NUMERICAL STUDY ON HEAT TRANSFER IN MULTILAYERED STRUCTURES OF MAIN GEOMETRIC FORMS MADE OF DIFFERENT MATERIALS

Roman M. Tatsiy; Oleg Yu Pazen; Sergiy Ya. Vovk; Lubomyr Ya. Ropyak; Tetiana O. Pryhorovska

doi:10.24874/jsscm.2019.13.02.04

Research paper

Published: 01.12.2018.

<< Prev | Next >>

PDF

https://doi.org/10.24874/jsscm.2019.13.02.04

NUMERICAL STUDY ON HEAT TRANSFER IN MULTILAYERED STRUCTURES OF MAIN GEOMETRIC FORMS MADE OF DIFFERENT MATERIALS

Abstract

The article proposed a general research scheme of heat transfer process in multilayer constructions for three basic geometric forms in order to simulate fire distribution. The scheme is based on linear differential equations, the Fourier method and the modified method of Eigen functions. The work considers five different layers’ design and does not take into account internal heat sources. In this regard, a one-parameter family of boundary problems were solved. The authors simulated heat transfer for the Cartesian, cylindrical and spherical coordinates. Structures comprised several materials each having thermal properties varying with temperature.

Keywords:

boundary problem,

quasi-derivative,

Cauchy matrix,

Fourier method,

eigen function method

References

Aliabadi M. The Boundary Element Method, Applications in Solids and Structures. . John Wiley & Sons. 2002;598.

Arsenin V, Ya. Methods of Mathematical Physics and Special Functions. . Nauka, Moscow. 1974;

Beck J. Green’s Function Solution for Transient Heat Conduction Problems. Int J Heat Mass Transfer. 1984;1235–44.

Buketov V, Dolgov N, Sapronov A. Mechanical characteristics of epoxy nanocomposite coatings with ultradisperse diamond particles. . Strength of Materials. 2017;464–71.

Bulavin P, Kascheev V. Solution of the non-homogeneous heat conduction equation for multilayered bodies. Int Chem Eng. 1965;112–5.

Dolgov M, Zubrets’ka N A, Buketov A, V. Use of the method of mathematical experiment planning for evaluating adhesive strength of protective coatings modified by energy fields. Strength Mater. 2012;(1):81–6.

En. Eurocode 1: Actions on structures -Part 1-2: General actions -Actions on structures exposed to fire Authority: The European Union Per Regulation 305. 1991;

Gay D. Composite Materials: Design and Application (3rd ed.). . New York: CRC Press. 2015;635.

Giere A. Transient Heat Flow in a Composite Slab -Constant Flux. Zero Flux Boundary Conditions, Appl Sci Research, Section A. 1965;(1):191–8.

10.

Gosz M. Finite Element Method: Applications in Solids, Structures, and Heat Transfer. 2017;400.

11.

Hahn D, Özişik M. Temperature solution in multidimensional multi-layer bodies. Int J Heat Mass Transfer. 2012;(9):1865–77.

12.

Haji-Sheikh A, Beck JV. Temperature solution in multidimensional multi-layer bodies. International Journal of Heat and Mass Transfer. 2002;45(9):1865–77.

13.

Jain P, Singh S, Rizwan-Uddin. An exact analytical solution for twodimensional, unsteady, multilayer heat conduction in spherical coordinates. Int J Heat Mass Transfer. 2010;(9):2133–42.

14.

Kayhani M, Norouzi M, Delouei A, A. A general analytical solution for heat conduction in cylindrical multilayer composite laminates. Int J Therm Sci. 2012;(1):73–82.

15.

Kolesov V, Vlasov N, Tisovskii L, O, Shatskii I. The stress-deformation state of an elastic half-space with a spheroidal thermal inclusion. International Applied Mechanics. 1992;(7):426–34.

16.

Kolodziejczyk W, Kul’chyts’kyi-Zhyhailo R. Pressure of the lateral surface of a cylinder on a periodically layered half space. Mater Sci. 2007;351–60.

17.

Yu K, Protsyuk M, V B, Sinyuta V, Shebanov S, Sharov S. Non-stationary temperature field in a multilayer orthotropic cylinder. Engineering Physics Journal. 1992;(2):325–30.

18.

