DOI: https://doi.org/10.15587/1729-4061.2017.96090

A simplified method for the numerical calculation of nonstationary heat transfer through a flat wall

Olexander Brunetkin, Maksym Maksymov, Оleksander Lysiuk

Abstract


The nonstationary operation modes of power equipment lead to the nonstationary regimes of heat exchange, in particular heat transfer. The transient processes, related to the accumulation of energy in the heat-transmitting surfaces, which manifest themselves in this case, may affect manageability of the work of equipment.

Although in many cases, with a proper approximation, the heat exchange surfaces can be represented in the form of a simple variant of an infinite plate, the existing methods and tools for solving the problems on nonstationary heat transfer are built from the positions of universalism, introducing unjustified complications and hampering the generalization of numerical results obtained. We developed a simplified discrete analog to solve the one-dimensional problems on nonstationary heat transfer through an infinite plate. The realized approach allowed us to obtain the analog and results of calculations based on it in the dimensionless form, which substantially facilitates their generalization.

A high stability of computational process is demonstrated relative to the selection of a number of nodes in computational grid and calculation step by time. The possibility of using the maximally small computational grids (3 nodes) makes it possible, at the current calculation step by time. To obtain an analytical solution for determining the temperatures at the surfaces of the plate at initial use of boundary conditions of the third kind. As a result, accumulated energy can be defined as a difference in the heat fluxes at the surfaces of the plate. Performing the calculations on the maximally small grids might be useful to solve the inverse problems on thermal conductivity.


Keywords


nonstationary heat transfer; flat wall; simplified numerical computation; small computational grid

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References


Brunetkin, А. I., Maksymov, M. V. (2015). Method for determining the composition of combustion gases when burned. Scientific Journal Natsionalnho Mining University, 5, 83–90.

Maksymov, M. V., Brunetkin, А. I., Bondarenko, A. V. (2013). Model and method for determining conditional formula hydrocarbon fuel combustion. Eastern-European Journal of Enterprise Technologies, 6 (8 (66)), 20–27. Available at: http://journals.uran.ua/eejet/article/view/18702/17074

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

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

Seem, J. E., Klein, S. A., Beckman, W. A., Mitchell, J. W. (1989). Transfer Functions for Efficient Calculation of Multidimensional Transient Heat Transfer. Journal of Heat Transfer, 111 (1), 5. doi: 10.1115/1.3250659

Vahabzadeh, A., Fakour, M., Ganji, D. D., Bakhshi, H. (2016). Analytical investigation of the one dimensional heat transfer in logarithmic various surfaces. Alexandria Engineering Journal, 55 (1), 113–117. doi: 10.1016/j.aej.2015.12.027

Ray Mahapatra, T., Kumar Nandy, S., Pop, I. (2014). Dual Solutions in Magnetohydrodynamic Stagnation-Point Flow and Heat Transfer Over a Shrinking Surface With Partial Slip. Journal of Heat Transfer, 136 (10), 104501. doi: 10.1115/1.4024592

Zhang, L.-Z. (2011). An Analytical Solution to Heat and Mass Transfer in Hollow Fiber Membrane Contactors for Liquid Desiccant Air Dehumidification. Journal of Heat Transfer, 133 (9), 092001. doi: 10.1115/1.4003900

Patankar, S. (1984). Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti. Moscow: Ehnergoatomizdat, 152.

Brunetkin, А. I., Nakosin, V. N. (1990). Modified method of controlling the amount used in the solution of nonlinear problems in fluid dynamics with free surface in tanks of complex shapes. The vibrations of elastic structures with a liquid. – Novosibirsk: Siberian Research Institute of Aviation them. S. A. Chaplygin, 26–30.

Kuznetsov, G. V., Sheremet, M. A. (2010). Numerical Simulation of Convective Heat Transfer Modes in a Rectangular Area With a Heat Source and Conducting Walls. Journal of Heat Transfer, 132 (8), 081401. doi: 10.1115/1.4001303

Lapka, P., Furmanski, P. (2016). Immersed Boundary Method for Radiative Heat Transfer Problems in Nongray Media With Complex Internal and External Boundaries. Journal of Heat Transfer, 139 (2), 022702. doi: 10.1115/1.4034772

He, Y.-L., Tao, W.-Q. (2015). Numerical Solutions of Nano/Microphenomena Coupled With Macroscopic Process of Heat Transfer and Fluid Flow: A Brief Review. Journal of Heat Transfer, 137 (9), 090801. doi: 10.1115/1.4030239

Brunetkin, А. I. (2014). Integrated approach to solving the fluid dynamics and heat transfer problems. Odes’kyi Politechnichnyi Universytet. Pratsi, 2, 108–115. doi: 10.15276/opu.2.44.2014.21


GOST Style Citations


Brunetkin, А. I. Method for determining the composition of combustion gases when burned [Text] / А. I. Brunetkin, M. V. Maksymov // Scientific Journal Natsionalnho Mining University. – 2015. – Issue 5. – P. 83–90.

