scholarly journals Mathematical model of a heat transducer with a cylindrical heat pipeline and with a focused heat source

2020 ◽  
Vol 1686 ◽  
pp. 012063
Author(s):  
N.I. Avezova ◽  
P.R. Ismatullaev ◽  
P.M. Matyakubova ◽  
Sh.A. Kodirova
Keyword(s):  
Mathematical Model ◽  
Heat Source

Fractional order generalized thermoelastic response in a half space due to a periodically varying heat source

2018 ◽  
Vol 14 (1) ◽  
pp. 2-15 ◽  
Author(s):  
Jitesh Tripathi ◽  
Shrikant Warbhe ◽  
K.C. Deshmukh ◽  
Jyoti Verma
Keyword(s):  
Mathematical Model ◽  
Heat Source ◽  
Laplace Transform ◽  
Half Space ◽  
Fractional Order ◽  
Order Parameter ◽  
Order Theory ◽  
Numerical Inversion ◽  
Content Type ◽  
Copper Material

Purpose The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues. Design/methodology/approach Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates. Findings This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter. Research limitations/implications Constructed purely on theoretical mathematical model by considering different parameters and the functions. Practical implications The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations. Originality/value In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.

Mathematical Model of Determination and Analysis of Heat Exchange in Elements of Digital Technology Devices

2021 ◽  
Vol 43 (4) ◽  
pp. 37-50
Author(s):  
V.I. Havrysh ◽  
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Fourier Transform ◽  
Heat Exchange ◽  
Analytical Solution ◽  
Heat Source ◽  
Point Heat Source ◽  
Integral Fourier Transform ◽  
Spatial Coordinates ◽  
Boundary Surfaces

A mathematical model of heat exchange analysis between an isotropic two-layer plate heated by a point heat source concentrated on the conjugation surfaces of layers and the environment has been developed. To do this, using the theory of generalized functions, the coefficient of thermal conductivity of the materials of the plate layers is shown as a whole for the whole system. Given this, instead of two equations of thermal conductivity for each of the plate layers and the conditions of ideal thermal contact, one equation of thermal conductivity in generalized derivatives with singular coefficients is obtained between them. To solve the boundary value problem of thermal conductivity containing this equation and boundary conditions on the boundary surfaces of the plate, the integral Fourier transform was used and as a result an analytical solution of the problem in images was obtained. An inverse integral Fourier transform was applied to this solution, which made it possible to obtain the final analytical solution of the original problem. The obtained analytical solution is presented in the form of an improper convergent integral. According to Simpson's method, numerical values of this integral are obtained with a certain accuracy for given values of layer thickness, spatial coordinates, specific power of a point heat source, thermal conductivity of structural materials of the plate and heat transfer coefficient from the boundary surfaces of the plate. The material of the first layer of the plate is copper, and the second is aluminum. Computational programs have been developed to determine the numerical values of temperature in the given structure, as well as to analyze the heat exchange between the plate and the environment due to different temperature regimes due to heating the plate by a point heat source concentrated on the conjugation surfaces. Using these programs, graphs are shown that show the behavior of curves constructed using numerical values of the temperature distribution depending on the spatial coordinates. The obtained numerical values of temperature indicate the correspondence of the developed mathematical model of heat exchange analysis between a two-layer plate with a point heat source focused on the conjugation surfaces of the layersand the environment, the real physical process.

scholarly journals MATHEMATICAL ANALYSIS OF UNSTEADY MHD BLOOD FLOW THROUGH PARALLEL PLATE CHANNEL WITH HEAT SOURCE

2020 ◽  
Vol 5 (1) ◽  
pp. 40-50
Author(s):  
M.V. Surseh ◽  
P. Sekar
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Numerical Model ◽  
Heat Source ◽  
Prandtl Number ◽  
Mathematical Analysis ◽  
Parallel Plate ◽  
Flow Through ◽  
Fractional Differential ◽  
Plate Channel

