scholarly journals Calculation of non-stationary heat exchange in multi-layer media by means of the theory of Markov chains

Vestnik IGEU ◽  
2021 ◽  
pp. 60-66
Author(s):  
A.V. Ogurtsov ◽  
E.I. Krupnov ◽  
E.R. Kormashova ◽  
V.E. Mizonov
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Heat Exchange ◽  
Markov Chains ◽  
Transition Probabilities ◽  
Average Power ◽  
Discrete Models ◽  
Stationary Heat ◽  
Real Process ◽  
The Matrix

Calculation of non-stationary heat exchange in multi-layer dissimilar media is the problem, which is often found in many industries including high temperature metallurgic technologies of production and treatment of metals, alloys and their products. The similar problems arise during the design of buildings and structures. The models used for calculation are mainly based on approximate solutions of classical heat conduction equations. The drawback of such models is a complex computational procedure, associated with the need to solve a large number of equations and to define a large number of identification parameters. At present, the calculation of one mode of heat transfer between the sections of a composite structure requires 6–8 hours of operation of a computer of average power. In this regard, the development of discrete models that require less computer time is of current importance. The proposed model of the process is based on the theory of Markov chains. A multi-layer medium is presented as a chain of small but finite cells. Each of them contains a certain amount of heat that can be transferred to the neighboring cells. The part of the transferred heat is directly proportional to the heat conduction coefficient and in inverse proportion to the material heat capacity, material density and the cell length. The matrix model to describe heat transfer between cell in a multi-layer media based on the theory of Markov chains is developed. Construction of the matrix of transition probabilities is described, evolution of the state vectors i.e. distribution of heat and temperature is carried out, and non-uniformity of the heater temperature is taken into account. Comparison of calculated and experimental data has showed the adequate description of the real process using the model. Analysis of identification parameters has given a satisfactory result.

scholarly journals Production of three-layer steel bimetallic strips in the unit of continuous casting and deformation. Report 1

2019 ◽  
Vol 62 (8) ◽  
pp. 594-599 ◽  
Author(s):  
O. S. Lekhov ◽  
A. V. Mikhalev ◽  
M. M. Shevelev
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Continuous Casting ◽  
Molten Metal ◽  
Alloyed Steel ◽  
Combined Process ◽  
Stationary Heat ◽  
Cladding Layer ◽  
Characteristic Points ◽  
Stationary Heat Conduction

High technical and economic efficiency of the use of bimetals in chemical, oil, transport and energy engineering and other industries is described. The urgency of creating high-performance continuous processes for the production of bimetallic strips is substantiated. The authors have established the main technological tasks for development of the processes of obtaining bimetal of wide class. The paper describes resource-saving production technology of three-layer bimetals alloyed steel – constructional steel – alloyed steel at the unit of combined process of continuous casting and deformation. Possibilities of the proposed technology are outlined from the standpoint of improving the quality of bimetallic strips. The initial data are given to determine the temperature change over time of the main steel strip as it passes through the molten metal of the alloyed steel. The equations are given for non-stationary heat conduction, initial and boundary conditions for determining the temperature fields of main strip and cladding layer when obtaining a three-layer bimetallic strip on the unit of a combined process of continuous casting and deformation. The values of density, thermal conductivity and heat capacity for steel St3 were determined in a given temperature range. A procedure is described for calculating temperatures in the ANSYS package by solving a non-stationary heat conduction problem in a flat formulation by the finite element method. The authors have described the geometric model for calculating the temperature of strip and molten metal of the cladding layer. Values of the coefficient of heat transfer between the main strip and molten metal of the cladding layers of bimetallic strip are given adopted for calculation. Characteristic points are indicated in the model for calculating the temperatures of main strip and molten metal of the cladding layer. The graphs show temporal changes in these temperatures at production of a three-layer bimetallic strip on the unit of combined process of continuous casting and deformation. Calculated data on the time variation of temperature of main strip and molten metal of the cladding layer at characteristic points are given for different values of the contact heat transfer coefficient.

Based on the Matrix of Silicon Nanocrystals a Modeling Study of Thermo-hydraulic Properties of Micro-channel Heat Transfer Elements

2021 ◽  
Vol 19 (3) ◽  
pp. 38-45
Author(s):  
Forat H. Alsultany ◽  
Qasim S. Kadhim
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Thermal Stabilization ◽  
Specific Power ◽  
Heat Sources ◽  
Ambient Temperatures ◽  
Pressure Losses ◽  
Geometric Configurations ◽  
Wide Range ◽  
The Matrix

The construction of a heat exchange element based on a matrix of silicon whiskers for thermal stabilization systems of miniature heat sources with specific power up to 100 W/cm2 operating over a wide range of ambient temperatures is proposed. Based on the developed mathematical model of convective heat transfer in a microchannel compact heat exchanger with a developed heat exchange surface, numerical simulation of the hydrodynamics and heat transfer processes for various configurations of microchannel insertions was carried out. Fields of pressures, flow velocities, coolant temperatures and matrix from silicon single crystals have been obtained in a wide range of coolant flow rates, criteria dependencies for the Nusselt number and pressure losses of various geometric configurations of heat exchangers have been determined. Critical operation modes are investigated; optimization directions are proposed. According to the developed technology, prototypes for testing have been manufactured.

