MODELLING OF TRANSIENT HEAT TRANSPORT IN CRYSTALLINE SOLIDS USING THE INTERVAL LATTICE BOLTZMANN METHOD (TWO-DIMENSIONAL MODEL)


Abstract

In the paper the two-dimensional numerical modelling of heat transfer in crystalline solids is considered. In the mathematical description the relaxation time and the boundary conditions are given as interval numbers. The problem formulated has been solved by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic.


Keywords

Boltzmann transport equation; interval lattice Boltzmann method; directed interval arithmetic

Escobar R.A., Ghai S.S., Jhon M.S., Amon C.H.: Multi-length and time scale thermal transport using the lattice Boltzmann method with application to electronics cooling, Journal of Heat and Mass Transfer, 2006, 49, pp. 97-107.

Eshraghi M., Felicelli S.D.: An implicite lattice Boltzmann model for heat conduction with chase chandr, International Journal of Heat and Masss Transfer, 2012, 55, pp. 2420-2428.

Markov S.M.: On Directed Interval Arithmetic and its Applications, Journal of Universal Computer Science, 1995, Vol. 1, pp. 514-526.

Narumanchi S., Murthy J.Y., Amon C.H.: Simulation of unsteady small heat source effects in sub-micron heat conduction, J. Heat Transfer, 2003, 123, pp. 896-903.

Neumaier A.: Interval methods for system of equations, Cambridge University Press, Cambridge, New York, Port Chester, Melbourne, Sydney, 1990.

Piasecka Belkhayat A.: Interval boundary element method for 2D transient diffusion problem using directed interval arithmetic, Engineering Analysis with Boundary Elements, 2011, Vol. 35, Issue 3, pp. 259-263.

Piasecka Belkhayat A.: The interval lattice Boltzmann method for transient heat transport, Scientific Research of the Institute of Mathematics and Computer Science, 2009, 1(8), Częstochowa, pp. 155-160.

Download

Published : 2014-03-12


Piasecka-Belkhayat, A., & Korczak, A. (2014). MODELLING OF TRANSIENT HEAT TRANSPORT IN CRYSTALLINE SOLIDS USING THE INTERVAL LATTICE BOLTZMANN METHOD (TWO-DIMENSIONAL MODEL). Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 4(1), 69-71. https://doi.org/10.5604/20830157.1093212

Alicja Piasecka-Belkhayat  alicja.piasecka@polsl.pl
Silesian University of Technology, Faculty of Mechanical Engineering, Institute of Computational Mechanics and Engineering  Poland
Anna Korczak 
Silesian University of Technology, Faculty of Mechanical Engineering, Institute of Computational Mechanics and Engineering  Poland