Micro-macro model for prediction of local temperature distribution in heterogeneous and two-phase media

• Autorzy: Furmański P. , Seredyński M. , Łapka P. , Banaszek J.
• Języki publikacji: EN

Abstrakty

EN

Heat flow in heterogeneous media with complex microstructure follows tortuous path and therefore determination of temperature distribution in them is a challenging task. Two-scales, micro-macro model of heat conduction with phase change in such media was considered in the paper. A relation between temperature distribution on the microscopic level, i.e., on the level of details of microstructure, and the temperature distribution on the macroscopic level, i.e., on the level where the properties were homogenized and treated as effective, was derived. The expansion applied to this relation allowed to obtain its more simplified, approximate form corresponding to separation of micro- and macro-scales. Then the validity of this model was checked by performing calculations for 2D microstructure of a composite made of two constituents. The range of application of the proposed micro-macro model was considered in transient states of heat conduction both for the case when the phase change in the material is present and when it is absent. Variation of the effective thermal conductivity with time was considered and a criterion was found for which application of the considered model is justified.

Słowa kluczowe

EN

heterogeneous media; heat conduction; micro-macro modeling

PL

materiały niejednorodne; przewodnictwo ciepła; mikro modelowanie; makromodelowanie

• Wydawca: Wydawnictwo Instytutu Maszyn Przepływowych PAN ; Komitet Termodynamiki i Spalania PAN
• Czasopismo: Archives of Thermodynamics
• Rocznik: 2014
• Tom: Vol. 35, no. 3
• Strony: 81--103
• Opis fizyczny: Bibliogr. 13 poz., il.

Twórcy

autor

Furmański P.

• Institute of Heat Engineering, Warsaw University of Technology, Nowowiejska 25, 00-665 Warszawa, Poland

autor

Seredyński M.

• Institute of Heat Engineering, Warsaw University of Technology, Nowowiejska 25, 00-665 Warszawa, Poland

autor

Łapka P.

• Institute of Heat Engineering, Warsaw University of Technology, Nowowiejska 25, 00-665 Warszawa, Poland

autor

Banaszek J.

• Institute of Heat Engineering, Warsaw University of Technology, Nowowiejska 25, 00-665 Warszawa, Poland

Bibliografia

• [1] BANASZEK J., FURMAŃSKI P. AND REBOW M.: Modelling of Transport Phenomena in Cooled and Solidifying Single Component and Binary Media. Warsow University of Technology, Warsaw 2005.
• [2] CIOBANAS A. I., FAUTRELLE Y.: Ensemble averaged multi-phase Eulerian model for columnar/equiaxed solidification of a binary alloy: II. Simulation of the columnar-to-eqmaxed transition (GET). J. Phys. D: Appl. Phys. 40(2007), 4310-4336.
• [3] DAS S.: Modeling mixed micro structures using a multi-level cellular automata finite dement framework. Computat. Mater. Sci. 47(2010), 705-711.
• [4] ESHRAGHI M., FELICELLI S.D.: An implicite lattice Boltzmann model for heat conduction with phase change. Int. J. Heat & Mass Trans. 55(2012), 2420-2428.
• [5] FURMAŃSKI P.: Microscopic-Macroscopic Modelling of Transport Phenomena During Solidification in Heterogeneous Systems, Courses and Lectures - No. 449 "Phase Change with Convection: Modelling and Validation", CISM Springer-Verlag 2004, 55-126.
• [6] GANAPATHYSUBRAMANIAN B., ZABARAS N.: A stochastic multi-scale framework for modeling flow through random heterogeneous porous media. J. Cornput. Phys. 228(2009), 591-618.
• [7] MISHRA S.M., BEHERA N.C., GARG A.K., MISHRA A.: Solidification of a 2-D semitransparent medium using the lattice Boltzmann method and the finite volume method. Int. J. Heat Mass Tran. 51(2008), 4447-4460.
• [8] RUAN CH., OUYANG J., Liu SH.: Multi-scale modeling and simulation of crystallization during cooling in short fiber reinforced composites. Int. J. Heat Mass Tran. 55(2012), 1911-1921.
• [9] SANYAL D., RAMACHANDRARAO P., GUPTA O.P.: A fast strategy for simulation of phase change phenomena at multiple length scales. Cornput. Mater. Sci. 37(2006), 166-177.
• [10] TAN L., ZABARAS N.: Multi-scale modeling of alloy solidification using a database approach. J. Comput. Phys. 227(2007), 728-754.
• [11] WANGJ.-L., WANG F.-M., ZHAO Y.-Y., ZHANG J.-M., REN W.: Numerical simulation of SD-microstructures in solidification processes based on the CAFE method. Int. J. Miner. Metall. Mater. 16(2009), 640 645.
• [12] ZENG Q.H., Yu A.B., Lu G.Q.: Multi-scale modeling and simulation of polymer nano-composites. Prog. Polym. Sci. 33(2008), 191-269.
• [13] ANSYS FLUENT version 14.0.

Uwagi

EN

The authors are grateful to the Polish Ministry of Science and Higher Education for funding from its Grant No. N N512 361634.