A mathematical model of flimsy blood move through parallel plate channel under the action of a connected steady transverse attractive field is proposed. The model is subjected to warm source. Expository articulations are gotten by picking the hub speed; temperature dispersion and the typical speed of the blood rely upon y and t just to change over the arrangement of fractional differential conditions into an arrangement of normal differential conditions under the conditions characterized in our model. The model has been breaking down to discover the impacts of different parameters, for example, Hart-mann number, warm source parameter and Prandtl number on the hub speed, temperature circulation, and the ordinary speed. The numerical arrangements of pivotal speed, temperature conveyances, and typical speed are demonstrated graphically for better comprehension of the issue. Subsequently, the present numerical model gives a straightforward type of pivotal speed, temperature circulation and typical speed of the bloodstream so it will help not just individuals working in the field of Physiological liquid elements yet in addition to the restorative professionals.

scholarly journals MATHEMATICAL MODEL OF HEAT EXCHANGE IN ELEMENTS OF DIGITAL DEVICES

2021 ◽  
Vol 3 (1) ◽  
pp. 15-21
Author(s):  
Havrysh Havrysh ◽  
◽  
W. Yu. W. Yu. ◽  
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Fourier Transform ◽  
Heat Exchange ◽  
Analytical Solution ◽  
Heat Source ◽  
Point Heat Source ◽  
Integral Fourier Transform ◽  
Spatial Coordinates ◽  
Boundary Surfaces

A mathematical model of heat exchange analysis between an isotropic two-layer plate heated ba point heat source concentrated on the conjugation surfaces of layers and the environment has been developed. To do this, using the theory of generalized functions, the coefficient of thermal conductivity of the materials of the plate layers is shown as a whole for the wholesystem.Given this, instead of two equations of thermal conductivity for each of the plate layers and the conditions of ideal thermal contact, one equation of thermal conductivity ingeneralized derivatives with singular coefficients is obtained between them. To solve the boundary value problem of thermal conductivity containing this equation and boundary conditions on the boundary surfaces of the plate, the integral Fourier transform was used and as a result an analytical solution of the problem in images was obtained. An inverse integral Fourier transform was applied to this solution, which made it possible to obtain the final analytical solution of the original problem. The obtained analytical solution is presented in the form of an improper convergent integral. According to Simpsons method, numerical values of this integral are obtained with a certain accuracy for given values of layer thickness, spatial coordinates, specific power of a point heat source, thermal conductivity of structural materials of the plate and heat transfer coefficient from the boundary surfaces of the plate. The material of the first layer of the plate is copper, and the second is aluminum. Computational programs have been developed to determine the numerical values of temperature in the given structure, as well as to analyze the heat exchange between the plate and the environment due to different temperature regimes due to heating the plate by a point heat source concentrated on the conjugation surfaces. Using these programs, graphs are shown that show the behavior of curves constructed using numerical values of the temperature distribution depending on the spatial coordinates. The obtained numerical values of temperature indicate the correspondence of the developed mathematical model of heat exchange analysis between a two-layer plate with a point heatsource focused on the conjugation surfaces of the layersand the environment, the real physical process.

Study on Mathematical Model of Temperature Field in the Laser Welding Process

2010 ◽  
Vol 426-427 ◽  
pp. 89-92
Author(s):  
Hong Feng Wang ◽  
Dun Wen Zuo ◽  
Ming Min Huang ◽  
Hong Miao
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Heat Source ◽  
Laser Welding ◽  
Welding Process ◽  
Actual Process ◽  
Analytical Results ◽  
The Mathematical Model ◽  
Laser Welding Process

From the laser welding actual process, the welding heat source model of laser welding process was established, that is, superposition heat source. According to the knowledge of thermodynamics, the establishment of a welding process, the mathematical model of temperature distribution of laser welding process was obtained by laser welding heat source. Finally, the finite element simulation of welding temperature distribution was used. The simulated results were compared with the analytical results of mathematical model of temperature field, it was proved consistent between simulated results and analytical results, at the same time it can account for the correctness of the mathematical model of temperature field.

scholarly journals Сorrection сalculation of the heat source power during plasma-powder surfacing of the necks of stepped shafts

