The Effect of Insulated Cracks on Heat Transfer of Thermoelectric Plates Using Peridynamics

2020 ◽  
Vol 10 (4) ◽  
pp. 25-39
Author(s):  
Migbar Assefa Zeleke ◽  
Lai Xin ◽  
Liu Lisheng
Keyword(s):  
Electric Fields ◽  
Crack Surface ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Electrical Potentials ◽  
Non Local ◽  
The One ◽  
Growing Cracks ◽  
Good Agreement ◽  
The Continuum

In this article, peridynamic (PD) theory is applied to analyze two-dimensional heat conduction of thermoelectric plate with discontinuities. It is a well-known fact that heat flux is undefined at the crack tip and causes the temperature field across the crack surface discontinuous. Hence, numerical procedures like finite element method (FEM) became unsuccessful to capture details of moving discontinuities like growing cracks. Therefore, this article proposes a PD theory that is appropriate in resolving moving discontinuities in thermal and electric fields. The PD equations were constructed by writing the continuum-based electrical potentials and temperature fields in the form of their respective non-local integrals that are remarkably powerful in solving continuum problems whether the authors have moving discontinuities or not. To elucidate the trustworthiness of the PD theory, the results in the case of stationary cracks are compared with the one from FEM and witnessed that they were in good agreement.

scholarly journals A Peridynamic Computational Scheme for Thermoelectric Fields

Materials ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2546 ◽  
Author(s):  
Migbar Assefa Zeleke ◽  
Xin Lai ◽  
Lisheng Liu
Keyword(s):  
Electric Fields ◽  
Thermoelectric Materials ◽  
Crack Surface ◽  
Temperature Gradients ◽  
Temperature Fields ◽  
Thermoelectric Effects ◽  
Electrical Potentials ◽  
Crack Tips ◽  
Good Agreement ◽  
The Continuum

Thermoelectric materials are materials that involve the coexistence of heat flux and electric current in the absence of magnetic field. In such materials, there is a coupling among electric potential and temperature gradients, causing the thermoelectric effects of Seebeck and Peltier. Those coupling effects make the design and analysis of thermoelectric materials complicated and sophisticated. The main aim of this work is dealing with thermoelectric materials with discontinuities. Since heat and electric fluxes are undefined at the crack tip and the temperature and electric fields across the crack surface are discontinuous, it is better to apply peridynamic (PD) theory to capture such details at the crack tips. Hence, we propose in this paper a PD theory which is suitable in tackling such discontinuities in thermal and electric fields. In this study, the continuum-based electrical potentials and temperature fields are written in the form of nonlocal integrals of the electrical potentials and temperature that are effective whether we have discontinuities or not. To illustrate the consistency of the peridynamic technique, a number of examples were presented and witnessed that PD results were in good agreement with those results from the literature, finite element solutions and analytical solutions.

CONTINUUM SCHWINGER-DYSON EQUATIONS AND UNIVERSAL STRUCTURES IN TWO-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (08) ◽  
pp. 1385-1406 ◽  
Author(s):  
MASAFUMI FUKUMA ◽  
HIKARU KAWAI ◽  
RYUICHI NAKAYAMA
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Square Root ◽  
Two Dimensional ◽  
Kp Hierarchy ◽  
Kdv Hierarchy ◽  
The One ◽  
Matter Fields ◽  
The Continuum

We study the continuum Schwinger-Dyson equations for nonperturbative two-dimensional quantum gravity coupled to various matter fields. The continuum Schwinger-Dyson equations for the one-matrix model are explicitly derived and turn out to be a formal Virasoro condition on the square root of the partition function, which is conjectured to be the τ function of the KdV hierarchy. Furthermore, we argue that general multi-matrix models are related to the W algebras and suitable reductions of KP hierarchy and its generalizations.

Theoretical validation of ground-based microwave ozone observations

1994 ◽  
Vol 12 (7) ◽  
pp. 664-673 ◽  
Author(s):  
P. Ricaud ◽  
G. Brasseur ◽  
J. Brillet ◽  
J. de La Noë ◽  
J.-P. Parisot ◽  
...  
Keyword(s):  
Ozone Concentration ◽  
Seasonal Variations ◽  
Temperature Fields ◽  
Microwave Measurements ◽  
Two Dimensional ◽  
Yearly Average ◽  
Large Maximum ◽  
Seasonal Analysis ◽  
2D Model ◽  
Good Agreement

Abstract. Ground-based microwave measurements of the diurnal and seasonal variations of ozoneat 42±4.5 and 55±8 km are validated by comparing with results from a zero-dimensional photochemical model and a two-dimensional (2D) chemical/radiative/dynamical model, respectively. O3 diurnal amplitudes measured in Bordeaux are shown to be in agreement with theory to within 5%. For the seasonal analysis of O3 variation, at 42±4.5 km, the 2D model underestimates the yearly averaged ozone concentration compared with the measurements. A double maximum oscillation (~3.5%) is measured in Bordeaux with an extended maximum in September and a maximum in February, whilst the 2D model predicts only a single large maximum (17%) in August and a pronounced minimum in January. Evidence suggests that dynamical transport causes the winter O3 maximum by propagation of planetary waves, phenomena which are not explicitly reproduced by the 2D model. At 55±8 km, the modeled yearly averaged O3 concentration is in very good agreement with the measured yearly average. A strong annual oscillation is both measured and modeled with differences in the amplitude shown to be exclusively linked to temperature fields.

