Modeling of microwave heating of particulate metals
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INTRODUCTION
MICROWAVE heating has been a unique contribution in the field of sintering of particulate materials.[1] As compared to conventional heating, microwave heating is more rapid, which results in reducing the overall sintering time.[2–5] In addition to the cost efficiency, the faster heating rate achieved in a microwave furnace minimizes microstructural coarsening and abnormal grain growth.[2,6] For powder compacts, sintering is usually associated with densification as well as concomitant microstructural coarsening.[7] If the latter is restricted, the mass atomic transport is enhanced due to the availability of more grain boundaries.[7,8] Recent studies on various systems have shown higher sintered density and mechanical property enhancement in microwave sintered compacts as compared to their conventionally sintered counterparts.[6,9,10] Despite the use of microwaves in sintering ceramics, it has only recently been shown that metals too can couple with microwave and get heated provided they are in powder form.[11] This has resulted in widespread interest in sintering of these compacts in microwave furnaces. Despite its potential for industrial applications, the phenomenology of microwave heating of metals remains to be fully understood. Although the large surface area in powders makes coupling of metal powders with microwave more amenable, yet a clear understanding of microwave interaction and its absorption lacks in terms of modeling of the heating process. This article describes a new approach to explain the microwave sintering of particulate metals using a twodimensional (2-D) coupled electromagnetic-thermal model. As part of the current study, the temporal temperature distribution was simulated using 2-D finite difference time domain (FDTD) calculations to obtain the electromagnetic field parameters. The model also incorporates the effect of particle size, emissivity, and susceptor on heating. The validation of predicted thermal profiles was done on tin, copper, and tungsten-alloys powders through careful mea-
surements of the temperature variation with time in a multimode-cavity microwave furnace. II.
MODELING APPROACH
Modeling of microwave heating involves solving the Maxwell’s equations of electromagnetism simultaneously with the heat-transfer equation.[12] To determine the electromagnetic fields in a cavity, the FDTD technique was used by Yee[13] and Zhang et al.[14] Zhang et al.’s[14] results showed that the numerical methodology can be used in proper designing of the microwave cavities for various applications. It was indicated that by appropriate selection of the field points, a set of finite difference equations can be formulated for a boundary condition involving perfectly conductive surfaces. These solutions were used for calculating power absorption, flow fields, and temperature patterns in nonmetallic systems.[14,15,16] Subsequently, a quasi-analytical model was proposed by Lasri et al.,[17] to examine energy conversion during the microwave sintering of a ceramic that is surrounded by a susceptor. El
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