Modelling of transient heat transfer in annealing furnaces

This is a study of heat transfer in a lift-off furnace which is employed in the batch annealing of a stack of coils of steel strip. The objective of the project is to investigate the various factors which govern the furnace design and the heat transfer resistances, so as to reduce the time of the annealing cycle, and hence minimize the operating costs. The work involved mathematical modelling of patterns of gas flow and modes of heat transfer. These models are: Heat conduction and its conjectures in the steel coils;Convective heat transfer in the plates separating the coils in the stack and in other parts of the furnace; and Radiative and convective heat transfer in the furnace by using the long furnace model. An important part of the project is the development of numerical methods and computations to solve the transient models. A limited number of temperature measurements was available from experiments on a test coil in an industrial furnace. The mathematical model agreed well with these data. The model has been used to show the following characteristics of annealing furnaces, and to suggest further developments which would lead to significant savings: - The location of the limiting temperature in a coil is nearer to the hollow core than to the outer periphery. - Thermal expansion of the steel tends to open the coils, reduces their thermal conductivity in the radial direction, and hence prolongs the annealing cycle. Increasing the tension in the coils and/or heating from the core would overcome this heat transfer resistance. - The shape and dimensions of the convective channels in the plates have significant effect on heat convection in the stack. An optimal design of a channel is shown to be of a width-to-height ratio equal to 9. - Increasing the cooling rate, by using a fluidized bed instead of the normal shell and tube exchanger, would shorten the cooling time by about 15%, but increase the temperature differential in the stack. - For a specific charge weight, a stack of different-sized coils will have a shorter annealing cycle than one of equally-sized coils, provided that production constraints allow the stacking order to be optimal. - Recycle of hot flue gases to the firing zone of the furnace would produce a. decrease in the thermal efficiency up to 30% but decreases the heating time by about 26%.

Octane requirement increase arising from the use of lead free fuel

Lead in petrol has been identified as a health hazard and attempts are being made to create a lead-free atmosphere. Through an intensive study a review is made of the various options available to the automobile and petroleum industry. The economic and atmospheric penalties coupled with automobile fuel consumption trends are calculated and presented in both graphical and tabulated form. Experimental measurements of carbon monoxide and hydrocarbon emissions are also presented for certain selected fuels. Reduction in CO and HC's with the employment of a three-way catalyst is also discussed. All tests were carried out on a Fiat 127A engine at wide open throttle and standard timing setting. A Froude dynamometer was used to vary engine speed. With the introduction of lead-free petrol, interest in combustion chamber deposits in spark ignition engines has ben renewed. These deposits cause octane requirement increase or rise in engine knock and decreased volumetric efficiency. The detrimental effect of the deposits has been attributed to the physical volume of the deposit and to changes in heat transfer. This study attempts to assess why leaded deposits, though often greater in mass and volume, yield relatively lower ORI when compared to lead-free deposits under identical operating conditions. This has been carried out by identifying the differences in the physical nature of the deposit and then through measurement of the thermal conductivity and permeability of the deposits. The measured thermal conductivity results are later used in a mathematical model to determine heat transfer rates and temperature variation across the engine wall and deposit. For the model, the walls of the combustion cylinder and top are assumed to be free of engine deposit, the major deposit being on the piston head. Seven different heat transfer equations are formulated describing heat flow at each part of the four stroke cycle, and the variation of cylinder wall area exposed to gas mixture is accounted for. The heat transfer equations are solved using numerical methods and temperature variations across the wall identified. Though the calculations have been carried out for one particular moment in the cycle, similar calculations are possible for every degree of the crank angle, and thus further information regarding location of maximum temperatures at every degree of the crank angle may also be determined. In conclusion, thermal conductivity values of leaded and lead-free deposits have been found. The fundamental concepts of a mathematical model with great potential have been formulated and it is hoped that with future work it may be used in a simulation for different engine construction materials and motor fuels, leading to better design of future prototype engines.

Design methodology for the servo control of high speed multi-axis machinery (BL): decoupling and synchronisation of a generic machine by blockwise decentralised MIMO control

