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.

Analysis of Heat and Moisture Transfer Beneath Freezer Foundations-Part II

2004 ◽  
Vol 126 (2) ◽  
pp. 726-731 ◽  
Author(s):  
Moncef Krarti ◽  
Pirawas Chuangchid ◽  
Pyeongchan Ihm
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Numerical Solution ◽  
Moisture Transfer ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Soil Thermal Conductivity ◽  
Heat And Moisture Transfer ◽  
Conduction Model ◽  
Heat And Moisture

This paper discusses selected results from a numerical solution of two-dimensional heat and moisture transfer within frozen and unfrozen soils beneath freezer slab foundations. In particular, the numerical solution is used to determine soil temperature profiles as well as freezer foundation heat gains. Finally, an effective soil thermal conductivity is successfully utilized in a pure heat conduction model to predict ground-coupled heat gains for freezers.

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>

Numerical solution of two-dimensional radially symmetric inverse heat conduction problem

2015 ◽  
Vol 23 (2) ◽  
Author(s):  
Zhi Qian ◽  
Benny Y. C. Hon ◽  
Xiang Tuan Xiong
Keyword(s):  
Heat Conduction ◽  
Numerical Solution ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Convergence Error ◽  
Regularization Techniques ◽  
Ill Posed

AbstractWe investigate a two-dimensional radially symmetric inverse heat conduction problem, which is ill-posed in the sense that the solution does not depend continuously on input data. By generalizing the idea of kernel approximation, we devise a modified kernel in the frequency domain to reconstruct a numerical solution for the inverse heat conduction problem from the given noisy data. For the stability of the numerical approximation, we develop seven regularization techniques with some stability and convergence error estimates to reconstruct the unknown solution. Numerical experiments illustrate that the proposed numerical algorithm with regularization techniques provides a feasible and effective approximation to the solution of the inverse and ill-posed problem.

On the Use of Spreadsheets in Heat Conduction Analysis

2000 ◽  
Vol 28 (2) ◽  
pp. 113-139 ◽  
Author(s):  
Esmail M. A. Mokheimer ◽  
Mohamed A. Antar
Keyword(s):  
Heat Conduction ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Single Layer ◽  
Transient Heat Conduction ◽  
New Technique ◽  
Two Dimensional ◽  
A New Technique ◽  
User Friendly

Detailed methodology and different techniques for simply utilizing the widely available and user friendly spreadsheet programs in heat conduction analysis are presented. Evaluation of analytical and numerical solution of heat conduction problems via spreadsheets is investigated. Detailed techniques of obtaining spreadsheet numerical solutions for one- and two-dimensional steady and transient heat conduction problems are introduced. A new technique of marching the transient numerical solution with time, in a single layer spreadsheet, for one- and two-dimensional heat conduction is explained. Creating macros that automate the spreadsheet processes, particularly calculations, is detailed. Utilization of the powerful graphical facility that is built in the spreadsheets to graphically represent the obtained solutions is outlined.

Identification of the Thermal Conductivity Coefficient for Quasi-Stationary Two-Dimensional Heat Conduction Equations

2017 ◽  
Vol 90 (6) ◽  
pp. 1295-1301 ◽  
Author(s):  
Yu. M. Matsevityi ◽  
S. V. Alekhina ◽  
V. T. Borukhov ◽  
G. M. Zayats ◽  
A. O. Kostikov
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Thermal Conductivity Coefficient ◽  
Two Dimensional
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