Development of the method of approximate solution to the nonstationary problem on heat transfer through a flat wall
DOI:
https://doi.org/10.15587/1729-4061.2017.118930Keywords:
non-stationary heat transfer, energy accumulation, flat wall, analytical calculation, approximate solutionAbstract
In the present work, we propose a method for approximate analytical solution to the nonstationary problem of heat transfer through a flat wall in the concentrated statement. In the course of the study, three issues were consistently addressed: 1. symmetrical heating of a body, 2. asymmetrical heating, 3. nonstationary heat transfer.
At the first stage, we solved in approximate analytical statement the problem on symmetrical heating of a plate. The solution obtained has an error. The availability in the scientific literature of exact analytical solution, in a distributed (one-dimensional) statement, allowed us to assess the accuracy of the obtained approximate solution. It does not exceed the limits permissible for engineering calculations. A special feature of the developed method is the possibility of its application as an integral part in solving the problems on nonstationary heat transfer.
At the second stage, we solved a problem on asymmetrical heating of a plate. By using numerical study, the character of displacement of the minimum in temperature profile for thickness of the plate was identified. This made it possible, when applying the method developed at the previous stage, to obtain a solution to the problem on asymmetrical heating of the body. A special feature of the solutions is the developed approach to determining position of the temperature minimum for thickness of the plate. Such an approach was employed as another constituent part for solving a problem on nonstationary heat transfer.
At the third stage, numerical study allowed us to identify a characteristic point of varying temperature profile and the trajectory of its motion in the process of nonstationary heat transfer. Based on these data and applying the developed method, we demonstrated the possibility of approximate analytical solution to the problem on nonstationary heat transfer through a flat wall.
In all cases, when the exact solutions were lacking, assessment of error in approximate representation was conducted by comparing with the results of numerical calculations. The error did not exceed 6 %References
- Brunetkin, А. I., Maksymov, M. V. (2015). Method for determining the composition of combustion gases when burned. Naukovyi visnyk Natsionalnho hirnychoho universytetu, 5, 83–90.
- Carslaw, H. S., Jaeger, J. C.; Pomerantsev, A. A. (Ed.) (1964). Conduction of heat in solids. Мoscow: Nauka, 488.
- Lykov, A. V. (1967). The theory of heat conduction. Мoscow: Higher School, 600.
- Grysa, K., Maciag, A., Adamczyk-Krasa, J. (2014). Trefftz Functions Applied to Direct and Inverse Non-Fourier Heat Conduction Problems. Journal of Heat Transfer, 136 (9), 091302. doi: 10.1115/1.4027770
- Hoshan, N. A. (2009). The triple integral equations method for solving heat conduction equation. Journal of Engineering Thermophysics, 18 (3), 258–262. doi: 10.1134/s1810232809030084
- Zarubin, V. S., Kuvyrkin, G. N., Savelyeva, I. Y. (2018). Two-sided thermal resistance estimates for heat transfer through an anisotropic solid of complex shape. International Journal of Heat and Mass Transfer, 116, 833–839. doi: 10.1016/j.ijheatmasstransfer.2017.09.054
- Damle, R. M., Ardhapurkar, P. M., Atrey, M. D. (2016). Numerical investigation of transient behaviour of the recuperative heat exchanger in a MR J–T cryocooler using different heat transfer correlations. Cryogenics, 80, 52–62. doi: 10.1016/j.cryogenics.2016.09.003
- Kang, Z., Zhu, P., Gui, D., Wang, L. (2017). A method for predicting thermal waves in dual-phase-lag heat conduction. International Journal of Heat and Mass Transfer, 115, 250–257. doi: 10.1016/j.ijheatmasstransfer.2017.07.036
- Karvinen, R. (2012). Use of Analytical Expressions of Convection in Conjugated Heat Transfer Problems. Journal of Heat Transfer, 134 (3), 031007. doi: 10.1115/1.4005129
- Shupikov, A. N., Smetankina, N. V., Svet, Y. V. (2007). Nonstationary Heat Conduction in Complex-Shape Laminated Plates. Journal of Heat Transfer, 129 (3), 335. doi: 10.1115/1.2427073
- Brunetkin, O., Maksymov, M., Lysiuk, О. (2017). A simplified method for the numerical calculation of nonstationary heat transfer through a flat wall. Eastern-European Journal of Enterprise Technologies, 2 (5 (86)), 4–13. doi: 10.15587/1729-4061.2017.96090
- Profos, P.; Davydov, N. I. (Ed.) (1967). Regulirovanie parosilovyh ustanovok. Moscow: Energiya, 368.
- Brunetkin, O. I., Gusak, A. V. (2015). Determining the range of variation of convective heat transfer coefficient during the combustion of alternative kinds of gaseous fuels. Odes’kyi Politechnichnyi Universytet. Pratsi, 2 (46), 79–84. doi: 10.15276/opu.2.46.2015.15
- Kuznetsov, Y. N. (1989). Heat transfer in the problem of the safety of nuclear reactors. Мoscow: Energoizdat, 296.
- Marcenyuk, E. V., Zeleniy, Yu. A., Reznik, S. B. et. al. (2015). Identifikatsiya granichnyh usloviy teploobmena turbiny po rezul'tatam ispytaniy [Identification of turbine heat transfer boundary conditions by using test results]. Vestnik NTU «KhPI», 41 (1150), 72–76.
- Brunetkin, O., Maksymov, M., Maksymova, O., Zosymchuk, A. (2017). Development of a method for approximate solution of nonlinear ordinary differential equations using pendulum motion as an example. Eastern-European Journal of Enterprise Technologies, 5 (4 (89)), 4–11. doi: 10.15587/1729-4061.2017.109569
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Olexander Brunetkin, Maksym Maksymov, Oksana Maksymova, Anton Zosymchuk
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.