Traditional machinery for manufacturing processes are characterised by actuators powered and co-ordinated by mechanical linkages driven from a central drive. Increasingly, these linkages are replaced by independent electrical drives, each performs a different task and follows a different motion profile, co-ordinated by computers. A design methodology for the servo control of high speed multi-axis machinery is proposed, based on the concept of a highly adaptable generic machine model. In addition to the dynamics of the drives and the loads, the model includes the inherent interactions between the motion axes and thus provides a Multi-Input Multi-Output (MIMO) description. In general, inherent interactions such as structural couplings between groups of motion axes are undesirable and needed to be compensated. On the other hand, imposed interactions such as the synchronisation of different groups of axes are often required. It is recognised that a suitable MIMO controller can simultaneously achieve these objectives and reconciles their potential conflicts. Both analytical and numerical methods for the design of MIMO controllers are investigated. At present, it is not possible to implement high order MIMO controllers for practical reasons. Based on simulations of the generic machine model under full MIMO control, however, it is possible to determine a suitable topology for a blockwise decentralised control scheme. The Block Relative Gain array (BRG) is used to compare the relative strength of closed loop interactions between sub-systems. A number of approaches to the design of the smaller decentralised MIMO controllers for these sub-systems has been investigated. For the purpose of illustration, a benchmark problem based on a 3 axes test rig has been carried through the design cycle to demonstrate the working of the design methodology.

Optimization of dispersion-managed optical fiber lines

We present various approaches to the optimization of optical fiber lines and discuss the ranges of validity of such methods. An effective scheme for upgrading of existing transmission lines using dispersion-management with optimization of the pre- and postcompensating fiber is examined. The theory and numerical methods are illustrated in application to the Upgrade of a specific installed Deutsche Telekom fiber line.

In memoriam: Dimitar Shishkov

Bulgarian and world computer science lost a prominent colleague: Dimitar Petrov Shishkov 22th January 1939, Varna – 8th March 2004, Sofia D. Shishkov graduated mathematics at Sofia University in 1962. In the last year of his studies he started a specialization as a programmer at the Joint Institute of Nuclear Research – Dubna which lasted three years. Then he worked at the Institute of Mathematics for two years. In 1966 D. Shishkov together with a group of experts transferred to the newly created Central Laboratory for Information Technologies. In 1976 he defended his PhD dissertation. He has been an associate professor in computer science at Sofia University since 1985 and a professor in computer science since 2000. His scientific interests and results were in the fields of computer architectures, computational linguistics, artificial intelligence, numerical methods, data structures, etc. He was remarkable with his teaching activities. D. Shishkov was the creator of high-quality software for the first Bulgarian electronic calculator “ELKA” – one of the first calculators in the world as well as for the series of next calculators and for specialized minicomputers. He was the initiator of the international project “Computerization of the natural languages”. He was a member of a range of international scientific organizations. Among his numerous activities was the organization of the I-st Programming competition in 1979. D. Shishkov was the initiator of sport dancing in Bulgaria (1967) and founder of the first sport-dancing high school education in the world. D. Shishkov was a highly accomplished person with a diversity of interests, with a developed social responsibility and accuracy in his work. In 1996 D. Shishkov was awarded with the International Prize ITHEA for outstanding achievements in the field of Information Theories and Applications. We are grateful to D. Shishkov for the chance to work together with him for establishment and development of IJ ITA.

Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

Елементи на обучение чрез синтаксис за студенти от професионално направление „Технически науки”

Доклад, поместен в сборника на Националната конференция "Образованието в информационното общество", Пловдив, май, 2011 г.

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

On a Hypersingular Equation of a Problem, for a Crack in Elastic Media

Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.

A Model of a Diagnostic Test for Controlling the Results of a Computer Based Education in Applied Mathematics at the University of Ruse

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

A Didactic Model of Computer Supported Education in Higher Mathematics

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

Development of a mathematical and computer model to assess water quality impacts of hazardous compounds from minor gasoline spills in the inter-tidal zone of the Miami River, Florida

The objective of this study was to develop a model to predict transport and fate of gasoline components of environmental concern in the Miami River by mathematically simulating the movement of dissolved benzene, toluene, xylene (BTX), and methyl-tertiary-butyl ether (MTBE) occurring from minor gasoline spills in the inter-tidal zone of the river. Computer codes were based on mathematical algorithms that acknowledge the role of advective and dispersive physical phenomena along the river and prevailing phase transformations of BTX and MTBE. Phase transformations included volatilization and settling. ^ The model used a finite-difference scheme of steady-state conditions, with a set of numerical equations that was solved by two numerical methods: Gauss-Seidel and Jacobi iterations. A numerical validation process was conducted by comparing the results from both methods with analytical and numerical reference solutions. Since similar trends were achieved after the numerical validation process, it was concluded that the computer codes algorithmically were correct. The Gauss-Seidel iteration yielded at a faster convergence rate than the Jacobi iteration. Hence, the mathematical code was selected to further develop the computer program and software. The model was then analyzed for its sensitivity. It was found that the model was very sensitive to wind speed but not to sediment settling velocity. ^ A computer software was developed with the model code embedded. The software was provided with two major user-friendly visualized forms, one to interface with the database files and the other to execute and present the graphical and tabulated results. For all predicted concentrations of BTX and MTBE, the maximum concentrations were over an order of magnitude lower than current drinking water standards. It should be pointed out, however, that smaller concentrations than the latter reported standards and values, although not harmful to humans, may be very harmful to organisms of the trophic levels of the Miami River ecosystem and associated waters. This computer model can be used for the rapid assessment and management of the effects of minor gasoline spills on inter-tidal riverine water quality. ^

