## THERMAL SCIENCE

International Scientific Journal

### ON HEAT CONDUCTION IN PERIODICALLY STRATIFIED COMPOSITES WITH SLANT LAYERING TO BOUNDARIES

**ABSTRACT**

The paper deals with the modelling of heat conduction in periodically stratified composites with slant layering to boundaries. The relations of the homogenized model with microlocal parameters for the case of layering parallel to the boundary are transformed to conform to requirements of the composite geometry. The plane problem of periodically stratified half-space with slant layering heated by given boundary temperature is solved analytically. The obtained results are analyzed and compared with the solutions for special cases: (1) homogenized half-space, (2) half-space with parallel layering to the boundary, (3) half-space with vertical layering to the boundary.

**KEYWORDS**

PAPER SUBMITTED: 2012-06-19

PAPER REVISED: 2013-01-14

PAPER ACCEPTED: 2013-02-27

PUBLISHED ONLINE: 2013-04-13

**THERMAL SCIENCE** YEAR

**2015**, VOLUME

**19**, ISSUE

**1**, PAGES [83 - 94]

- Aurialt, J. L., Effective Macroscopic Description for Heat Conduction in Periodic Composites, International Journal of Heat and Mass Transfer, 26 (1983), pp. 861-869
- Backhalov, N. S., Panasenko, G. P., Averaged Processes in Periodic Media, Science, Moscow, 1984, (in Russian)
- Bedford, A., Stern, M., Toward Diffusing Continuum Theory of Composite Materials, Journal of Applied Mechanics, 38 (1971), pp. 8-14
- Bufler, H., Stationary Heat Conduction in a Macro- and Microperiodically Layered Solid, Archives of Applied Mechanics, 70 (2000), pp. 103-114
- Furmański, P., Heat Conduction in Composites: Homogenization and Macroscopic Behavior, Applied Mechanics Reviews, 50 (1997), pp. 327-356
- Ignaczak, J., Baczyński, Z. F., On a Refined Heat-conduction Theory of Microperiodic Layered Solids, Journal of Thermal Stresses, 20 (1997), pp. 749 - 771
- Woźniak, Cz., A Nonstandard Method of Modeling of Thermoelastic Composites, International Journal of Engineering Science, 25 (1987), pp. 483-499
- Maewal, A., Homogenization for Transient Heat Conduction, ASME Journal of Applied Mechanics, 46 (1979), pp. 945-946
- Manevith, L. I., Adrianov, I. V., Osmyan, V. G., Mechanics of Periodically Layered Heterogenous Structures, Springer, Berlin, 2002
- Matysiak, S. J., Woźniak, Cz., On the Modelling of Heat Conduction Problem in Laminated Bodies, Acta Mechanica, 65 (1986), pp. 223-238
- Woźniak, Cz., Wierzbicki, E., Averaging Techniques in Thermomechanics of Composite Solids. Tolerance Averaging Versus Homogenization, Wydawnictwo Politechniki Częstochowskiej, Częstochowa, 2000
- Matysiak, S. J., Yevtushenko, A. A., Ivanyk, E. G., Temperature Field in a Microperiodic Two - layered Composite Caused by a Circular Laser Heat Source, Heat and Mass Transfer, 34 (1998) pp. 127-133
- Matysiak, S. J., Yevtushenko, A. A., Konieczny, S., Distribution of Friction Heat During Cold - rolling of Metals by Using Composite Rolls, Numerical Heat Transfer, Part A, 34 (1998), pp. 719-729
- Matysiak, S. J., Pauk, V., Plane Contact Problem for Periodic Laminated Composite Involving Frictional Heating, Archive of Applied Mechanics, 66 (1995), pp. 82 - 89
- Kaczyński, A., Matysiak,,S. J., On the Three Dimensional Problem of an Interface Crack Under Uniform Heat Flow in a Bimaterial Periodically-layered Space, International Journal of Fracture, 123 (2003), pp. 127-138
- Kaczyński, A., Matysiak, S. J., Thermal Stresses in a Laminate Composite with a Row of Interface Cracks, International Journal of Engineering Science, 27 (1989), pp. 131-147
- Matysiak, S. J., Yevtushenko, A. A., Kuciej, M., Temperature Field in the Process of Braking of a Massive Body with Composite Coating, Materials Sciences, 43 (2007), pp. 62-69
- Kulchytsky - Zhyhailo, R., Matysiak, S. J., On Heat Conduction Problem in a Semi-infinite Periodically Laminated Layer, International Communications in Heat and Mass Transfer, 32 (2005), pp. 123-132
- Kulchytsky - Zhyhailo, R., Matysiak, S. J., On Some Heat Conduction Problem in a Periodically Two-layered Body: Comparative Results, International Communications in Heat and Mass Transfer, 32 (2005), pp. 332-340
- Matysiak, S. J., Perkowski, D. M., On Heat Conduction in a Semi-infinite Laminated Layer. Comparative Results for Two Approaches, International Communications in Heat and Mass Transfer, 37 (2010), pp. 343-349
- Gradshteyn, I. S., Ryzhik, I. M., Tables of Integrals, Series and Products, Science, Moscow, (1971), (in Russian)