One mathematical model for internal thermal transport with movement of the heat source along a boundary

1996 ◽  
Vol 39 (4) ◽  
pp. 323-325
Author(s):  
A. A. Avaev ◽  
O. I. Mikryukova ◽  
N. V. Stepanova
Keyword(s):  
Mathematical Model ◽  
Heat Source ◽  
Thermal Transport

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.

Sensitivity Analysis of Parameters for the Simulation of Thermal Transport in Aquifer: A GSHP System in Chengdu, China

2011 ◽  
Vol 261-263 ◽  
pp. 1523-1528
Author(s):  
Yan Zhang Zhou ◽  
Rong Wu ◽  
Zhi Min Fu ◽  
Yue Gui
Keyword(s):  
Sensitivity Analysis ◽  
Heat Source ◽  
Thermal Transport ◽  
Global Sensitivity Analysis ◽  
Local Analysis ◽  
Global Sensitivity ◽  
Study Case ◽  
Groundwater Source ◽  
Thermal Affected Zone ◽  
Variation Tendency

Based on the theory of sensitivity analysis, the local/global sensitivity analysis of parameters for the modeling of thermal transport in aquifer under special groundwater flow and heat source conditions were carried out with the summer running of Groundwater Source Heat Pump (GSHP) system as a study case, by taking the temperature of typical observation points and thermal affected zone (TAZ) of injecting water at the end of summer as the model outputs. The results showed that the sensitivity of each modeling output was various for the different parameter in local analysis. The orders of local sensitivity coefficients of the nine parameters for two modeling outputs were almost coincident. In global sensitivity analysis, the sensitivity of the parameter being investigated was influenced by the different values of other parameters. The two modeling outputs almost had the same variation tendency of global sensitivity with different parameter combinations.

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 Analytical solution for thermal transport in packed beds with volumetric heat source

2017 ◽  
Vol 316 ◽  
pp. 131-136 ◽  
Author(s):  
Mohammad-Sadegh Salehi ◽  
Maryam Askarishahi ◽  
Stefan Radl
Keyword(s):  
Analytical Solution ◽  
Heat Source ◽  
Thermal Transport ◽  
Packed Beds ◽  
Volumetric Heat Source

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
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