Elastic modulus study of gold thin film for use as an actuated membrane in a superconductive radio frequency (RF) microelectromechanical (MEM) switch

The objective of this research was to find Young's elastic modulus for thin gold films at room and cryogenic temperatures based on the flexional model which has not been previously attempted. Electrical Sonnet simulations and numerical methods using Abacus for the mechanical responses were employed for this purpose. A RF MEM shunt switch was designed and a fabrication process developed in house. The switch is composed of a superconducting YBa2 Cu3O7 coplanar waveguide structure with an Au bridge membrane suspended above an area of the center conductor covered with BaTiO3 dielectric. The Au membrane is actuated by the electrostatic attractive force acting between the transmission line and the membrane when voltage is applied. The value of the actuation force will greatly depend on the switch pull-down voltage and on the geometry and mechanical properties of the bridge material. Results show that the elastic modulus for Au thin film can be 484 times higher at cryogenic temperature than it is at room temperature. ^

Essays on political economy

The first chapter analizes conditional assistance programs. They generate conflicting relationships between international financial institutions (IFIs) and member countries. The experience of IFIs with conditionality in the 1990s led them to allow countries more latitude in the design of their reform programs. A reformist government does not need conditionality and it is useless if it does not want to reform. A government that faces opposition may use conditionality and the help of pro-reform lobbies as a lever to counteract anti-reform groups and succeed in implementing reforms.^ The second chapter analizes economies saddled with taxes and regulations. I consider an economy in which many taxes, subsidies, and other distortionary restrictions are in place simultaneously. If I start from an inefficient laissez-faire equilibrium because of some domestic distortion, a small trade tax or subsidy can yield a first-order welfare improvement, even if the instrument itself creates distortions of its own. This may result in "welfare paradoxes". The purpose of the chapter is to quantify the welfare effects of changes in tax rates in a small open economy. I conduct the simulation in the context of an intertemporal utility maximization framework. I apply numerical methods to the model developed by Karayalcin. I introduce changes in the tax rates and quantify both the impact on welfare, consumption and foreign assets, and the path to the new steady-state values.^ The third chapter studies the role of stock markets and adjustment costs in the international transmission of supply shocks. The analysis of the transmission of a positive supply shock that originates in one of the countries shows that on impact the shock leads to an inmediate stock market boom enjoying the technological advance, while the other country suffers from depress stock market prices as demand for its equity declines. A period of adjustment begins culminating in a steady state capital and output level that is identical to the one before the shock. The the capital stock of one country undergoes a non-monotonic adjustment. The model is tested with plausible values of the variables and the numeric results confirm the predictions of the theory.^

Essays On Political Economy

The first chapter analizes conditional assistance programs. They generate conflicting relationships between international financial institutions (IFIs) and member countries. The experience of IFIs with conditionality in the 1990s led them to allow countries more latitude in the design of their reform programs. A reformist government does not need conditionality and it is useless if it does not want to reform. A government that faces opposition may use conditionality and the help of pro-reform lobbies as a lever to counteract anti-reform groups and succeed in implementing reforms. The second chapter analizes economies saddled with taxes and regulations. I consider an economy in which many taxes, subsidies, and other distortionary restrictions are in place simultaneously. If I start from an inefficient laissez-faire equilibrium because of some domestic distortion, a small trade tax or subsidy can yield a first-order welfare improvement, even if the instrument itself creates distortions of its own. This may result in "welfare paradoxes". The purpose of the chapter is to quantify the welfare effects of changes in tax rates in a small open economy. I conduct the simulation in the context of an intertemporal utility maximization framework. I apply numerical methods to the model developed by Karayalcin. I introduce changes in the tax rates and quantify both the impact on welfare, consumption and foreign assets, and the path to the new steady-state values. The third chapter studies the role of stock markets and adjustment costs in the international transmission of supply shocks. The analysis of the transmission of a positive supply shock that originates in one of the countries shows that on impact the shock leads to an inmediate stock market boom enjoying the technological advance, while the other country suffers from depress stock market prices as demand for its equity declines. A period of adjustment begins culminating in a steady state capital and output level that is identical to the one before the shock. The the capital stock of one country undergoes a non-monotonic adjustment. The model is tested with plausible values of the variables and the numeric results confirm the predictions of the theory.