## THERMAL SCIENCE

International Scientific Journal

### A COMPUTATIONAL METHOD TO SOLVE FOR THE HEAT CONDUCTION TEMPERATURE FIELD BASED ON DATA-DRIVEN APPROACH

**ABSTRACT**

In this paper, a computational method for solving for the 1-D 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 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 1-D steady-state and three examples of 1-D transient state are selected, and the calculated values are compared to those obtained by traditional numerical methods. The mean-absolute error of the steady-state is only 0.2508, and among the three transient cases, the maximum mean-square error is only 2.6875, indicating that the model is highly accurate in both steady-state and transient conditions. This shows that the hidden temperature method simulation can be applied to the solution of the heat conduction temperature field. This study provides a basis for the further optimization of the hidden temperature method algorithm.

**KEYWORDS**

PAPER SUBMITTED: 2020-08-22

PAPER REVISED: 2021-02-27

PAPER ACCEPTED: 2021-03-08

PUBLISHED ONLINE: 2021-05-16

**THERMAL SCIENCE** YEAR

**2022**, VOLUME

**26**, ISSUE

**Issue 1**, PAGES [233 - 246]

- Mosayebidorcheh, S., et al., Transient thermal analysis of longitudinal fins with internal heat generation considering temperature - dependent properties and different fin profiles, Energy Conversion & Management, 86 ( 2014 ), Oct., pp. 365 - 370
- Mohammed, H. A., et al., Numerical simulation of heat transfer enhancement in wavy microchannel heat sink, International Communications in Heat & Mass Transfer, 38 ( 2011 ), 1, pp. 63 - 68
- Yang, K., et al., Using analytical expressions in radial integration BEM for variable coefficient heat conduction problems, Engineering analysis with boundary elements 35 ( 2011 ), 10, pp. 1085 - 1089
- Yang, K., et al., Radial integration BEM for transient heat conduction problems, Engineering analysis with boundary elements, 34 ( 2010 ), 6, p p. 557 - 563
- Chang, C. W., Liu, C. S., A new algorithm for direct and backward problems of heat conduction equation, International journal of heat and mass transfer, 53 ( 2010 ), 23 - 24, pp. 5552 - 5 569
- Gu, Y., et al., Singular boundary method for steady - state heat conduction in three dimensional general anisotropic media, International Journal of Heat and Mass Transfer, 55 ( 2012 ), 17 - 18, pp. 4837 - 4848
- Cheng, R. J., Liew, K. M., A meshless analysis of three - dimensional transient heat conduction problems, Engineering Analysis with Boundary Elements, 36 ( 2012 ), 2, pp. 203 - 210
- Rook, R., et al., Modeling transient heat transfer using SPH and implicit time integration, Numerical Heat Transfer, Part B: Fundamentals, 51 ( 2007 ), 1, pp. 1 - 23
- Waters, J., et al., Global versus localized RBF meshless methods for solving incompressible fluid flow with heat transfer, Numerical Heat Transfer, Part B: Fundamentals, 68 ( 2015 ), 3, pp. 185 - 203
- Mohammad, A., et al., A deep neural network surrogate for high - dimensional random partial differential equations, Probabilistic Engineering Mechanics, 57 (2019), Aug., pp. 14 - 25
- Deng, S., et al., Solving the temperature distribution field in nonlinear heat conduction problems using the Hopfield neural network, Numerical Heat Transfer, Part B: Fundamentals, 51 ( 2007 ), 4, pp. 375 - 389
- Deng, S., et al., Applying neural networks to the solution of forward and inverse heat conduction problems, International Journal of Heat and Mass Transfer, 49 ( 2006 ), 25 - 26, pp. 4732 - 4750
- Hwang, Y., et al., Applying neural networks to the solution of the inverse heat conduction problem in a gun barrel, Journal of pressure vessel technology, 130 ( 2008 ), 3, 031203
- Sudheer, K., et al., A data driven algorithm for constructing artificial neural network rainfall runoff models, Hydrological processes, 16 ( 2002 ), 6, pp. 1325 - 1330
- Bar - Sinai, Y., et al., Learning data - driven discretizations for partial differential equations, Proceedings of the National Academy of Sciences, 116 (2019), 31, pp. 15344 - 15349
- Kirchdoerfer, T., Ortiz, M., Data driven computing in dynamics, International Journal for Numerical Methods in Engineering, 113 ( 2018), 11, pp. 1697 - 1710
- Ye, I., et al., Numerical modeling of slag flow and heat transfer on the wall of an entrained coal gasifier, Fuel, 150 ( 2015 ), Feb, pp. 64 - 74
- Wong, H., et al., Improved finite - difference methods based on a critical evaluation of the approximation errors, Numerical Heat Transfer, Part A: Applications, 2 ( 1979 ), 2, pp. 139 - 163
- Chung, K., et al., A generalized finite - difference method for heat transfer problems of irregular geometries, Numerical Heat Transfer, 4 ( 1981 ), 3, pp. 345 - 357
- Rafiq, M., et al., Neural network design for engineering applications, Computers & Structures, 79 ( 2001 ), 17, pp. 1541 - 1552
- Zhao, Y., Zhou, D., Yan, H., An improved retrieval method of atmospheric parameter profiles based on the BP neural network, Atmospheric research, 213 ( 2018 ), Jun., pp. 389 - 397