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.

Tanmay Basak

Department Of Chemical Engineering

Madhuchhanda Bhattacharya

Rajtharun Senagala

mathematical modeling

MICROWAVE EFFICIENCY

Nonisothermal

Reaction engineering

Simulation

Mathematical models

MICROWAVE GENERATION

Microwave heating

MICROWAVE POWER TRANSMISSION

heating

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IIT Madras

Chemical Engineering Science

Microwaves are shown to provide higher heating rates, however, the destructive interference of propagating waves leads to poor heating performance for specific lengths of samples. Enhanced processing rates for all length scales due to microwave incidence would be important for material processing and current work on discrete material processing involving intermediate air layers with microwave incidence attempts to fill the gap. Simulation studies involve electric field, microwave power and temperature which are obtained based on microwave propagation and energy balance equations. A preliminary investigation on average power absorption within beef (highly lossy) and bread (low dielectric loss) samples vs sample thickness exhibits a few local minima of average power which forms the basis of investigation on the role of discrete samples. The thickness of air layer plays a significant role to dramatically alter the interference of waves and power absorption within each sample layer. It is observed that three discrete sample layers (case 3) exhibit larger heating rate than that within the continuous sample (case 1) for specific sample thicknesses. In general, case 2 samples (with one intermediate air layer) show lesser power or heating enhancement in the presence of either one side or both sides microwave incidence. Based on two factors, 'large heating rate' and 'optimal thermal runaway', the efficient heating strategy may be derived for both high and low lossy food substances. © 2013 Elsevier Ltd.

Role of various distributions of discrete samples on efficient microwave associated material processing

This work presents a theoretical analysis on savings of energy during an endothermic reaction under microwave heating compared to conventional heating and shows the use of metal coated bounding surface to enhance the energy savings in otherwise low saving zones. Main thrust of this work is the quantification of energy savings for various probable microwave heating scenarios that may arise either due to varying reactor dimension (2L) over thin, intermediate and thick regimes or due to varying dielectric properties of the reactor. The analysis considers detailed transport equations in conjunction with Helmholtz equation for microwave propagation within a semiinfinite batch reactor. Simulations show that use of microwave can significantly save energy (as high as 60%) depending on reactor configuration. Simulations also show efficient use of metal coated bounding surface to enhance energy savings for reactors with 2L/λeff = 0.5n-0.25, where n = 1, 2, 3... and λeff is wavelength of microwave within the reactor. The enhancement is found to be 2 and 1.5 times at 2L/λeff = 0.25 and 0.75, respectively. Various regions of efficient use of metal coated bounding surface for different microwave heating scenarios have been identified in a series of master curves. © 2013.

Energy

A theoretical study on the use of microwaves in reducing energy consumption for an endothermic reaction: Role of metal coated bounding surface

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).

AIChE Journal

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

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

A theoretical analysis has been carried out to study efficient microwave heating of porous dielectrics. The heating effects are analyzed for two types of porous material: beef-air (b/a) and beef-oil (b/o) with and without ceramic supports (Al2O3 and SiC). Three test cases for porosities (φ{symbol}) 0.3, 0.45 and 0.6 are considered. The maxima in average power corresponding to resonances occur at various sample thicknesses for all porous materials with and without supports and two dominant resonance modes R1 and R2 are considered where the average power at R1 is larger than that at R2. It is interesting to observe that average power absorption is enhanced for samples (b/a and b/o) in presence of Al2O3 support whereas the average power is smaller with SiC support. From the analysis on spatial distribution of electric field, power and temperature, it is seen that runaway heating is observed at the face which is not attached with support for b/a samples, and the intensity of thermal runaway increases with porosity whereas lower thermal runaway is observed for b/o samples at all porosity values. An efficient heating strategy has been investigated for various distributions of microwave incidences. It is observed that one side incidence may correspond to the largest heating rates whereas distributed sources may correspond to smaller thermal runaway for both beef-air (b/a) and beef-oil (b/o) samples. © 2006 Elsevier Ltd. All rights reserved.

International Journal of Heat and Mass Transfer

Effect of ceramic supports on microwave processing of porous food samples

This paper presents a comprehensive material invariant analysis on asymptotes and resonances of absorbed power distribution. A closed-form solution for absorbed power in the presence of distributed microwave source has been derived from the first principle, which shows the existence of two distinct asymptotic regimes: thin and thick samples. Within thin samples, absorbed power is shown to be weak function of position, while it decays exponentially within thick sample. In between thick and thin samples, absorbed power is shown to exhibit resonances, where a detailed analysis has been performed to reveal various resonating characteristics of average power. The main purpose of the analysis is to predict the occurrence of resonances and establish correlations for a priori prediction of resonating sample dimensions in the presence of various distributed microwave incidences. The closed-form analysis has been shown to be useful in forecasting the heating characteristics: hot spot vs uniform heating. It has been shown that the heating characteristics can be tuned by suitable distribution of microwave source towards optimal material processing. © 2006 Elsevier Ltd. All rights reserved.

Journal	Chemical Engineering Science
ISSN	00092509
Open Access	No