Generalized scaling on forecasting heating patterns for microwave processing

Abstract

in Wiley InterScience (www.interscience.wiley.com).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 5 L 2 q 0 /kT ref . For N G ( 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 American Institute of Chemical Engineers AIChE J, 54: 56-73, 2008 Keywords: microwave heating, modeling, analytical solution, Finite Fourier Transformation IntroductionMicrowave radiations within frequency range 300 MHz-300 GHz are commonly used for material processing due to their ability to generate volumetric heat sources. [1][2][3][4][5] Volumetric heating results in enhanced processing rate and various applications, based on microwave radiations have been reported by earlier researchers. A number of experimental, as well as theoretical/numerical studies have been carried out for microwave heating, thawing, drying, material processing etc. [1][2][3][4][5][6][7][8][9][10][11][12][13] Ayappa et al. 1,2 carried out theoretical and numerical studies of microwave power and temperature dynamics in presence of uniform plane wave. The numerical predictions of temperature within one and two-dimensional (2-D) samples were obtained using finite element method (FEM). Further, FEM has also been used by Basak and Ayappa 5 and Bhattacharya et al. 6 for microwave thawing of 1-D samples in the presence of uniform plane wave. Liu et al. 7 carried out theoretical studies on evaluation of microwave power in lossy dielectric materials within 3-D cavities. They obtained electric and magnetic fields using finite difference time domain (FDTD) algorithm. Later Liu et al. 8 extended FDTD algorithm to evaluate power and temperature within polymeric materials inside a ridge waveguide. FDTD method was further used by Zhang et al. 9,10 for analyzing microwave heating of tissues and natural convection within 3-D waveguides.Correspondence concerning this article should be addressed to T. Basak at tanmay@ iitm.a...

Microwave material processing—a review

“…Figure 14 shows the dimensionless temperature distribution and absorbed power distribution for microwave processing of shrimp, bread, potato and alumina slabs of length 2.5 cm and heat transfer coefficient 2 W m À2 K À1 . 59 It can be seen that the temperature distribution of shrimp and potato were in accordance with absorbed power profiles and whereas alumina sample exhibited uniform temperature distributions. Also, for shrimp and potato samples, the internal oscillations were found to die off with time.…”

“…71 Similarly, discrete samples with large air thickness have the tendency to minimize thermal runaway than continuous samples, especially for high lossy substances (beef samples). 101 Further, Bhattacharya and Basak 59 provided a closed form solution of energy balance equation with microwave power absorption, which is a function of spatially distributed electric field. finite Fourier transformation was used to obtain the closed form solution for temperature field.…”

“…Also, for shrimp and potato samples, the internal oscillations were found to die off with time. 59 Vriezinga 102 has modeled the microwave heating of slabs of water bound with a gel and it was found that the phenomenon of thermal runaway was basically caused by resonance of the electromagnetic waves within the object, combined with heat loss. Thermal runaway can be described using the average temperature of the nonisothermal slab, regardless of the Biot number.…”

Microwave Sintering: Fundamentals and Modeling

“…This is usually referred to as an inverse temperature profile, specific for microwave heating. If the distribution of the absorbed microwave power, w , is nonuniform, then the temperature distribution follows the power distribution on short timescales, but on longer timescales it is determined by thermal conduction across the entire workpiece dimensions . A simple comparative analysis of the temperature uniformity versus heating rate for microwave and conventional heating can be found in Ref.…”

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

“…It may be noted that microwave heating can be highly nonuniform and lead to local hot spots depending on the configurations of the reacting system. Local hot spots may cause dramatic enhancement of reaction rate locally and result in the observed acceleration of overall progress of reaction. In such cases, use of average temperature (as has been done in earlier works) may lead to speculation of athermal effect of microwave heating.…”