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ME608 project_Ravi_Hemanth

ME608 project_Ravi_Hemanth - Proceedings of Project 2006 ME...

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1 Copyright © 1996 by ASME Proceedings of Project 2006 ME 608 April 19 th , 2006, West Lafayette, IN -47907, USA PREDICTION OF EFFECTIVE THERMAL CONDUCTIVITY OF PARTICULATE COMPOSITES S. Ravi Annapragada Hemanth K. Dhavaleswarapu School of Mechanical Engineering Purdue University West Lafayette, IN 47907-2808, USA Email: [email protected] School of Mechanical Engineering Purdue University West Lafayette, IN 47907-2808, USA Email: [email protected] ABSTRACT An RVE (Representative Volume Element) based finite volume numerical model is developed to predict the effective thermal conductivity of particulate composites. A random packing algorithm is implemented to construct the two dimensional and three dimensional periodic particle distributions in the particle composite. The particles are approximated as squares and cuboids. A finite volume conduction solver is implemented to obtain the effective conductivity of the particulate composite. A harmonic mean approach is used to obtain the face conductivities between adjoining cells of the finite volume grid. Numerical experiments are performed varying the RVE size, particle conductivity and particle fraction of the particles. The results are shown to be grid independent. The predicted effective conductivities are compared with the Maxwell Solution [1] and the Hashin – Shtrikman [2] bounds. NOMENCLATURE k eff Effective thermal conductivity k Particle Thermal conductivity of particle k Matrix Thermal conductivity of matrix φ Particle fraction n RVE Particles in RVE T L Temperature of left boundary wall T R Temperature of right boundary wall q Heat flux through the RVE θ Non-Dimensional Temperature Dia o Outer Diameter Dia i Inner Diameter Subcripts old Value at Current Iteration new Value at Next Iteration INTRODUCTION To overcome individual deficiencies of homogeneous materials, composites have been used. Particulate composites are a class of composites where particles are embedded in a matrix. The prediction of thermophysical properties of such particulate composites is complicated as the heat flow paths are complicated and hence volume averaging or harmonic means fail to predict the actual effective values. Experimental studies are tedious and filled with experimental errors due to contact resistance and gap conductance between the test piece and the measuring setup. Hence we resort to numerical modeling. To predict the effective thermal conductivity of particulate composites, the whole system level size of the composite need not be considered. A Representative Volume Element (RVE) [3] could be considered on which we could perform the numerical experiments. In this current work, the numerical predictions of the overall composite material are based on the testing done on an RVE.
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