Mathematical Model of Thermal Spikes in Microwave Heating of Oxide Ceramic Fibers

1994 ◽  
Vol 347 ◽  
Author(s):  
J. R. Thomas ◽  
Wesley P. Unruh ◽  
Gerald J. Vogt
Keyword(s):  
Mathematical Model ◽  
Hot Spots ◽  
Elevated Temperatures ◽  
Solid Phase ◽  
Microwave Sintering ◽  
Single Mode ◽  
Heat Transfer Process ◽  
Oxide Ceramic ◽  
Ceramic Fibers ◽  
Radiation Losses

ABSTRACTExperiments on microwave sintering of ceramic fibers in a single-mode cavity have revealed the presence of thermal spikes and “hot spots” which sometimes travel along the fiber and eventually disappear. They are triggered by relatively small increases in microwave power, and thus have obvious implications for the development of practical microwave-based fiber processing systems. These hot spots are conjectured to originate at slight irregularities in the tow morphology, and propagate as the result of solid phase transitions which take place at elevated temperatures and reduce the dielectric loss coefficient є”.An elementary mathematical model of the heat transfer process was developed which reproduces the essential features of the observed phenomena, thus lending support to our conjecture. This model is based on the assumption of one-dimensional heat conduction along the axis of the fiber tow, and radiation losses at the surface.

Cavity Effects and Hot Spot Formulation Inmicrowave Heated Ceramic Fibers

1996 ◽  
Vol 430 ◽  
Author(s):  
G. A. Kriegsmann
Keyword(s):  
Electric Field ◽  
Hot Spots ◽  
Hot Spot ◽  
Single Mode ◽  
Uniform Electric Field ◽  
Ceramic Fibers ◽  
Entire Sample ◽  
Mathematical Equations ◽  
Cavity Effects ◽  
Ceramic Cylinder

AbstractRecently the heating of a thin ceramic cylinder in a single mode applicator was modeled and analyzed assuming a small Biot number and a known uniform electric field through out the sample. The resulting simplified mathematical equations explained the mechanism for the generation and growth of localized regions of high temperature. The results predicted that a hot-spot, once formed, will grow until it consumes the entire sample. Most experimental observations show that the hot-spot stabilizes and moves no further.A new model is proposed which incorporates the effect of the cavity and the nlonuiniform character of the electric field along the axis of the sample. The resulting simplified mathematical equations indicate that these effects stabilize the growth of hot-spots.

Growth and Stabilization of Hot Spots in Microwave Heated Ceramic Fibers

1994 ◽  
Vol 347 ◽  
Author(s):  
Gregory A. Kriegsmann
Keyword(s):  
Electric Field ◽  
Hot Spots ◽  
Hot Spot ◽  
Single Mode ◽  
Uniform Electric Field ◽  
Fiber Axis ◽  
Ceramic Fibers ◽  
Mathematical Equations ◽  
Effective Heat Transfer Coefficient ◽  
Ceramic Cylinder

ABSTRACTRecently the heating of a thin ceramic cylinder in a single mode applicator was modeled and analyzed assuming a small Biot number and a known uniform electric field through out the sample. The resulting simplified mathematical equations explained the mechanism for the generation and growth of localized regions of high temperature. The results predicted that a hot-spot, once formed, will grow until it consumes the entire sample. Although this phenomenon is seen in some experiments, others show that the hot-spot stabilizes and moves no further.A new model is proposed which incorporates the dependence of the thermal conductivity and the effective heat transfer coefficient upon temperature, and the nonuniformity of the electric field along the fiber axis. The resulting simplified mathematical equations indicate that these effects may stabilize the growth of hot-spots.

INFLUENCE OF VAPOR AND CRYSTAL FORMATION PROCESSES ON HEAT EXCHANGE IN FILM VAPORATORS

2021 ◽  
pp. 32-40
Author(s):  
O. Koshelnik ◽  
V. Pavlova ◽  
T. Pugacheva ◽  
O. Kruglyakova ◽  
O. Dolobovska
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Energy Consumption ◽  
Heat Exchange ◽  
Solid Phase ◽  
Heat Transfer Process ◽  
Operating Conditions ◽  
Crystal Formation ◽  
Phase Content ◽  
Three Phase

