A detailed analysis has been carried out by solving coupled energy and mass balance equations along with Helmholtz equation of microwave propagation to investigate the role of microwave heating strategies in enhancing the progress of a first-order endothermic reaction in "thin," "intermediate," and "thick" regimes of microwave heating. It has been shown that heating strategy plays a critical role in maximizing the efficiency of microwave heated reactors, where progress of reactor can be greatly accelerated at a given input power by either configuring microwave sources at both sides of the reactor or preferentially focusing them on one side. A series of master curves have been provided showing percentage saving of reaction time in various configurations of microwave heated reactors compared to their conventional counterparts, which can be efficiently used to select appropriate heating strategy for different dimension and dielectric properties of the reacting medium. © 2012 American Institute of Chemical Engineers (AIChE).

Tanmay Basak

Department Of Chemical Engineering

Madhuchhanda Bhattacharya

Sandeep Kr Venkata

ENDOTHERMIC REACTIONS

Energy

First-order

Heating strategy

INPUT POWER

MASS BALANCE EQUATIONS

Master curve

microwave propagation

MICROWAVE SOURCES

numerical solution

Transport

Dielectric properties

Heat transfer

HELMHOLTZ EQUATION

Mathematical models

Reaction intermediates

Microwave heating

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IIT Madras

AIChE Journal

A comprehensive theoretical analysis has been carried out to study the effect of microwave heating on a first order endothermic reactions. The mathematical model considers detailed description of microwave power absorption along with transport of heat and mass within the reacting domain. The effect of microwave heating on the progress of the endothermic reaction has been analyzed in terms of spatial nonuniformities as well as overall progress of the reaction compared to the case of conventional heating. The analysis is carried out for all possible spectrum of microwave power absorption, which enables us to quantify the effect of microwave heating in terms of percentage savings of reaction time. The detail mathematical model also allows to identify and study the effect of various parameters responsible for describing the interaction between the heat and mass transport in presence of volumetric heating. A systematic and thorough analysis on the effect of these parameters demonstrate an interesting regime, where volumetric heating may not yield better progress than conventional heating. © 2011 Elsevier Ltd.

Chemical Engineering Science

A comprehensive theoretical analysis for the effect of microwave heating on the progress of a first order endothermic reaction

This work performs linear stability analysis to investigate the onset of convection due to microwave incidences in a horizontal oil layer. The probability of onset has been characterized in terms of critical Rayleigh number (Rac), while the microwave power required to initiate convection has been quantified in terms of modified Rayleigh number (Ra- c). The associated convection cell size has been illustrated by critical wave number (kc). These critical numbers (Rac, Ra-c, and kc) have been determined for the entire spectrum of oil thicknesses ranging from thin to thick samples and various possible microwave source configurations starting from one sided to distributed incidences. It has been shown that the critical numbers oscillate with oil thickness in intermediate regime indicating preferential onset for specific oil thicknesses. It has also been shown that microwave source configuration plays an important role in controlling the onset of convection. Finally, the variations of Rac and kc have been correlated to the spatial patterns of absorbed microwave power within oil, while modified Rayleigh numbers are shown to follow the qualitative trends of Δ Ts, where Δ Ts is the base state temperature difference between top and bottom plate. The results are useful not only for forecasting the onset but also for controlling onset of convection by selecting suitable experimental parameters. © 2009 American Institute of Physics.

Fulltext

Journal of Applied Physics

Linear stability analysis for the onset of convection during microwave heating of oil confined within horizontal plates

A closed form analysis based on Finite Fourier Transformation (FFT) has been carried out to predict the heating characteristics in the presence of microwave induced volumetric heat sources. A scaling analysis shows that temperature distributions within a material during microwave heating evolve in two stages, namely small time and large time. The inverse of square of second eigenvalue along with thermal diffusivity determines the threshold time scale between these two regimes. During small time evolution, the spatial temperature distribution follows absorbed power profiles, whereas the temperature distributions are slaved by first eigenfunction and independent of volumetric heat distribution at large time evolution. In all the cases, the variation of temperature within the material is guided by a dimensionless number N G = L2q0/kTref. For NG ≪ 1, almost uniform temperature distributions are attained and a lump parameter model can be used. In contrast, nonuniformity in absorbed power distributions amplifies in temperature distribution for materials with N G ≫ 1, where there exists a possibility of local hot spot formation if absorbed power exhibits local maxima. The applicability of this analysis has been illustrated to forecast heating characteristics within various materials. © 2007 American Institute of Chemical Engineers.

