scholarly journals A computational method to solve for the heat conduction temperature field based on data-driven approach

2021 ◽  
pp. 165-165
Author(s):  
Kun Li ◽  
Shiquan Shan ◽  
Qi Zhang ◽  
Xichuan Cai ◽  
Zhou Zhijun
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Steady State ◽  
Transient State ◽  
Absolute Error ◽  
Computational Method ◽  
Data Driven ◽  
One Dimensional ◽  
Data Driven Approach ◽  
The One

In this paper, a computational method for solving for the one-dimensional heat conduction temperature field is proposed based on a data-driven approach. The traditional numerical solution requires algebraic processing of the heat conduction differential equations, and necessitates the use of a complex mathematical derivation process to solve for the temperature field. In this paper, a temperature field solution model called HTM (Hidden Temperature Method) is proposed. This model uses an artificial neural network to establish the correspondence relationship of the node temperature values during the iterative process, so as to obtain the "Data to Data" solution. In this work, one example of one-dimensional steady state and three examples of one-dimensional transient state are selected, and the calculated values are compared to those obtained by traditional numerical methods. The mean-absolute error(MAE)of the steady state is only 0.2508, and among the three transient cases, the maximum mean-square error(MSE) is only 2.6875, indicating that the model is highly accurate in both steady-state and transient conditions. This shows that the HTM simulation can be applied to the solution of the heat conduction temperature field. This study provides a basis for the further optimization of the HTM algorithm.

scholarly journals Non-steady-state heat conduction in composite walls

2014 ◽  
Vol 470 (2165) ◽  
pp. 20130605 ◽  
Author(s):  
Bernard Deconinck ◽  
Beatrice Pelloni ◽  
Natalie E. Sheils
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Composite Materials ◽  
Solution Method ◽  
One Dimensional ◽  
Infinite Domains ◽  
Steady State Heat ◽  
The One ◽  
Composite Walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux is prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.

Research on the Issue of LED’s Cooling Based on Heat Conduction Equations

2012 ◽  
Vol 507 ◽  
pp. 137-141
Author(s):  
Zhi Qin Huang ◽  
Pei Ying Quan ◽  
Yong Qing Pan
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Heat Conduction Equation ◽  
Rapid Development ◽  
Three Dimensional ◽  
Conduction Equation ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
The One

With the rapid development of power type LED, the issue of the cooling of LED has been prominent. How to make the heat generated by LED chip go out quickly in order to cool the LED chip has become an urgent problem. The form of heat goes through the substrate has been widely used and has become the best way to solve the heat problem. There are three types of LED substrate. They are metal substrate, ceramic substrate and composite substrate. At first, In this paper I analyze the theoretical of three-dimensional non-steady state and steady state heat conduction equation, then the three-dimensional model is simplified as one-dimensional model and I get the results of heat conduction equation under the one-dimensional stationary and non-steady state.

scholarly journals Simplified Grinding Temperature Model Study

2019 ◽  
Vol 6 (2) ◽  
pp. a1-a7
Author(s):  
N. V. Lishchenko ◽  
V. P. Larshin ◽  
H. Krachunov
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Heat Source ◽  
Boundary Conditions ◽  
Grinding Temperature ◽  
Temperature Model ◽  
One Dimensional ◽  
Heating And Cooling ◽  
Equation Of Heat Conduction ◽  
The One

A study of a simplified mathematical model for determining the grinding temperature is performed. According to the obtained results, the equations of this model differ slightly from the corresponding more exact solution of the one-dimensional differential equation of heat conduction under the boundary conditions of the second kind. The model under study is represented by a system of two equations that describe the grinding temperature at the heating and cooling stages without the use of forced cooling. The scope of the studied model corresponds to the modern technological operations of grinding on CNC machines for conditions where the numerical value of the Peclet number is more than 4. This, in turn, corresponds to the Jaeger criterion for the so-called fast-moving heat source, for which the operation parameter of the workpiece velocity may be equivalently (in temperature) replaced by the action time of the heat source. This makes it possible to use a simpler solution of the one-dimensional differential equation of heat conduction at the boundary conditions of the second kind (one-dimensional analytical model) instead of a similar solution of the two-dimensional one with a slight deviation of the grinding temperature calculation result. It is established that the proposed simplified mathematical expression for determining the grinding temperature differs from the more accurate one-dimensional analytical solution by no more than 11 % and 15 % at the stages of heating and cooling, respectively. Comparison of the data on the grinding temperature change according to the conventional and developed equations has shown that these equations are close and have two points of coincidence: on the surface and at the depth of approximately threefold decrease in temperature. It is also established that the nature of the ratio between the scales of change of the Peclet number 0.09 and 9 and the grinding temperature depth 1 and 10 is of 100 to 10. Additionally, another unusual mechanism is revealed for both compared equations: a higher temperature at the surface is accompanied by a lower temperature at the depth. Keywords: grinding temperature, heating stage, cooling stage, dimensionless temperature, temperature model.

scholarly journals Fractional Heat Conduction Models and Thermal Diffusivity Determination

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Monika Žecová ◽  
Ján Terpák
Keyword(s):  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Numerical Methods ◽  
Fractional Order ◽  
Experimental Verification ◽  
Heat Conduction Equation ◽  
Historical Overview ◽  
One Dimensional ◽  
The One ◽  
Fractional Heat Conduction

The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.

scholarly journals A Data-Driven Approach to Development of a Taxonomy Framework for Triple Bottom Line Metrics

2019 ◽  
Vol 11 (9) ◽  
pp. 2717
Author(s):  
Fátima L. Vieira ◽  
Paulo A. Vieira ◽  
Denis A. Coelho
Keyword(s):  
Screening Tool ◽  
Triple Bottom Line ◽  
Computational Approach ◽  
Data Driven ◽  
Specific Context ◽  
Bottom Line ◽  
Conscious Decision ◽  
Data Driven Approach ◽  
The Subject ◽  
The One

This paper proposes a data-driven approach to develop a taxonomy in a data structure on list for triple bottom line (TBL) metrics. The approach is built from the authors reflection on the subject and review of the literature about TBL. The envisaged taxonomy framework grid to be developed through this approach will enable existing metrics to be classified, grouped, and standardized, as well as detect the need for further metrics development in uncovered domains and applications. The approach reported aims at developing a taxonomy structure that can be seen as a bi-dimensional table focusing on feature interrogations and characterizing answers, which will be the basis on which the taxonomy can then be developed. The interrogations column is designed as the stack of the TBL metrics features: What type of metric is it (qualitative, quantitative, or hybrid)? What is the level of complexity of the problems where it is used? What standards does it follow? How is the measurement made, and what are the techniques that it uses? In what kinds of problems, subjects, and domains is the metric used? How is the metric validated? What is the method used in its calculation? The column of characterizing answers results from a categorization of the range of types of answers to the feature interrogations. The approach reported in this paper is based on a screening tool that searches and analyzes information both within abstracts and full-text journal papers. The vision for this future taxonomy is that it will enable locating for any specific context, discern what TBL metrics are used in that context or similar contexts, or whether there is a lack of developed metrics. This meta knowledge will enable a conscious decision to be made between creating a new metric or using one of those that already exists. In this latter case, it would also make it possible to choose, among several metrics, the one that is most appropriate to the context at hand. In addition, this future framework will ease new future literature revisions, when these are viewed as updates of this envisaged taxonomy. This would allow creating a dynamic taxonomy for TBL metrics. This paper presents a computational approach to develop such taxonomy, and reports on the initial steps taken in that direction, by creating a taxonomy framework grid with a computational approach.

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