dominate their solutions and are
subjected to Courant-Friedrichs-Lewy (CFL) stability conditions, which put a restriction on
the size of time steps taken in numerical simulations. Galerkin-characteristic methods (also
known by semi-Lagrangian methods in meteorological community) on the other hand, make
use of the transport nature of the governing equations. The idea in these methods is to rewrite
the governing equations in term of Lagrangian co-ordinates as dened by the particle trajectories
(or characteristics) associated with the problem. Then, the Lagrangian total derivative
is approximated, thanks to a divided dierence operator. The Lagrangian treatment in these
methods greatly reduces the time truncation errors in the Eulerian methods. In addition,
these methods are known to be unconditionally stable, independent of the diusion coecient,
and optimally accurate at least when the inner products in the Galerkin procedure are calculated
exactly. In Galerkin-characteristic methods, the time derivative and the advection term
are combined as a directional derivative along the characteristics, leading to a characteristic
time-stepping procedure. Consequently, the Galerkin-characteristic methods symmetrize and
stabilize the governing equations, allow for large time steps in a simulation without loss of
accuracy, and eliminate the excessive numerical dispersion and grid orientation eects present
in many upwind methods. This class of numerical methods have been implemented in this
thesis to solve the developed models for mixed and natural convection-radiation applications.
Extensive validations for the numerical simulations have been carried out and full comparisons
with other published numerical results (obtained using commercial softwares) and experimental
results are illustrated for natural and forced radiative heat transfer. The obtained convectionradiation
results have been studied under the eect of dierent heat transfer characteristics to
improve the existing applications and to help in the furnace designs
Topics in Magnetohydrodynamics
To understand plasma physics intuitively one need to master the MHD behaviors. As sciences advance, gap between published textbooks and cutting-edge researches gradually develops. Connection from textbook knowledge to up-to-dated research results can often be tough. Review articles can help. This book contains eight topical review papers on MHD. For magnetically confined fusion one can find toroidal MHD theory for tokamaks, magnetic relaxation process in spheromaks, and the formation and stability of field-reversed configuration. In space plasma physics one can get solar spicules and X-ray jets physics, as well as general sub-fluid theory. For numerical methods one can find the implicit numerical methods for resistive MHD and the boundary control formalism. For low temperature plasma physics one can read theory for Newtonian and non-Newtonian fluids etc
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
Chemical Kinetics
Chemical Kinetics relates to the rates of chemical reactions and factors such as concentration and temperature, which affects the rates of chemical reactions. Such studies are important in providing essential evidence as to the mechanisms of chemical processes. The book is designed to help the reader, particularly students and researchers of physical science, understand the chemical kinetics mechanics and chemical reactions. The selection of topics addressed and the examples, tables and graphs used to illustrate them are governed, to a large extent, by the fact that this book is aimed primarily at physical science (mainly chemistry) technologists. Undoubtedly, this book contains "must read" materials for students, engineers, and researchers working in the chemistry and chemical kinetics area. This book provides valuable insight into the mechanisms and chemical reactions. It is written in concise, self-explanatory and informative manner by a world class scientists in the field
Theoretical Approaches in Non-Linear Dynamical Systems
From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare
The Twenty-Fifth Lunar and Planetary Science Conference. Part 3: P-Z
Various papers on lunar and planetary science are presented, covering such topics as: impact craters, tektites, lunar geology, lava flow, geodynamics, chondrites, planetary geology, planetary surfaces, volcanology, tectonics, topography, regolith, metamorphic rock, geomorphology, lunar soil, geochemistry, petrology, cometary collisions, geochronology, weathering, and meteoritic composition