Kul’chyts’kyi-Zhyhailo R. Elastic half space with laminated coating of periodic structure under the action of Hertz’s pressure. Mater Sci. 2012;527–34.

19.

Kumar M. Applications of Composite Materials. 2017;273.

20.

Li M, Lai ACK. Analytical solution to heat conduction in finite hollow composite cylinders with a general boundary condition. Int J Heat and Mass Transfer. 2013;549–56.

21.

Lu X, Tervola P, Viljanen M. A new analytical method to solve heat equation for multidimensional composite slab. J Phys A: Math Gen. 2005;2873–90.

22.

Lu X, Tervola P, Viljanen M. Transient analytical solution to heat conduction in composite circular cylinder. Int J Heat Mass Transfer. 2006;(1–2):341–8.

23.

Lykov A. Heat Conduction Theory. Moscow: Vysshaya Shkola. 1967;

24.

Malanchuk N, Slobodyan B, Martynyak R. Friction Sliding of Elastic Bodies in the Presence of Subsurface Inclusions. Mater Sci. 2017;819–26.

25.

Mikhailov M, Özişik M. Transient conduction in a three-dimensional composite slab. Int J Heat Mass Transfer. 2017;(2):340–2.

26.

De M. An analytic approach to the unsteady heat conduction processes in onedimensional composite media. Int J Heat Mass Transfer. 2002;(6):1333–43.

27.

De M. Unsteady heat conduction in two-dimensional two slab-shaped regions. Exact closed-form solution and results. Int J Heat Mass Transfer. 2003;1455–69.

28.

Norouzi M, Rahmani H, Birjandi A, Joneidi A. A general exact analytical solution for anisotropic non-axisymmetric heat conduction in composite cylindrical shells. Int J Heat Mass Transfer. 2016;41–56.

29.

Özişik M, Orlande H, R B, Colaço M, Cotta R. Finite Difference Methods in Heat Transfer. 2017;580.

30.

Ropyak L Ya, Shatskyi I, Makoviichuk M. Influence of the oxide-layer thickness on the ceramic-aluminium coating resistance to indentation. Metallofizika i Noveishie Tekhnologii. 2017;(4):517–24.

31.

Salt H. Transient conduction in a two-dimensional composite slab-I. Theoretical development of temperature modes. Int J Heat Mass Transfer. 1983;(11):1611–6.

32.

Semerak M, Tatsii R M, Pazen O. Multilayer thermal insulation capacity construction with regard to damage arbitrary layer. Vestnik Kokshetauskogo tekhnicheskogo instituta, Issue. 2015;8–17.

33.

Shats’kyi І P, Ropyak L, Makoviichuk M. Strength optimization of a two-layer coating for the particular local loading conditions. Strength of Materials. 2016;(5):726–30.

34.

Shevchuk V. Thermoelasticity problem for a multilayer coating/half-space assembly with undercoat crack subjected to convective thermal loading. Journal of Thermal Stresses. 2017;(10):1215–30.

35.

Shevchuk V. Analytical solution of nonstationary heat conduction problem for a halfspace with a multilayer coating. J Eng Phys Thermophy. 2013;(1):450–9.

36.

Siegel R. Transient thermal analysis of parallel translucent layers by using Green’s functions. J Thermophys Heat Transfer (AIAA). 1999;(1):10–7.

37.

Singh S, Jain P K, Rizwan-Uddin. Finite integral transform method to solve asymmetric heat conduction in a multilayer annulus with time-dependent boundary conditions. Nucl Eng Des. 2011;(1):144–54.

38.

Tatsii R M, Stasiuk MF, Vlasii M, O. Generalized equation kvazidyferentsialni. Prepr/AN Ukraini IPPMM. 2011;(2–94):1–4.

39.

Tatsiy R, Pazen O. Direct method for calculating a non-stationary temperature field under fire conditions. Pozhezhna bezpeka: Zb nauk Pr. 2015;135–41.

40.

Tatsiy R, Pazen O. General boundary-value problems for the heat conduction equation with piecewise-continuous coefficients. Journal of Engineering Physics and Thermophysics. 2016;(2):357–68.

41.

Tatsiy R M, Stasiuk M, Vlasii O, Pazen O, Yu. The direct method of studying the temperature field in a multilayer pipeline under fire conditions, Information Technologies and Computer Modeling, Collection of articles of the International scientific and practical conference. 2017;436–40.