Evaporators for changing the concentration of solutions have a different design, depending on the type of processed substance. Significant energy consumption in such equipment is associated with the need for removing large quantity of liquid phase. Multiple-effect evaporators are used to reduce the energy consumption of the evaporation process, but such equipment is quite expensive. Evaporators with secondary vapor heat reusing that operate in film mode can be an alternative to multi-effect evaporators. This equipment can operate efficiently across minimal temperature differences due to secondary vapor compressors. The disadvantage of this device is strict requirements for impurities in solutions. Impurities create deposits (incrustations) of various substances on the heat transfer surfaces, which worsens the operating conditions. If crystallizing solutions are used in evaporators with reusing of secondary vapor heat, then one of the ways to reduce the rate of heating surfaces incrustation is to add a solid phase to the initial solution. A mathematical model is proposed to describe the processes of heat and mass transfer during the film flow of crystallizing solutions, which are accompanied by a change in the physical characteristics of the solution and the formation of deposits. The model considers a three-phase liquid suspension with a varying phase content. Two stages of vaporization including vaporization on the surface of the liquid and on the surface of heat exchange are presented. The mathematical model involves the equations of continuity, energy and heat transfer, as well as the equations of motion of a three-phase flow with a changing phase content for both stages of vaporization, taking into account that solid phase turbulizes the flow and intensifies the heat transfer process. This mathematical model makes it possible to study the effect of the solid phase on heat transfer processes and the rate of incrustation in evaporators with reuse of secondary vapor heat.

scholarly journals Microwave Sintering of Continuous Zirconia Ceramic Fibers

1994 ◽  
Vol 347 ◽  
Author(s):  
Gerald. J. Vogt ◽  
Wesley. P. Unruh ◽  
Ross. H. Plovnick
Keyword(s):  
Microwave Sintering ◽  
Single Mode ◽  
Ambient Air ◽  
Tensile Tests ◽  
Grain Structure ◽  
Microwave Cavity ◽  
Zirconia Ceramic ◽  
Ceramic Fibers ◽  
Single Filament ◽  
Tetragonal Crystal

ABSTRACTContinuous yttria-stabilized zirconia ceramic fibers approximately 10–15 μm in diameter have been rapidly sintered by pulling them through a tuned, 2.45 GHz single-mode TE103 microwave cavity in ambient air. The resulting fibers were analyzed by X-ray diffraction, scanning electron microscopy, and single-filament tensile tests. They were found to be unsplit, to have a submicron grain structure and a tetragonal crystal structure, and to exhibit considerable strength and flexibility.

Design of the Blast Furnace Wall Structure Made of Efficient Materials. Part 4. Calculation Examples

2020 ◽  
Vol 786 (11) ◽  
pp. 30-34
Author(s):  
A.M. IBRAGIMOV ◽  
◽  
L.Yu. GNEDINA ◽  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Blast Furnace ◽  
Boundary Value Problems ◽  
Transfer Process ◽  
Rational Design ◽  
Boundary Value ◽  
Heat Transfer Process ◽  
Furnace Wall ◽  
Time Interval

This work is part of a series of articles under the general title The structural design of the blast furnace wall from efficient materials [1–3]. In part 1, Problem statement and calculation prerequisites, typical multilayer enclosing structures of a blast furnace are considered. The layers that make up these structures are described. The main attention is paid to the lining layer. The process of iron smelting and temperature conditions in the characteristic layers of the internal environment of the furnace is briefly described. Based on the theory of A.V. Lykov, the initial equations describing the interrelated transfer of heat and mass in a solid are analyzed in relation to the task – an adequate description of the processes for the purpose of further rational design of the multilayer enclosing structure of the blast furnace. A priori the enclosing structure is considered from a mathematical point of view as the unlimited plate. In part 2, Solving boundary value problems of heat transfer, boundary value problems of heat transfer in individual layers of a structure with different boundary conditions are considered, their solutions, which are basic when developing a mathematical model of a non-stationary heat transfer process in a multi-layer enclosing structure, are given. Part 3 presents a mathematical model of the heat transfer process in the enclosing structure and an algorithm for its implementation. The proposed mathematical model makes it possible to solve a large number of problems. Part 4 presents a number of examples of calculating the heat transfer process in a multilayer blast furnace enclosing structure. The results obtained correlate with the results obtained by other authors, this makes it possible to conclude that the new mathematical model is suitable for solving the problem of rational design of the enclosing structure, as well as to simulate situations that occur at any time interval of operation of the blast furnace enclosure.

