Tanmay Basak

Role of length scales on microwave thawing dynamics in 2D cylinders

Microwave (MW) thawing of 2D frozen cylinders exposed to uniform plane waves from one face, is modeled using the effective heat capacity formulation with the MW power obtained from the electric field equations. Computations are illustrated for tylose (23% methyl cellulose gel) which melts over a range of temperatures giving rise to a mushy zone. Within the mushy region the dielectric properties are functions of the liquid volume fraction. The resulting coupled, time dependent non-linear equations are solved using the Galerkin finite element method with a fixed mesh. Our method efficiently captures the multiple connected thawed domains that arise due to the penetration of MWs in the sample. For a cylinder of diameter D, the two length scales that control the thawing dynamics are D/D-p and D/lambda(m), where D-p and lambda(m) are the penetration depth and wavelength of radiation in the sample respectively. For D/D-p, D/lambda(m) much less than 1 power absorption is uniform and thawing occurs almost simultaneously across the sample (Regime I). For D/D-p much greater than 1 thawing is seen to occur from the incident face, since the power decays exponentially into the sample (Regime III). At intermediate values, 0.2 < D/D-p, D/lambda(m) < 2.0 (Regime II) thawing occurs from the unexposed face at smaller diameters, from both faces at intermediate diameters and from the exposed and central regions at larger diameters. Average power absorption during thawing indicates a monotonic rise in Regime I and a monotonic decrease in Regime III. Local maxima in the average power observed for samples in Regime II are due to internal resonances within the sample. Thawing time increases monotonically with sample diameter and temperature gradients in the sample generally increase from Regime I to Regime III

Analysis of resonances during microwave thawing of slabs

Resonances or maxima in power absorption due to microwaves incidence within a slab are analyzed via transmitted and reflected waves. A generalized mathematical formulation for uniform plane waves has been established to analyze traveling waves, stationary waves and microwave power absorption within a multiphase sample. Preliminary studies based on the generalized mathematical analysis in ice and water slabs illustrate that greater amplitudes of traveling and stationary waves occur within ice samples, whereas, greater intensity of spatial resonances in microwave power occurs for water samples due to a greater dielectric loss of water. Microwave thawing is studied for specific sample thicknesses which are selected based on greater power distribution within water samples. The enthalpy method is employed for modeling of thawing of ice samples where a superficial mushy region is assumed around the melting point. Depending on the sample thickness, thawing may occur from the unexposed face as well as both the faces when the sample is exposed to microwaves at one face only, whereas thawing may originate from both the center as well as the faces when the sample is exposed to microwaves at both faces. Our analysis based on the generalized mathematical formulation validates the local maxima in spatial power distribution during intermediate thawing stages obtained with the finite element based enthalpy formulation. The generalized mathematical analysis on multiple thawed regimes further illustrates the role of traveling waves on resonances in microwave power. The influence of resonance is attributed by a non-monotonic variation of thawing time with sample thicknesses either for one side incidence or both side incidence due to microwaves. Optimal thawing strategies are recommended based on greater power savings.

A fixed-grid finite element based enthalpy formulation for generalized phase change problems: role of superficial mushy region

Abstract The enthalpy method is primarily developed for studying phase change in a multicomponent material, characterized by a continuous liquid volume fraction ( φ l ) vs temperature ( T ) relationship. Using the Galerkin finite element method we obtain solutions to the enthalpy formulation for phase change in 1D slabs of pure material, by assuming a superficial phase change region (linear φ l vs T ) around the discontinuity at the melting point. Errors between the computed and analytical solutions are evaluated for the fluxes at, and positions of, the freezing front, for different widths of the superficial phase change region and spatial discretizations with linear and quadratic basis functions. For Stefan number ( St ) varying between 0.1 and 10 the method is relatively insensitive to spatial discretization and widths of the superficial phase change region. Greater sensitivity is observed at St =0.01, where the variation in the enthalpy is large. In general the width of the superficial phase change region should span at least 2–3 Gauss quadrature points for the enthalpy to be computed accurately. The method is applied to study conventional melting of slabs of frozen brine and ice. Regardless of the forms for the φ l vs T relationships, the thawing times were found to scale as the square of the slab thickness. The ability of the method to efficiently capture multiple thawing fronts which may originate at any spatial location within the sample, is illustrated with the microwave thawing of slabs and 2D cylinders.

Role of ceramic supports on microwave heating of materials

A detailed analysis has been carried out to study efficient heating due to microwaves for one-dimensional samples placed on ceramic supports (Al2O3, SiC). The greater effects on microwave heating of samples have been illustrated via average power within a sample versus sample thickness diagram for various cases. The maxima in power, also termed as “resonances,” is observed for specific sample thicknesses and the two consecutive maxima in average power are termed as R1 and R2 modes. The greater heating effects leading to hot spots would occur in water samples during both-sides incidence when the sample is kept on Al2O3 support. SiC support may be recommended for water samples due to uniform heating throughout the sample. In contrast, SiC support could cause local hot spots or thermal runaway for oil samples. The localized hot spots are more pronounced for the samples exposed to microwaves on both faces. The choice of support may not be trivial due to the complex dielectric response of sample-support assemb...

A Model For Heat Transfer In A Honey Bee Swarm

A swarm is a temporary structure formed when several thousand honey bees leave their hive and settle on some object such as the branch of a tree. They remain in this position until a suitable site for a new home is located by the scout bees. A continuum model based on heat conduction and heat generation is used to predict temperature profiles in swarms. Since internal convection is neglected, the model is applicable only at low values of the ambient temperature T-a. Guided by the experimental observations of Heinrich (1981a-c, J. Exp. Biol. 91, 25-55; Science 212, 565-566; Sci. Am. 244, 147-160), the analysis is carried out mainly for non-spherical swarms. The effective thermal conductivity is estimated using the data of Heinrich (1981a, J. Exp. Biol. 91, 25-55) for dead bees. For T-a = 5 and 9 degrees C, results based on a modified version of the heat generation function due to Southwick (1991, The Behaviour and Physiology of Bees, PP 28-47. C.A.B. International, London) are in reasonable agreement with measurements. Results obtained with the heat generation function of Myerscough (1993, J. Theor. Biol. 162, 381-393) are qualitatively similar to those obtained with Southwicks function, but the error is more in the former case. The results suggest that the bees near the periphery generate more heat than those near the core, in accord with the conjecture of Heinrich (1981c, Sci. Am. 244, 147-160). On the other hand, for T-a = 5 degrees C, the heat generation function of Omholt and Lonvik (1986, J. Theor. Biol. 120, 447-456) leads to a trivial steady state where the entire swarm is at the ambient temperature. Therefore an acceptable heat generation function must result in a steady state which is both non-trivial and stable with respect to small perturbations. Omholt and Lonviks function satisfies the first requirement, but not the second. For T-a = 15 degrees C, there is a considerable difference between predicted and measured values, probably due to the neglect of internal convection in the model.