42.

Tikhonov A, Samarskii A. Mathematical physics equation. 1977;735.

43.

Tittle C. Boundary value problems in composite media: quasiorthogonal functions. J Appl Phys. 1965;1486–8.

44.

Tokovyy Y, Ma CC. Analytical solutions to the axisymmetric elasticity and thermoelasticity problems for an arbitrarily inhomogeneous layer. International Journal of Engineering Science. 2015;(1):1–17.

45.

Yasniy O, Yu P, Yasniy V, Lapusta Y. Residual lifetime assessment of thermal power plant superheater header. Engineering Failure Analysis. 2017;(10):390–403.

46.

Yasniy O, Vuherer T, Yasniy V, Sobchak A. Mechanical behaviour of material of thermal power plant steam superheater collector after exploitation. Engineering Failure Analysis. 2013;(1):262–71.

47.

Yasniy V, Maruschak P, Yasniy O, Lapusta Y. On thermally induced multiple cracking of a surface: An experimental study. International Journal of Fracture. 2013;(2):293–300.

Citation

Copyright

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Article metrics

Google scholar: See link

Vol 13, Issue 2, 2019

RESIDUAL FATIGUE LIFE ESTIMATION OF CRACKED AIRCRAFT STRUCTURAL COMPONENTS UNDER LOAD SPECTRUM MODELING OF DAMAGED CONCRETE USING INITIAL DEGRADATION PARAMETER ELECTROHYDRODYNAMIC THERMAL INSTABILITY IN A WALTERS’ (MODEL B') ROTATING NANOFLUID SATURATING A POROUS MEDIUM NUMERICAL STUDY ON HEAT TRANSFER IN MULTILAYERED STRUCTURES OF MAIN GEOMETRIC FORMS MADE OF DIFFERENT MATERIALS VISCOSITY VARIATION EFFECT ON THE MAGNETIC FLUID LUBRICATION OF A SHORT BEARING See full issue

Citations

V. M. Moysyshyn, М. V. Lyskanych, L. V. Borysevych, O. Yu. Vytyaz, I. I. Voznyi

(2021)

Experimental Estimation of Design and Drilling Regime Option Influence on Drilling Tool Dynamics

METALLOFIZIKA I NOVEISHIE TEKHNOLOGII, 43(5)

10.15407/mfint.43.05.0689

V. M. Moysyshyn, A. P. Ivasyutyn, L. V. Borysevych, O. M. Vytvyts’ka

(2024)

Multifactor Empirical Models of Energy of Low-Frequency and Toothed Oscillations of the Dynamic Component of Torque on the Bit

METALLOFIZIKA I NOVEISHIE TEKHNOLOGII, 45(10)

10.15407/mfint.45.10.1205

Т. М. Kovbasiuk, Z. А. Duriagina, D. Mierzwinski, V. V. Kulyk

(2021)

Thermophysical Properties of Glass-Ceramic Coatings of PbO–ZnO–B$_2$O$_3$ System Doped with Al$_2$O$_3$, SiO$_2$, and BaO Oxides

METALLOFIZIKA I NOVEISHIE TEKHNOLOGII, 43(10)

10.15407/mfint.43.10.1313

Oleg Bazaluk, Andriy Chuzhak, Vadym Sulyma, Andrii Velychkovych, Liubomyr Ropyak, Vasyl Vytvytskyi, Vasyl Mykhailiuk, Vasyl Lozynskyi

(2022)

Determining the Tightrope Tightening Force for Effective Fixation of the Tibiofibular Syndesmosis during Osteomeatal Synthesis of Fibula Injuries

Applied Sciences, 12(10)

10.3390/app12104903

R. Liutyi, D. Liuta, I. Petryk, Robert Černý

(2021)

Structural Construction of Binders Based on Orthophosphoric Acid and Refractory Materials

Advances in Materials Science and Engineering, 2021(1)

10.1155/2021/6667769

L Ya Ropyak, V S Vytvytskyi, A S Velychkovych, T O Pryhorovska, M V Shovkoplias

(2021)

Study on grinding mode effect on external conical thread quality

IOP Conference Series: Materials Science and Engineering, 1018(1)