Growth of Epitaxial IrSi3 Layers on Si(111)

1989 ◽  
Vol 160 ◽  
Author(s):  
T. L. Lin ◽  
C. W. Nieh
Keyword(s):  
Surface Morphology ◽  
Molecular Beam ◽  
Solid Phase ◽  
Single Mode ◽  
Growth Conditions ◽  
Tem Analysis ◽  
Mbe Growth ◽  
Good Surface ◽  
Transmission Electron

AbstractEpitaxial IrSi3 films have been grown on Si (111) by molecular beam epitaxy (MBE) at temperatures ranging from 630 to 800 °C and by solid phase epitaxy (SPE) at 500 °C. Good surface morphology was observed for IrSi3 layers grown by MBE at temperatures below 680 °C, and an increasing tendency to form islands is noted in samples grown at higher temperatures. Transmission electron microscopy (TEM) analysis reveals that the IrSi3 layers grow epitaxially on Si(111) with three epitaxial modes depending on the growth conditions. For IrSi3 layers grown by MBE at 630 °C, two epitaxial modes were observed with ~ 50% area coverage for each mode. Single mode epitaxial growth was achieved at a higher MBE growth temperature, but with island formation in the IrSi3 layer. A template technique was used with MBE to improve the IrSi3 surface morphology at higher growth temperatures. Furthermore, single-crystal IrSi3 was grown on Si(111) at 500 °C by SPE, with annealing performed in-situ in a TEM chamber.

Racemization in stepwise solid-phase peptide synthesis at elevated temperatures

Tetrahedron ◽  
2004 ◽  
Vol 60 (21) ◽  
pp. 4671-4681 ◽  
Author(s):  
Marcos P. Souza ◽  
Marina F.M. Tavares ◽  
M.Terêsa M. Miranda
Keyword(s):  
Peptide Synthesis ◽  
Elevated Temperatures ◽  
Solid Phase ◽  
Solid Phase Peptide Synthesis

scholarly journals Mathematical modeling and algorithm for calculation of thermocatalytic process of producing nanomaterial

2021 ◽  
Vol 23 (3) ◽  
pp. 1590
Author(s):  
Bakhtiyar Ismailov ◽  
Zhanat Umarova ◽  
Khairulla Ismailov ◽  
Aibarsha Dosmakanbetova ◽  
Saule Meldebekova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Phase ◽  
Nonlinear Effects ◽  
Operating Characteristics ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Wide Range ◽  
The Laplace Transform ◽  
Complex Mathematical Model

<p>At present, when constructing a mathematical description of the pyrolysis reactor, partial differential equations for the components of the gas phase and the catalyst phase are used. In the well-known works on modeling pyrolysis, the obtained models are applicable only for a narrow range of changes in the process parameters, the geometric dimensions are considered constant. The article poses the task of creating a complex mathematical model with additional terms, taking into account nonlinear effects, where the geometric dimensions of the apparatus and operating characteristics vary over a wide range. An analytical method has been developed for the implementation of a mathematical model of catalytic pyrolysis of methane for the production of nanomaterials in a continuous mode. The differential equation for gaseous components with initial and boundary conditions of the third type is reduced to a dimensionless form with a small value of the peclet criterion with a form factor. It is shown that the laplace transform method is mainly suitable for this case, which is applicable both for differential equations for solid-phase components and calculation in a periodic mode. The adequacy of the model results with the known experimental data is checked.</p>

scholarly journals Tuning, Impedance Matching, and Temperature Regulation during High-Temperature Microwave Sintering of Ceramics

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Sylvain Marinel ◽  
Nicolas Renaut ◽  
Etienne Savary ◽  
Rodolphe Macaigne ◽  
Guillaume Riquet ◽  
...  
Keyword(s):  
Material Processing ◽  
High Temperature ◽  
Microwave Sintering ◽  
Impedance Matching ◽  
Single Mode ◽  
Electrical Circuit ◽  
Ease Of Use ◽  
Heating Process ◽  
Process Technology ◽  
Volumetric Heating

Over the years, microwave radiation has emerged as an efficient source of energy for material processing. This technology provides a rapid and a volumetric heating of material. However, the main issues that prevent microwave technology from being widespread in material processing are temperature control regulation and heating distribution within the sample. Most of the experimental works are usually manually monitored, and their reproducibility is rarely evaluated and discussed. In this work, an originally designed 915 MHz microwave single-mode applicator for high-temperature processing is presented. The overall microwave system is described in terms of an equivalent electrical circuit. This circuit has allowed to point out the different parameters which need to be adjusted to get a fully controlled heating process. The basic principle of regulation is then depicted in terms of a block function diagram. From it, the process has been developed and tested to sinter zirconia- and spinel-based ceramics. It is clearly shown that the process can be successfully used to program multistep temperature cycles up to ∼1550°C, improving significantly the reproducibility and the ease of use of this emerging high-temperature process technology.

Sign in / Sign up

Export Citation Format

Share Document