Maksymov, M. V. Model and method for determining conditional formula hydrocarbon fuel combustion [Text] / M. V. Maksymov, А. I. Brunetkin, A. V. Bondarenko // Eastern-European Journal of Enterprise Technologies. – 2013. – Vol. 6, Issue 8 (66). – P. 20–27. – Available at: http://journals.uran.ua/eejet/article/view/18702/17074

Karvinen, R. Use of Analytical Expressions of Convection in Conjugated Heat Transfer Problems [Text] / R. Karvinen // Journal of Heat Transfer. – 2012. – Vol. 134, Issue 3. – P. 031007. doi: 10.1115/1.4005129 

Shupikov, A. N. Nonstationary Heat Conduction in Complex-Shape Laminated Plates [Text] / A. N. Shupikov, N. V. Smetankina, Y. V. Svet // Journal of Heat Transfer. – 2007. – Vol. 129, Issue 3. – P. 335. doi: 10.1115/1.2427073 

Grysa, K. Trefftz Functions Applied to Direct and Inverse Non-Fourier Heat Conduction Problems [Text] / K. Grysa, A. Maciag, J. Adamczyk-Krasa // Journal of Heat Transfer. – 2014. – Vol. 136, Issue 9. – P. 091302. doi: 10.1115/1.4027770 

Seem, J. E. Transfer Functions for Efficient Calculation of Multidimensional Transient Heat Transfer [Text] / J. E. Seem, S. A. Klein, W. A. Beckman, J. W. Mitchell // Journal of Heat Transfer. – 1989. – Vol. 111, Issue 1. – P. 5. doi: 10.1115/1.3250659 

Vahabzadeh, A. Analytical investigation of the one dimensional heat transfer in logarithmic various surfaces [Text] / A. Vahabzadeh, M. Fakour, D. D. Ganji, H. Bakhshi // Alexandria Engineering Journal. – 2016. – Vol. 55, Issue 1. – P. 113–117. doi: 10.1016/j.aej.2015.12.027 

Mahapatra, T. R. Dual Solutions in Magnetohydrodynamic Stagnation-Point Flow and Heat Transfer Over a Shrinking Surface With Partial Slip [Text] / T. R. Mahapatra, S. K. Nandy, I. Pop // Journal of Heat Transfer. – 2014. – Vol. 136, Issue 10. – P. 104501. doi: 10.1115/1.4024592 

Zhang, L.-Z. An Analytical Solution to Heat and Mass Transfer in Hollow Fiber Membrane Contactors for Liquid Desiccant Air Dehumidification [Text] / L.-Z. Zhang // Journal of Heat Transfer. – 2011. – Vol. 133, Issue 9. – P. 092001. doi: 10.1115/1.4003900 

Patankar, S. Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti [Text] / S. Patankar. – Moscow: Ehnergoatomizdat, 1984. – 152 p.

Brunetkin, А. I. Modified method of controlling the amount used in the solution of nonlinear problems in fluid dynamics with free surface in tanks of complex shapes [Text]: proc. of the VI symp. / А. I. Brunetkin, V. N. Nakosin // The vibrations of elastic structures with a liquid. – Novosibirsk: Siberian Research Institute of Aviation them. S. A. Chaplygin, 1990. – P. 26–30.

Kuznetsov, G. V. Numerical Simulation of Convective Heat Transfer Modes in a Rectangular Area With a Heat Source and Conducting Walls [Text] / G. V. Kuznetsov, M. A. Sheremet // Journal of Heat Transfer. – 2010. – Vol. 132, Issue 8. – P. 081401. doi: 10.1115/1.4001303 

Lapka, P. Immersed Boundary Method for Radiative Heat Transfer Problems in Nongray Media With Complex Internal and External Boundaries [Text] / P. Lapka, P. Furmanski // Journal of Heat Transfer. – 2016. – Vol. 139, Issue 2. – P. 022702. doi: 10.1115/1.4034772 

He, Y.-L. Numerical Solutions of Nano/Microphenomena Coupled With Macroscopic Process of Heat Transfer and Fluid Flow: A Brief Review [Text] / Y.-L. He, W.-Q. Tao // Journal of Heat Transfer. – 2015. – Vol. 137, Issue 9. – P. 090801. doi: 10.1115/1.4030239 

Brunetkin, А. I. Integrated approach to solving the fluid dynamics and heat transfer problems [Text] / А. I. Brunetkin // Odes’kyi Politechnichnyi Universytet. Pratsi. – 2014. – Issue 2. – P. 108–115. doi: 10.15276/opu.2.44.2014.21 







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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061