10.1088/1757-899X/1018/1/012014

Maciej Dutkiewicz, Taras Dalyak, Ivan Shatskyi, Tetyana Venhrynyuk, Andrii Velychkovych

(2021)

Stress Analysis in Damaged Pipeline with Composite Coating

Applied Sciences, 11(22)

10.3390/app112210676

Andriy Chuzhak, Vadym Sulyma, Lіubomyr Ropyak, Andrii Velychkovych, Vasyl Vytvytskyi, Saverio Maietta

(2021)

Mathematical Modelling of Destabilization Stress Factors of Stable-Elastic Fixation of Distal Trans- and Suprasyndesmotic Fibular Fractures

Journal of Healthcare Engineering, 2021()

10.1155/2021/6607364

V Tarelnyk, D Hlushkova, V Martsynkovskyy, M Dumanchuk, B Antoszewski, Cz Kundera, Ie Konoplianchenko, N Tarelnyk, S Hudkov, A Zahorulko

(2021)

Increasing fretting resistance of flexible element pack for rotary machine flexible coupling Part 1. Analysis of the reasons affecting fretting resistance of flexible elements for expansion couplings

Journal of Physics: Conference Series, 1741(1)

10.1088/1742-6596/1741/1/012048

Oleg Bazaluk, Orest Slabyi, Vasyl Vekeryk, Andrii Velychkovych, Liubomyr Ropyak, Vasyl Lozynskyi

(2021)

A Technology of Hydrocarbon Fluid Production Intensification by Productive Stratum Drainage Zone Reaming

Energies, 14(12)

10.3390/en14123514

L Y Ropyak, A S Velychkovych, V S Vytvytskyi, M V Shovkoplias

(2021)

Analytical study of “crosshead – slide rail” wear effect on pump rod stress state

Journal of Physics: Conference Series, 1741(1)

10.1088/1742-6596/1741/1/012039

Pavlo Prysyazhnyuk, Olexandr Ivanov, Oleh Matvienkiv, Sergiy Marynenko, Oleh Korol, Ihor Koval

(2022)

Impact and abrasion wear resistance of the hardfacings based on high-manganese steel reinforced with multicomponent carbides of Ti-Nb-Mo-V-C system

Procedia Structural Integrity, 36()

10.1016/j.prostr.2022.01.014

Liubomyr Ropyak, Thaer Shihab, Andrii Velychkovych, Vitalii Bilinskyi, Volodymyr Malinin, Mykola Romaniv

(2023)

Optimization of Plasma Electrolytic Oxidation Technological Parameters of Deformed Aluminum Alloy D16T in Flowing Electrolyte

Ceramics, 6(1)

10.3390/ceramics6010010

V. S. Antonyuk, I. Iu. Bondarenko, S. P. Vislouh, O. V. Voloshko, M. O. Bondarenko

(2023)

Heat Exchange in a Contact Zone of Nanoinstrumentation with Elements of the Microsystem Technology

Journal of Engineering Sciences, 10(1)

10.21272/jes.2023.10(1).f1

Michał Bembenek, Mykola Makoviichuk, Ivan Shatskyi, Liubomyr Ropyak, Igor Pritula, Leonid Gryn, Volodymyr Belyakovskyi

(2022)

Optical and Mechanical Properties of Layered Infrared Interference Filters

Sensors, 22(21)

10.3390/s22218105

R. M. Tatsiy, O. Yu. Pazen, S. Ya. Vovk, D. V. Kharyshyn

(2021)

Direct method of studying heat exchange in multilayered bodies of basic geometric forms with imperfect heat contact

Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (1)

10.33271/nvngu/2021-1/060

(2023)

Design of a Two-Layer Al–Al2O3 Coating with an Oxide Layer Formed by the Plasma Electrolytic Oxidation of Al for the Corrosion and Wear Protections of Steel

Progress in Physics of Metals, 24(2)

10.15407/ufm.24.02.319

Oleg M. Mandryk, Lubomur S. Shlapak, Oleh M. Tuts, Iryna L. Bodnaruk

(2023)

New Technologies, Development and Application VI

Lecture Notes in Networks and Systems, 707()

10.1007/978-3-031-34721-4_9

O. Ya. Dubei, T. F. Tutko, L. Ya. Ropyak, M. V. Shovkoplias

(2022)

Development of Analytical Model of Threaded Connection of Tubular Parts of Chrome-Plated Metal Structures

