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.

Comparative Assessment of the Finite Difference, Finite Element, and Finite Volume Methods for a Benchmark One-Dimensional Steady-State Heat Conduction Problem

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Energy Conservation ◽  
Heat Conduction Problem ◽  
Mesh Size ◽  
The Other ◽  
One Dimensional ◽  
Steady State Heat

The finite difference (FD), finite element (FE), and finite volume (FV) methods are critically assessed by comparing the solutions produced by the three methods for a simple one-dimensional steady-state heat conduction problem with heat generation. Three issues are assessed: (1) accuracy of temperature, (2) accuracy of heat flux, and (3) satisfaction of global energy conservation. It is found that if the order of accuracy of the numerical discretization schemes is the same (central difference for FD and FV, linear basis functions for FE), the accuracy of the temperature produced by the three methods is similar, except close to the boundaries where the FV method outshines the other two methods. Consequently, the FV method is found to predict more accurate heat fluxes at the boundaries compared to the other two methods and is found to be the only method that guarantees both local and global conservation of energy irrespective of mesh size. The FD and FE methods both violate energy conservation, and the degree to which energy conservation is violated is found to be mesh size dependent. Furthermore, it is shown that in the case of prescribed heat flux (Neumann) and Newton cooling (Robin) boundary conditions, the accuracy of the FD method depends in large part on how the boundary condition is implemented. If the boundary condition and the governing equation are both satisfied at the boundary, the predicted temperatures are more accurate than in the case where only the boundary condition is satisfied.

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.

One-Dimensional Steady-State Heat Conduction

2018 ◽  
pp. 53-116
Author(s):  
Sadık Kakaç ◽  
Yaman Yener ◽  
Carolina P. Naveira-Cotta
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
One Dimensional ◽  
State Heat ◽  
Steady State Heat
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