Modelling stress state in reaction columns

2003 ◽  
Vol 3 ◽  
pp. 72-81
Author(s):  
R.R. Mavlyutov ◽  
L.Н. Gorchakov ◽  
Sh.Sh. Galyaliev ◽  
N.M. Tuykin ◽  
A.G. Khakimov ◽  
...  
Keyword(s):  
Stress State ◽  
Thermal Stresses ◽  
Heat Removal ◽  
Temperature Gradients ◽  
Large Temperature ◽  
Simulation Approach ◽  
Negative Effects ◽  
Chemical Reactors ◽  
Thermal Regimes ◽  
Deformed State

The operation of chemical reactors, particularly those for producing benzene, is associated with the generation of a large amount of heat. Inaccurately chosen thermal regimes of performance in the reaction columns at large temperature gradients can be responsible for the occurrence of high thermal stresses that decrease the endurance of equipment elements. Therefore, it is quite topical to reveal, using the mathematical simulation approach, both positive and negative effects in relation to stress deformed state of equipment elements under different regimes of heat removal from the outside surface of the reaction columns.

End Thermal Stresses in a Long Circular Rod

1968 ◽  
Vol 35 (2) ◽  
pp. 267-273 ◽  
Author(s):  
W. H. Chu ◽  
F. T. Dodge
Keyword(s):  
Temperature Gradient ◽  
General Solution ◽  
Thermal Stresses ◽  
Linear Interpolation ◽  
Temperature Gradients ◽  
Characteristic Functions ◽  
Large Temperature ◽  
End Effect ◽  
Title Problem ◽  
Characteristic Values

The title problem is solved by the method of collocation utilizing complex nonorthogonal characteristic functions. It is shown that the characteristic values can be obtained by repeated linear interpolation without much difficulty. Ten roots are given for the case of Poisson’s ratio equaling 0.3. For large temperature gradients, an example is given which shows high end stresses. The general solution due to the end effect dies down at the rate of exp (–2.722 z/a) or faster, but its magnitude depends on the steepness of the temperature gradient. This paper also shows that the Saint-Venant principle may not always be sufficient, that the end stress could be critical, and that, therefore, it should be calculated.

scholarly journals Hidden Attractors in Discrete Dynamical Systems

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 616
Author(s):  
Marek Berezowski ◽  
Marcin Lawnik
Keyword(s):  
Dynamical Systems ◽  
Chaos Theory ◽  
Scientific Literature ◽  
Discrete Systems ◽  
Discrete Dynamical Systems ◽  
Continuous Systems ◽  
Hidden Attractors ◽  
Negative Effects ◽  
Chemical Reactors ◽  
Points Of View

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

Thermo-Fluid-Stress-Deformation Analysis of Two-Layer Microchannels for Cooling Chips With Hot Spots

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Abas Abdoli ◽  
George S. Dulikravich ◽  
Genesis Vasquez ◽  
Siavash Rastkar
Keyword(s):  
Heat Flux ◽  
Thermal Stresses ◽  
Hot Spot ◽  
Heat Removal ◽  
High Heat ◽  
Heat Transfer Analysis ◽  
Deformation Analysis ◽  
High Heat Flux ◽  
Cooling Design ◽  
Microchannel Cooling

Two-layer single phase flow microchannels were studied for cooling of electronic chips with a hot spot. A chip with 2.45 × 2.45 mm footprint and a hot spot of 0.5 × 0.5 mm in its center was studied in this research. Two different cases were simulated in which heat fluxes of 1500 W cm−2 and 2000 W cm−2 were applied at the hot spot. Heat flux of 1000 W cm−2 was applied on the rest of the chip. Each microchannel layer had 20 channels with an aspect ratio of 4:1. Direction of the second microchannel layer was rotated 90 deg with respect to the first layer. Fully three-dimensional (3D) conjugate heat transfer analysis was performed to study the heat removal capacity of the proposed two-layer microchannel cooling design for high heat flux chips. In the next step, a linear stress analysis was performed to investigate the effects of thermal stresses applied to the microchannel cooling design due to variations of temperature field. Results showed that two-layer microchannel configuration was capable of removing heat from high heat flux chips with a hot spot.

Bi-Layered Model of Interfacial Thermal Stresses with the Effect of Different Temperatures in the Layers

2011 ◽  
Vol 87 ◽  
pp. 63-70 ◽  
Author(s):  
Sujan Debnath ◽  
Muhammad Ekhlasur Rahman ◽  
Woldemichael Dereje Engida ◽  
M. V. V. Murthy ◽  
K.N. Seetharamu
Keyword(s):  
Thermal Stresses ◽  
Physical Design ◽  
Temperature Gradients ◽  
Interfacial Stress ◽  
Stress Model ◽  
Interfacial Stresses ◽  
Linear Temperature ◽  
Layered Model ◽  
Die Attach ◽  
Different Temperatures

An interfacial shearing and peeling stress model is proposed to account for different uniform temperatures and thickness wise linear temperature gradients in the layers. This upgraded model can be viewed as a more generic form to determine interfacial stresses under different temperature conditions in a bi-layered assembly. The selected shearing and peeling stress results are presented for the case of die and die attach as commonly seen in electronic packaging. The obtained results can be useful in interfacial stress evaluations and physical design of bi-material assemblies, which are used in microelectronics and photonic applications.

scholarly journals A Computer Programme With Temperature Gradient Capability for the Network Analysis of Hybrid Circuits