METALLOFIZIKA I NOVEISHIE TEKHNOLOGII, 44(2)

10.15407/mfint.44.02.0251

(2023)

Equilibrium of Laminated Cu/Ni/Cr Coating Under Local Load

Nanosistemi, Nanomateriali, Nanotehnologii, 21(2)

10.15407/nnn.21.02.379

O Onysko, V Panchuk, V Kopei, Y Havryliv, I Schuliar

(2021)

Investigation of the influence of the cutter-tool rake angle on the accuracy of the conical helix in the tapered thread machining

Journal of Physics: Conference Series, 1781(1)

10.1088/1742-6596/1781/1/012028

Oleh Onysko, Iulia Medvid, Vitalii Panchuk, Vesna Rodic, Cristian Barz

(2021)

Advances in Design, Simulation and Manufacturing IV

Lecture Notes in Mechanical Engineering, ()

10.1007/978-3-030-77719-7_47

Oksana Karabyn, Olga Smotr, Andrij Kuzyk, Igor Malets, Vasy Karabyn

(2023)

Lecture Notes in Data Engineering, Computational Intelligence, and Decision Making

Lecture Notes on Data Engineering and Communications Technologies, 149()

10.1007/978-3-031-16203-9_9

V. M. Moysyshyn, М. V. Lyskanych, L. V. Borysevych, R. A. Zhovniruk

(2020)

Multifactorial Empirical Model of Three-Cone Bit Gear Oscillation Energy

METALLOFIZIKA I NOVEISHIE TEKHNOLOGII, 42(12)

10.15407/mfint.42.12.1729

Sviatoslav Kurnosov, Liubomyr Ropyak, Andriy Velychkovych, Tetiana Pryhorovska, Vasyl Vytvytskyi

(2021)

New Technologies, Development and Application IV

Lecture Notes in Networks and Systems, 233()

10.1007/978-3-030-75275-0_48

Roman Tutko, Vasyl Lozynskyi

(2025)

Oscillations of the Oil Pipeline Axis with Consideration of the Inertia Component When Pumping Diesel Fuel

Energies, 18(10)

10.3390/en18102472

B Trembach

(2023)

Comparative studies of the three-body abrasion wear resistance of hardfacing Fe-Cr-C-B-Ti alloy

IOP Conference Series: Materials Science and Engineering, 1277(1)

10.1088/1757-899X/1277/1/012016

V Melnyk, V Vlasovets, Ie Konoplianchenko, V Tarelnyk, M Dumanchuk, Vas Martsynkovskyy, Yu Semirnenko, S Semirnenko

(2021)

Developing a system and criteria for directed choice of technology to provide required quality of surfaces of flexible coupling parts for rotor machines

Journal of Physics: Conference Series, 1741(1)

10.1088/1742-6596/1741/1/012030

Z. A. Duriagina, V. V. Kulyk, O. S. Filimonov, A. M. Trostianchyn, N. B. Sokulska

(2021)

The Role of Stress–Strain State of Gas Turbine Engine Metal Parts in Predicting Their Safe Life

Uspehi Fiziki Metallov, 22(4)

10.15407/ufm.22.04.643

Oleg Bazaluk, Andrii Velychkovych, Liubomyr Ropyak, Mykhailo Pashechko, Tetiana Pryhorovska, Vasyl Lozynskyi

(2021)

Influence of Heavy Weight Drill Pipe Material and Drill Bit Manufacturing Errors on Stress State of Steel Blades

Energies, 14(14)

10.3390/en14144198

(2020)

Stressed state of laminated interference-absorption filter under local loading

Functional Materials, 27(3)

10.15407/fm27.03.638

Oleh Onysko, Vitalii Panchuk, Yaroslav Kusyi, Zenovii Odosii, Tetiana Lukan

(2022)

Advances in Design, Simulation and Manufacturing V

Lecture Notes in Mechanical Engineering, ()

10.1007/978-3-031-06025-0_31

About

NUMERICAL STUDY ON HEAT TRANSFER IN MULTILAYERED STRUCTURES OF MAIN GEOMETRIC FORMS MADE OF DIFFERENT MATERIALS

Abstract

Keywords:

References

Citation

Copyright

Article metrics

Vol 13, Issue 2, 2019

Citations

Disclaimer