2019 ◽  
Vol 298 ◽  
pp. 00123
Author(s):  
G.R. Latypova ◽  
N.N. Karpenko ◽  
R.A. Latypov
Keyword(s):  
Mathematical Model ◽  
Heat Source ◽  
Heat Equation ◽  
Penetration Depth ◽  
Calculation Method ◽  
Temperature Fields ◽  
Lambert Function ◽  
Practical Application ◽  
Differential Heat ◽  
Source Power

A mathematical model is proposed for calculating temperature fields during arc surfacing of limited cylinders, eliminating the need for dimensionless parameters, when solving the differential heat equation, which facilitates the practical application of the developed calculation method. It is proposed that the penetration depth be calculated using the Lambert function. The obtained dependences make it possible to quantify the required correction of the heat source power in the process of surfacing the necks of stepped shafts.

Temperature and Stress Field Measurement at Friction-Stir Welding of an Aluminum Alloy Probe

2013 ◽  
Vol 486 ◽  
pp. 96-101
Author(s):  
Pavel Élesztős ◽  
Roland Jančo ◽  
Ladislav Écsi ◽  
Gregor Izrael
Keyword(s):  
Mathematical Model ◽  
Aluminum Alloy ◽  
Temperature Field ◽  
Friction Stir Welding ◽  
Stress Field ◽  
Heat Source ◽  
Strain Measurements ◽  
Friction Stir ◽  
Stationary Temperature Field

The presented work is devoted to an experimental determination of a non-stationary temperature field during friction-stir welding using a thermo camera and thermocouples respectively. The aim of the measurements was to tune up the heat source originating from friction between the rotating tool and a stationary probe by finding appropriate parameters of an employed mathematical model. After having identified the parameters, the friction-stir welding simulation was carried out using an aluminium alloy probe. Strain measurements were also performed during welding at selected locations on the probe. The experimentally determined results have been compared with the results of the numerical simulations.

Mathematical Approaching and Experimental Assembly to Evaluate the Risks of In-Service Welding in Hot Tapping

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Ivo Andrei de O. L Lima ◽  
Alex Alisson Bandeira Santos
Keyword(s):  
Mathematical Model ◽  
Heat Source ◽  
Arc Welding ◽  
Numerical Models ◽  
Temperature Fields ◽  
Physical Situation ◽  
Rectilinear Motion ◽  
Heat Sources ◽  
The Mathematical Model ◽  
Burn Through

The welding onto in-service pipeline (operation condition) results in three possibilities of high risks: leaking and/or explosion by burn-through, chemical reactions to instability, or even explosion due to the heat on internal fluid and cracking in heat affected zone (HAZ). The numerical methods have a useful role in the assessment of welding conditions for the safe in-service welding of pipelines. Only limited published works have considered direct calculation of burn-through using a combination of thermal and stress analysis. The mathematical model of the heat source is the most important part of these numerical models, and actually the mathematical model which described better the heat distribution of the arc welding through gas-shielded tungsten arc welding (GTAW) process or shielded metal arc welding process is the double ellipsoidal heat source (DEHS) model of Goldak and Akhlaghi (2010, Computational Welding Mechanics, Springer Books, New York, pp. 32–35). However, that model has considered the heat source in rectilinear motion only, and it depends on three parameters (a, b, c) which are related with the weld bead size and shape to define the geometry and co-ordinates of heat source, and they are determined empirically or experimentally. Few researchers published works that could determine these parameters mathematically, from the welding data. The publication that best analytically addressed this issue was the work of Eagar and Tsai (1983, “Temperature Fields Produced by Traveling Distributed Heat Sources,” Weld. J., 62(12), pp. 346–355). First, this paper presents a new equation for heat source in double ellipsoid considering the circular motion, trying to develop a model closer to the physical situation of hot tapping onto pipeline. Second, a proposal for determination of the parameters a, b analytically from the Eagar model and Tsai (1983, “Temperature Fields Produced by Traveling Distributed Heat Sources,” Weld. J., 62(12), pp. 346–355), and third, an experimental facility to get the temperature field that was used to validate the numerical finite element models.

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