A generalized analysis on material invariant characteristics for microwave heating of slabs

A generalized dimensionless formulation has been developed to predict the spatial distribution of microwave power and temperature. The ‘dimensionless analysis’ is mainly based on three numbers: wave number, ; free space wave number, ; and penetration number, , where is the ratio of sample thickness to wavelength of microwaves within a material, is based on wavelength within free space and is the ratio of sample thickness to penetration depth. The material dielectric properties and sample thicknesses form the basis of these dimensionless numbers. The volumetric heat source due to microwaves can be expressed as a combination of dimensionless numbers and electric field distributions. The spatial distributions of microwave power for uniform plane waves can be obtained from the combination of transmitted and reflected waves within a material. Microwave heating characteristics are obtained by solving energy balance equations where the dimensionless temperature is scaled with respect to incident microwave intensity. The generalized trends of microwave power absorption are illustrated via average power plots as a function of , and . The average power contours exhibit oscillatory behavior with corresponding to smaller for smaller values of . The spatial distributions of dimensionless electric fields and power are obtained for various and . The spatial resonance or maxima on microwave power is represented by zero phase difference between transmitted and reflected waves. It is observed that the number of spatial resonances increases with for smaller regimes whereas the spatial power follows the exponential decay law for higher regimes irrespective of and . These trends are observed for samples incident with microwaves at one face and both the faces. The heating characteristics are shown for various materials and generalized heating patterns are shown as functions of , and . The generalized heating characteristics involve either spatial temperature distributions or uniform temperature profiles based on both thermal parameters and dimensionless numbers ().     

A kinetic study on anaerobic reduction of sulphate, part II: incorporation of temperature effects in the kinetic model

The effects of temperature on the kinetics of anaerobic sulphate reduction were studied in continuous bioreactors using acetate as an electron donor. Across the range of temperatures applied from 20 to , the increasing of volumetric loading rate up to 0.08 to resulted in a linear increase in reduction rate of sulphate. The increasing reaction rate showed a lower dependence on volumetric loading rate in the range 0.1-. Further increase in volumetric loading rate above was accompanied by wash out of bacterial cells and a sharp decrease in reaction rate. Despite a similar pattern for dependency of reaction rate on volumetric loading at all temperatures tested, the magnitude of reaction rate was influenced by temperature, with a maximum rate of observed at . The effect of temperature on maximum specific growth rate (μ_max) and bacterial yield was insignificant. The values of maximum specific growth rate and yield were and 0.56-0.60 kg bacteria (), respectively. The decay coefficient (k_d) and apparent saturation constant () were both temperature dependent. The increase of temperature resulted in decreased values of , and higher values for k_d. Using the experimental data effect of temperature was incorporated in a kinetic model previously developed for anaerobic reduction of sulphate.