Occupation times for two state Markov chains

1971 ◽  
Vol 8 (02) ◽  
pp. 381-390 ◽  
Author(s):  
P. J. Pedler
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Random Variables ◽  
Time Parameter ◽  
Conditional Probabilities ◽  
Occupation Times ◽  
The Matrix ◽  
Image Position

Consider first a Markov chain with two ergodic states E 1 and E 2, and discrete time parameter set {0, 1, 2, ···, n}. Define the random variables Z 0, Z 1, Z 2, ···, Zn by then the conditional probabilities for k = 1,2,···, n, are independent of k. Thus the matrix of transition probabilities is

Occupation times for two state Markov chains

1971 ◽  
Vol 8 (2) ◽  
pp. 381-390 ◽  
Author(s):  
P. J. Pedler
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Random Variables ◽  
Time Parameter ◽  
Conditional Probabilities ◽  
Occupation Times ◽  
The Matrix ◽  
Image Position

Consider first a Markov chain with two ergodic states E1 and E2, and discrete time parameter set {0, 1, 2, ···, n}. Define the random variables Z0, Z1, Z2, ···, Znby then the conditional probabilities for k = 1,2,···, n, are independent of k. Thus the matrix of transition probabilities is

scholarly journals Model of Thermal Mechanism of Subclass A1 Fire Extinguishing with General Purpose Fire Extinguishing Powder in Non-Stationary Heat Exchange Conditions

2019 ◽  
Vol 10 (4) ◽  
pp. 391-401
Author(s):  
A. I. Kitsak
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
General Purpose ◽  
Short Term ◽  
Stationary Heat ◽  
Fire Extinguishing ◽  
Thermal Mechanism ◽  
Powder Particles ◽  
The Mathematical Model ◽  
Intensity Of Feeding

The aim of the paper was to develop a model of thermal extinguishing mechanism using dry chemical powder taking into account the inertia of heat transfer to powder particles during unsteady heat exchange to identify the optimal conditions for extinguishing of A1 class fires with powders.The method of experimental and mathematical modelling of fire extinguishing process using dry chemical powder with short-term effect on the fire was used to achieve the goal. The experimental dependences of the extinguishing time and unit consumption of the extinguishing powder on the intensity of the powder supply to the combustion zone in extinguishing of subclass A1 fire in same area and in a limited volume were obtained. The mathematical model of a thermal extinguishing mechanism using dry chemical powder has been developed, taking into account the inertia of heat transfer to powder particles during unsteady heat exchange.Analysis of the regularities of extinguishing the subclass A1 fire using powder with a short feeding it into the fire indicates the presence of optimum values of unity consumption of powder on the fire from the intensity of feeding it into the fire. The presence of this optimum is due to the inertia of extinguishing the subclass A1 fire using powder due to the finiteness of the heat transfer time to the particles of the extinguishing powder and the limited time of interaction of particles with the combustible material.The theoretical analysis of the fire extinguishing process over the area taking into account the inertia of heat transfer to the powder particles at non-stationary heat exchange are carried out. The results of the analysis are in qualitative agreement with the results of the experimental study of the regularities of extinguishing of model fire foci of subclass A1 with General-purpose fire extinguishing powder.

Topics of Heat Transfer Related to Single-Walled Carbon Nanotubes

2007 ◽  
Author(s):  
Shigeo Maruyama
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Heat Conduction ◽  
Single Walled Carbon Nanotubes ◽  
Phonon Transport ◽  
Hot Water ◽  
Single Walled Carbon ◽  
Stationary Heat ◽  
Stationary Heat Conduction ◽  
Walled Carbon Nanotubes

Using an alcohol catalytic CVD method shown to produce high-quality single-walled carbon nanotubes (SWNTs), films of vertically aligned (VA-)SWNTs were synthesized on quartz substrates. The VA-SWNTs can be removed from the substrate and transferred onto an arbitrary surface—without disturbing the vertical alignment—using a hot-water assisted technique. This ability makes experimental measurements of the anisotropic properties of SWNTs considerably less challenging. A series of molecular dynamics simulations have been performed to investigate a variety of heat conduction characteristics of SWNTs. Investigations of stationary heat conduction identifies diffusive-ballistic heat conduction regime in a wide range of nanotube-lengths. Furthermore, studies on non-stationary heat conduction show that the extensive ballistic phonon transport gives rise to wave-like non-Fourier heat conduction. Finally, several case studies are presented for SWNT heat transfer in more practical situations.

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