Generalized scaling on forecasting heating patterns for microwave processing

This paper presents a comprehensive, closed-form-based material-invariant analysis on the occurrence and characterization of spatial resonances in microwave-induced absorbed-power distribution within a material. We have shown that occurrence of resonance depends on competitive interactions between sinusoidal and exponential position dependencies characterized by wave number (Nw) and penetration number (Np) confining the resonating regime of absorbed power within thick- (Np ≫. 1) and thin-sample (Nw ≪ 0.5) asymptotic limits, where it has been shown for the first time that the thick-sample limit depends on distribution of microwave source (φ0) while the thin-sample limit is invariant of φ0. Within the resonating regime, distribution of microwave source (φ0) and wave number of surrounding free space (N w,0) have shown to play an important role in deciding resonating features of absorbed power in addition to Nw and Np, which in the literature have been considered to be the only governing factors for resonance. For example, absorbed power for the case of one-side incidence (φ0 = 0 or 1) shows resonance only if Nw,0 √Nw2+Np2/4π2, where locations of resonating peaks are strong function of Nw,0 in addition to Nw and Np. On the other hand, for both-side incidence with equal power input from left and right sides (φ0 = 1/2), occurrence of resonance as well as locations of resonating peaks are independent of Nw,0. For intermediate φ0, the absorbed power shows resonance if Nw, Np, Nw,0, and φ0 satisfy the condition Cn,3 ≠ 0 as given in this work. We have performed a detail analysis for all the cases in order to quantify various resonating features of absorbed power and derived correlations for predicting the locations of resonating peaks, which are shown to be in good accordance with actual positions. © 2007 American Chemical Society.

Industrial and Engineering Chemistry Research

Detailed material-invariant analysis on spatial resonances of power absorption for microwave-assisted material processing with distributed sources

A new closed form material invariant analysis on resonances of microwave induced power absorption is presented. It is shown that resonances in average power is confined within two asymptotic limits of thin and thick samples, and the resonances occur if λm ≤ l.5Dp.mfor λm ≈ λo and λm ≤ 3Dp,m for λm ≉ λo. Here λm and Dp,m denote the wavelength and penetration depth within the sample, respectively, and λo is the wavelength within the free space. It has been shown that average absorbed power does not exhibit resonance for one side incidence if λm ≈ λo, while the occurrence of resonance is independent of Φl for λm ≈ Ao. Here, Φl is the fractional power input from the left side. The amplitudes of subsequent resonating peaks are also shown to decay monotonically with sample length for λm ≈ Ao, while they vary nonmonotonically for λm ≉ λo and Φl ≉ 0, 1 or 1/2 due to suppressions of odd (for λm &lt; λo), or even (for λm &gt; λo) resonating peaks, which increase as Φl approaches 1/2 from either 0 or 1. Finally, at Φl ≈1/2 with λm ≉ λo odd (for λm &lt; λo), or even (for λm &gt; λo) resonating peaks of average absorbed power vanish reducing the number of resonating points by a factor of two from one side incidence (Φ, ≈ 0 or 1), to both side incidence with equal power input from left and right sides (Φ≈ .1/2). This work provides correlations (corresponding to λm ≈ λo and λm ≈ λo) forpredicting the locations of resonating peaks as function of λm/λo, λm/Dp,m, and Φl. The theoretical prediction on average power characteristics have been shown to be useful in forecasting the heating patterns for efficient material processing. © 2006 American Institute of Chemical Engineers.

New closed form analysis of resonances in microwave power for material processing

Role of microwave heating strategies in enhancing the progress of a first-order endothermic reaction

Journal	AIChE Journal
ISSN	00011541
Open Access	No