1980 ◽  
Vol 6 (3-4) ◽  
pp. 227-229
Author(s):  
Carl R. Zimmer
Keyword(s):  
Thermal Analysis ◽  
Input Data ◽  
Steady State Solution ◽  
Temperature Gradients ◽  
Large Temperature ◽  
Computer Programme ◽  
System Operation ◽  
Linear Network ◽  
Periodic Inputs ◽  
Additional Option

A modified version of the computer programme SINC-S is described which permits the user to specify independently up to 30 different device temperatures in a given problem when the proper control statement is included. An additional option is an algorithm for the steady-state solution of a non-linear network with periodic inputs, so that realistic system operation may be simulated. The programme may be used to provide more accurate simulation of circuits where large temperature gradients are present, and to furnish input data for other thermal analysis programmes

Analysis of Residual Stresses in a Polymer Cylinder when it is Stopped and then Cooled in a Nonlinear and Linearized Problem Settings

2021 ◽  
Vol 899 ◽  
pp. 486-492
Author(s):  
Liubov I. Lesnyak ◽  
Vladimir I. Andreev ◽  
Serdar B. Yazyev ◽  
Arthur A. Avakov ◽  
Irina G. Doronkina
Keyword(s):  
Stress State ◽  
Residual Stresses ◽  
The Body ◽  
Linearized Problem ◽  
Deformed State ◽  
Problem Setting

In conclusion, one should say that, to determine the approximate stress state in the body, it is quite enough to consider the problem in a linearized problem setting. When determining the deformed state, it is necessary to consider the problem exclusively in a nonlinear setting.

CALCULATIONS OF STRESS-DEFORMED STATE OF LOW-DENSITY MATERIALS AND ITS APPLICATIONS TO BORON CARBIDE DURING EXPLOSIVE LOADING

2004 ◽  
Vol 18 (08) ◽  
pp. 1203-1215
Author(s):  
A. PEIKRISHVILI ◽  
P. LEMIS-PETROPOULOS ◽  
V. KAPAKLIS ◽  
C. POLITIS
Keyword(s):  
Stress State ◽  
Boron Carbide ◽  
High Temperatures ◽  
Shock Loading ◽  
Explosive Loading ◽  
Theoretical Density ◽  
Low Density ◽  
Two Stage ◽  
Constant Rate ◽  
Deformed State

Using hot explosive compacting technology and consolidating B 4 C powders in two stage at high temperatures enabled us to obtain compacts with high value of hardness and near theoretical density. This work contains results of calculations of B 4 C stress state under the shock loading that is being distributed evenly at a constant rate through the boundary retaining samples.

Designing Lightweight Tensegrity-Based Structures and Materials of Tailorable Thermal Expansion

2019 ◽  
Author(s):  
Rochelle E. Silverman ◽  
Edwin A. Peraza Hernandez
Keyword(s):  
Thermal Expansion ◽  
Thermal Stresses ◽  
Low Complexity ◽  
Aerospace Engineering ◽  
Positive Zero ◽  
Large Temperature ◽  
New Materials ◽  
Temperature Changes ◽  
Wide Range ◽  
First Time

Abstract In this work, we analyze and design structures and materials that possess custom thermal expansion. These structures and materials are composed of a base unit inspired by the tensegrity “D-bar” (or double-pyramid) topology. We derive, for the first time, analytical equations for the linearized and geometrically exact coefficients of thermal expansion (CTEs) of bi-material D-bar structures with arbitrary shape and complexity. Numerical results obtained using the geometrically exact CTE equations are compared with results obtained using the linearized CTE equations, showing that the latter are accurate only in cases where temperature changes are small. Further results show that D-bar structures of low complexity can produce a wide range of CTEs, including positive, zero, and negative values. These CTE values are exhibited for a range of materials that allows for easy manufacturing (materials with CTE ratios as low as 2). Thus, it is concluded that D-bar structures show promise for applications in aerospace engineering and other fields where new materials of tailorable thermal expansion are needed to decrease the substantial thermal stresses caused by large temperature changes.

Thermal Rectification by Ballistic Phonons

2008 ◽  
Author(s):  
John Miller ◽  
Wanyoung Jang ◽  
Chris Dames
Keyword(s):  
Distribution Function ◽  
Mean Free Path ◽  
Temperature Gradients ◽  
Reverse Direction ◽  
Large Temperature ◽  
Thermal Rectification ◽  
Einstein Distribution ◽  
Ballistic Phonons ◽  
Dimensional Electron Gas ◽  
Bose Einstein

In analogy to the asymmetric transport of electricity in a familiar electrical diode, a thermal rectifier transports heat more favorably in one direction than in the reverse direction. One approach to thermal rectification is asymmetric scattering of phonons and/or electrons, similar to suggestions in the literature for a sawtooth nanowire [1] or 2-dimensional electron gas with triangular scatterers [2]. To model the asymmetric heat transport in such nanostructures, we have used phonon ray-tracing, focusing on characteristic lengths that are small compared to the mean free path of phonons in bulk. To calculate the heat transfer we use a transmission-based (Landauer-Buttiker) method. The system geometry is described by a four-dimensional transfer function that depends on the position and angle of phonon emission and absorption from each of two contacts. At small temperature gradients, the phonon distribution function is very close to the usual isotropic equilibrium (Bose-Einstein) distribution, and there is no thermal rectification. In contrast, at large temperature gradients, the anisotropy in the phonon distribution function becomes significant, and the resulting heat flux vs. temperature curve (analogous to I-V curve of a diode) reveals large thermal rectification.

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