A new mathematical model of heat conduction processes

1990 ◽  
Vol 42 (2) ◽  
pp. 210-216 ◽  
Author(s):  
V. I. Fushchich ◽  
A. S. Galitsyn ◽  
A. S. Polubinskii
Keyword(s):  
Mathematical Model ◽  
Heat Conduction

scholarly journals Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity

2021 ◽  
Vol 321 ◽  
pp. 03005
Author(s):  
George Kuvyrkin ◽  
Inga Savelyeva ◽  
Daria Kuvshinnikova
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Numerical Solution ◽  
Complex Structure ◽  
Modern World ◽  
Nonlocal Term ◽  
Material Structure ◽  
Two Dimensional ◽  
Differential Heat

Nonlocal models of thermodynamics are becoming more and more popular in the modern world. Such models make it possible to describe materials with a complex structure and unique strength and temperature properties. Models of nonlocal thermodynamics of a continuous medium establish a relationship between micro and macro characteristics of materials. A mathematical model of thermal conductivity in nonlocal media is considered. The model is based on the theory of nonlocal continuum by A.K. Eringen. The interaction of material particles is described using local and nonlocal terms in the law of heat conduction. The nonlocal term describes the effect of decreasing the influence of the surrounding elements of the material structure with increasing distance. The effect of nonlocal influence is described using the standard non-locality function based on the Gaussian distribution. The nonlocality function depends on the distance between the elements of the material structure. The mathematical model of heat conduction in a nonlocal medium consists of an integro-differential heat conduction equation with initial and boundary conditions. A numerical solution to the problem of heat conduction in a nonlocal plate is obtained. The numerical solution of a two-dimensional problem based on the finite element method is described. The influence of nonlocal effects and material parameters on the thermal conductivity in a plate under highintensity surface heating is analyzed. The importance of nonlocal characteristics in modelling the thermodynamic behaviour of materials with a complex structure is demonstrated.

Comprehesive Solution of Heat Conduction Problem Using Mathematical Model of Heat and Mass Transfer in Permafrost Soils

2014 ◽  
Vol 50 (6) ◽  
pp. 262-266 ◽  
Author(s):  
L. A. Duginov ◽  
N. B. Kutvitskaya ◽  
M. A. Magomedgadzhieva ◽  
E. A. Melˈnikova ◽  
M. Kh. Rozovskii
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Heat Conduction ◽  
Heat And Mass Transfer ◽  
Heat Conduction Problem ◽  
Permafrost Soils

Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

2017 ◽  
Vol 1 ◽  
pp. 114
Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
The Finite Difference Method ◽  
The Mathematical Model

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>

Mathematical model of gas-charged accumulator considering heat conduction

2018 ◽  
Vol 2018 (0) ◽  
pp. YC2018-081
Author(s):  
Kazushi SANADA ◽  
Shuce ZHANG ◽  
Shuto MIYASHITA
Keyword(s):  
Mathematical Model ◽  
Heat Conduction

scholarly journals Parameterising continuum models of heat transfer in heterogeneous living skin using experimental data

2018 ◽  
Author(s):  
Sean McInerney ◽  
Elliot J Carr ◽  
Matthew J Simpson
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Layered Structure ◽  
Experimental Studies ◽  
Synthetic Data ◽  
Spatial Location ◽  
Recent Experimental Data ◽  
Data Set ◽  
Experimental Constraint

AbstractIn this work we consider a recent experimental data set describing heat conduction in living porcine tissues. Understanding this novel data set is important because porcine skin is similar to human skin. Improving our understanding of heat conduction in living skin is relevant to understanding burn injuries, which are common, painful and can require prolonged and expensive treatment. A key feature of skin is that it is layered, with different thermal properties in different layers. Since the experimental data set involves heat conduction in thin living tissues of anesthetised animals, an important experimental constraint is that the temperature within the living tissue is measured at one spatial location within the layered structure. Our aim is to determine whether this data is sufficient to reliably infer the heat conduction parameters in layered skin, and we use a simplified two-layer mathematical model of heat conduction to mimic the generation of experimental data. Using synthetic data generated at one location in the two-layer mathematical model, we explore whether it is possible to infer values of the thermal diffusivity in both layers. After this initial exploration, we then examine how our ability to infer the thermal diffusivities changes when we vary the location at which the experimental data is recorded, as well as considering the situation where we are able to monitor the temperature at two locations within the layered structure. Overall, we find that our ability to parameterise a model of heterogeneous heat conduction with limited experimental data is very sensitive to the location where data is collected. Our modelling results provide guidance about optimal experimental design that could be used to guide future experimental studies.NomenclatureA brief description of all variables used in the document are given in Table 1.Table 1:Variable nomenclature and description.

Sharp Interface Numerical Modeling of Solidification Process of Pure Metal / Sposób Modelowania Numerycznego Procesu Krzepnięcia Z Ostrym Frontem

2012 ◽  
Vol 57 (4) ◽  
pp. 1189-1199 ◽  
Author(s):  
T. Skrzypczak
Keyword(s):  
Mathematical Model ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Level Set ◽  
Distance Function ◽  
Solidification Process ◽  
System Of Equations ◽  
Signed Distance Function ◽  
Interface Motion ◽  
Signed Distance

The paper is focused on the study of the solidification process of pure metals, in which the solidification front is smooth. It has the shape of a surface separating liquid from solid in three dimensional space or a curve in 2D. The location and topology of moving interface change over time and its velocity depends on the values of heat fluxes on the solid and liquid side of it. Such a formulation belongs to a group called Stefan problems. A mathematical model of the Stefan problem is based on differential equations of heat conduction and interface motion. This system of equations is supplemented by appropriate initial and boundary conditions as well as the continuity conditions at the solidification interface. The solution involves the determination of temporary temperature field and interface position. Typically, it is impossible to obtain the exact solution of such problem. This paper presents a mathematical model for the two-dimensional problem. The equation of heat conduction is supplemented with Dirichlet and Neumann boundary conditions. Interface motion is described by the level set equation which solution is sought in the form of temporary distribution of the signed distance function. Zero level of the distance field coincides with the position of the front. Values of the signed distance function obtained from the level set equation require systematic reinitialization. Numerical model of the process based on the finite element method (FEM) is also presented. FEM equations are derived and discussed. The explicit time integration scheme is proposed. It helps to avoid solving the system of equations during each time step. The reinitialization procedure of the signed distance function is described in detail. Examples of numerical analysis of the solidification process of pure copper within the complex geometry are presented. Results obtained from the use of constant material properties are compared with those obtained from the use of temperature dependent properties.

A study of heat conduction in structural ceramic materials. Part III. Mathematical model of measuring cell

2000 ◽  
Vol 41 (3-4) ◽  
pp. 140-143
Author(s):  
R. I. Abraitis ◽  
A. K. Dargis ◽  
A. A. Rusyatskas ◽  
é. I. Sakalauskas
Keyword(s):  
Mathematical Model ◽  
Heat Conduction ◽  
Ceramic Materials ◽  
Structural Ceramic ◽  
Measuring Cell
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