Development of the method of approximate solution to the nonstationary problem on heat transfer through a flat wall

Authors

DOI:

https://doi.org/10.15587/1729-4061.2017.118930

Keywords:

non-stationary heat transfer, energy accumulation, flat wall, analytical calculation, approximate solution

Abstract

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 %

Author Biographies

Olexander Brunetkin, Odessa National Polytechnic University Shevchenka ave., 1, Odessa, Ukraine, 65044

PhD, Associate Professor

Department of thermal power automation processes

Maksym Maksymov, Odessa National Polytechnic University Shevchenka ave., 1, Odessa, Ukraine, 65044

Doctor of Technical Sciences, Professor, Head of Department

Department of thermal power automation processes

Oksana Maksymova, Odessa National Academy of Food Technologies Kanatna str., 112, Odessa, Ukraine, 65039

PhD

Department of Computer Systems and Business Process Management 

Anton Zosymchuk, Odessa National Polytechnic University Shevchenka ave., 1, Odessa, Ukraine, 65044

Department of thermal power automation processes

References

  1. 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.
  2. Carslaw, H. S., Jaeger, J. C.; Pomerantsev, A. A. (Ed.) (1964). Conduction of heat in solids. Мoscow: Nauka, 488.
  3. Lykov, A. V. (1967). The theory of heat conduction. Мoscow: Higher School, 600.
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. Profos, P.; Davydov, N. I. (Ed.) (1967). Regulirovanie parosilovyh ustanovok. Moscow: Energiya, 368.
  13. 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
  14. Kuznetsov, Y. N. (1989). Heat transfer in the problem of the safety of nuclear reactors. Мoscow: Energoizdat, 296.
  15. 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.
  16. 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

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Published

2017-12-25

How to Cite

Brunetkin, O., Maksymov, M., Maksymova, O., & Zosymchuk, A. (2017). Development of the method of approximate solution to the nonstationary problem on heat transfer through a flat wall. Eastern-European Journal of Enterprise Technologies, 6(5 (90), 31–40. https://doi.org/10.15587/1729-4061.2017.118930

Issue

Section

Applied physics