The one-dimensional minesweeper game: What are your chances of winning?

2016 ◽  
Vol 27 (11) ◽  
pp. 1650127 ◽  
Author(s):  
M. Rodríguez-Achach ◽  
H. F. Coronel-Brizio ◽  
A. R. Hernández-Montoya ◽  
R. Huerta-Quintanilla ◽  
E. Canto-Lugo
Keyword(s):  
Numerical Simulations ◽  
Critical Density ◽  
Computer Game ◽  
Simple System ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Np Completeness ◽  
The One ◽  
Good Agreement

Minesweeper is a famous computer game consisting usually in a two-dimensional lattice, where cells can be empty or mined and gamers are required to locate the mines without dying. Even if minesweeper seems to be a very simple system, it has some complex and interesting properties as NP-completeness. In this paper and for the one-dimensional case, given a lattice of n cells and m mines, we calculate the winning probability. By numerical simulations this probability is also estimated. We also find out by mean of these simulations that there exists a critical density of mines that minimize the probability of winning the game. Analytical results and simulations are compared showing a very good agreement.

Numerical Calculation on Steel Coil during Annealing Process

2011 ◽  
Vol 402 ◽  
pp. 472-475
Author(s):  
Chao Chen ◽  
De Gang Ouyang ◽  
Zhong Hua Song ◽  
Sheng Chen
Keyword(s):  
Mathematical Model ◽  
Annealing Process ◽  
Temperature Fields ◽  
Temperature History ◽  
Two Dimensional ◽  
Steel Coil ◽  
Cylindrical Coordinate ◽  
Calculation Results ◽  
History Of ◽  
Good Agreement

A two-dimensional mathematical model in cylindrical coordinate system was developed to simulate the temperature history of steel coil during annealing process. Based on finite difference method, the equations were calculated, and the temperature history of steel coil was obtained. Compared with experimental results, the calculation results are in good agreement with measurements. The temperature fields of steel coil at different time were analyzed, which can provide reference for optimizing of annealing process.

Flexural tensegrity of segmental beams

2020 ◽  
Vol 476 (2237) ◽  
pp. 20200062 ◽  
Author(s):  
Claudio Boni ◽  
Marco Silvestri ◽  
Gianni Royer-Carfagni
Keyword(s):  
Unilateral Contact ◽  
Functionally Graded ◽  
3D Printer ◽  
Aerospace Applications ◽  
Theoretical Predictions ◽  
Double Couple ◽  
Constitutive Response ◽  
Non Local ◽  
Good Agreement ◽  
The Continuum

The term ‘flexural tensegrity’ applies to beam-like structures composed of segments in unilateral contact, whose integrity under flexion is provided by tendons (cables), tensioned and later anchored at the end segments. In addition to the cable tension, the constitutive response depends upon the shape of the contact surfaces between consecutive segments, identified by the corresponding pitch lines and constructed with a double couple of conjugate profiles, in order to achieve an internal constraint equivalent to a spring hinge. The response is non-local in type, because the cable elongation, and consequently the stiffness of the spring hinges, depends upon the rotations of all the segments, but this effect becomes negligible under moderate deflections. In this case, the structure can be approximated with an elastica in the continuum limit. Testing of prototypes, manufactured with a 3D printer, shows a very good agreement with the theoretical predictions for different designs of the spring hinges. The system, whose stiffness can be functionally graded and actively controlled, can be packaged when the cable is slack and deployed by pulling the cable at one extremity. It appears particularly suitable to build soft arms for robotics or deployable compliant booms for aerospace applications.

F.VIII R:Ag in Hepatitis

1979 ◽  
Author(s):  
R. Kotitschke ◽  
J. Scharrer
Keyword(s):  
Chronic Hepatitis ◽  
Blood Donors ◽  
Blood Donation ◽  
Normal Population ◽  
Rabbit Antiserum ◽  
Two Dimensional ◽  
Plastic Plate ◽  
Significant Difference ◽  
Acute Hepatitis B ◽  
The One

F.VIII R:Ag was determined by quantitative immunelectrophoresis (I.E.) with a prefabricated system. The prefabricated system consists of a monospecific f.VIII rabbit antiserum in agarose on a plastic plate for the one and two dimensional immunelectrophoresis. The lognormal distribution of the f.VIII R:Ag concentration in the normal population was confirmed (for n=70 the f.VIII R:Ag in % of normal is = 95.4 ± 31.9). Among the normal population there was no significant difference between blood donors (one blood donation in 8 weeks; for n=43 the f.VIII R:Ag in % of normal is = 95.9 ± 34.0) and non blood donors (n=27;f.VIII R:Ag = 94.6 ± 28.4 %). The f.VIII R:Ag concentration in acute hepatitis B ranged from normal to raised values (for n=10, a factor of 1.8 times of normal was found) and was normal again after health recovery (n=10, the factor was 1.0). in chronic hepatitis the f.VIII R:Ag concentration was raised in the majority of the cases (for n=10, the factor was 3.8). Out of 22 carrier sera 20 showed reduced, 2 elevated levels of the f.VIII R:Ag concentration. in 5 sera no f.VIII R:Ag could be demonstrated. The f.VIII R:Ag concentration was normal for n=10, reduced for n=20 and elevated for n=6 in non A-non B hepatitis (n=36). Contrary to results found in the literature no difference in the electrophoretic mobility of the f.VIII R:Ag was found between hepatitis patients sera and normal sera.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

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