Mathematical Models of Heat Exchange in Multilayer Constructions with Various Thermalphysic Characteristics in Industrial Installations

A. I. Akimov; E. O. Karakulina; I. A. Akimov; Vitaly Tugov

doi:10.15866/iremos.v11i2.13904

Mathematical Models of Heat Exchange in Multilayer Constructions with Various Thermalphysic Characteristics in Industrial Installations

A. I. Akimov⁽¹⁾, E. O. Karakulina⁽²⁾, I. A. Akimov⁽³⁾, Vitaly Tugov^(4*)

^(*) Corresponding author

Authors' affiliations

DOI: https://doi.org/10.15866/iremos.v11i2.13904

Abstract

The article presents the developed mathematical models of heat exchange in multilayer flatconstructions with honeycomb filler. The mathematical description of temperature process in composite materials polymerization at three production stages is made. This work continues researches in the field of thermalphysic processes modeling in multilayered designs. The application features of the method of finite integral transformations with Green's function and the isothermal surfaces method are considered. Describing the product cooling process the Laplace finite integral transformation has been used. Heat emission is measured in the course of polymerization. The universality of the developed mathematical apparatus allows to create the software for experimentations on the computer. The authors offer also further directions of the research.
Copyright © 2018 Praise Worthy Prize - All rights reserved.

Keywords

Heat Exchange; Polymerization; Multilayer Constructions; Composites; Thermal Stresses; Deformations

Full Text:

PDF

References

Kartashov, E.M. Analytical methods in the theory of heat conductivity of solid bodies. – Moscow: Higher school, 1985. – 479 p.

Lykov, A.V. Theory of heat conductivity. – Moscow: Publishing house «Higher school», 1967. – 600 p.

Akimov, I.A., Tugov, V.V. Creation of mathematical model of polymerization process at products production from composite materials // Computer integration of production and IPI-technology: Materials of the VII All-Russian scientific and practical conference. - Orenburg, 2015. – pp. 228–231.

El Youbi, M., Rougui, M., Modeling the Effect of Boundary Conditions on the Stability of Multilayer Composite Structures: Case of Buckling Bifurcation. Analytical and Numerical Results Using “SHELL 181” Element, (2015) International Review of Mechanical Engineering (IREME), 9 (3), pp. 307-313.
http://dx.doi.org/10.15866/ireme.v9i3.6082

Abdul Azeez, M.F., Vakakis, A.F. Axisymmetric transient solutions of the heat diffusion problem in layered composite media, Int. J. Heat Mass Transfer 43 (2000) 3883–3895.
http://dx.doi.org/10.1016/s0017-9310(99)00386-5

Aviles-Ramos, C., Haji-Sheikh, A., Beck, J.V. Exact solution of heat conduction in composites and application to inverse problems, ASME J. Heat Transfer 120 (1998), pp. 592-599.
http://dx.doi.org/10.1115/1.2824316

de Monte, F. «Unsteady heat Conduction in Two-Dimensional Two Slab-Shaped Regions. Exact Closed-Form Solution and Results», Int. J. Heat Mass Transfer, 46, 8, 2003, pp. 1455–1469.
http://dx.doi.org/10.1016/s0017-9310(02)00417-9

de Monte, F. An analytic approach to the unsteady heat conduction processes in one-dimensional composite media International Journal of Heat and Mass Transfer 45 (2002) 1333–1343.
http://dx.doi.org/10.1016/s0017-9310(01)00226-5

Heidemann W., Mandel H., Hahne E. Computer aided determination of closed form solutions for linear transient heat conduction problems in inhomogeneous bodies, in: L.C. Wrobel, C.A. Brebbia, A.J. Nowak (Eds.), Advanced Computational Methods in Heat Transfer III, Computational Mechanics Publications, Southampton, Boston, 1994, pp. 19–26.

Lu, X., Viljanen, M. An analytical method to solve heat conduction in layered spheres with time-dependent boundary conditions, Phys. Lett. A 351 (2006) 274–282.
http://dx.doi.org/10.1016/j.physleta.2005.11.017

Prashant K. Jaina, Suneet Singh, Rizwan-uddin An exact analytical solution for two-dimensional, unsteady, multilayer heat conduction in spherical coordinates International Journal of Heat and Mass Transfer 53 (2010) 2133–2142.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2009.12.035

Akimov, I.A., Akimov, A.I., Karakulina, O.E. Research and development of mathematical model at the first stage of composite materialsproduction in Scholz installations // theVolga Scientific and Technical Bulletin. – 2016. – Vol. 1. – pp. 54–58.

Tugolukov, E.N. Solution of problems of heat conductivity by method of final integral transformations: manual. – Tambov: Tambov State Technical University, 2005. – 116 p.

Akimov, I.A, Karakulina, O.E. Research and development of mathematical model at the second stage of composite materials production in Scholz installations // the Volga Scientific and Technical Bulletin. – 2016. – Vol. 2. – pp. 93–97.

Refbacks

There are currently no refbacks.

Username
Password
Remember me