A theoretical analysis has been carried out to study the role of microwave on endothermic homogeneous gas phase reaction occurring within a semi-infinite bed packed with inert materials. The packing materials act as susceptors while exposed to microwave radiations and transfer the absorbed power to gas phase. The bed is assumed to be saturated with the reactant before the exposure to microwave. As microwave is irradiated on the bed, reaction proceeds within the entrapped gas phase. A mathematical model has been developed in order to study the variations of concentration and temperature with time in various regimes of microwave power absorption measured in terms of three dimensionless numbers ($N_w$ or $N_p$, $f_p$ and $f_w$). Here, $N_w$ and $N_p$ represent relative length of packed bed compared to effective wavelength and penetration depth within the bed, respectively. On the other hand, $f_p$ and $f_w$ measure effective wavelength within the packed bed with respect to its effective penetration depth and free space wavelength, respectively and depend on the structure, dielectric properties and porosity of packing. In each regime of power absorption, the influence of microwave incidence has been analyzed based on (i) spatial nonuniformities and (ii) overall progress of reaction compared to those in corresponding conventional reactors, where entire heat equivalent to the total absorbed power is supplied from the surface. It has been shown that microwave homogenize the localized reaction rate of conventional heating and enhances overall progress of the reactor based on diffusional limitations. The enhancement of reaction gets sequentially pronounced with the increase of diffusional limitations (measured in terms of Thiele modulus for homogeneous reaction) and total amount absorbed power. The extent of enhancement has been quantified and shown to have one-to-one correlation with power absorption characteristics. The effect of various other transport related parameters are also analyzed in details, which show the enhancement of reaction due to microwave incidence to be valid in most of the cases except for reactors with much higher heat transfer limitations than mass transfer and relatively slow reaction rate compared to diffusional rate to reactant.
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Role of Microwave Incidence On First Order Endothermic Reactions
A theoretical analysis has been carried out to study the role of microwave on endothermic homogeneous gas phase reaction occurring within a semi-infinite bed packed with inert materials. The packing materials act as susceptors while exposed to microwave radiations and transfer the absorbed power to gas phase. The bed is assumed to be saturated with the reactant before the exposure to microwave. As microwave is irradiated on the bed, reaction proceeds within the entrapped gas phase. A mathematical model has been developed in order to study the variations of concentration and temperature with time in various regimes of microwave power absorption measured in terms of three dimensionless numbers ($N_w$ or $N_p$, $f_p$ and $f_w$). Here, $N_w$ and $N_p$ represent relative length of packed bed compared to effective wavelength and penetration depth within the bed, respectively. On the other hand, $f_p$ and $f_w$ measure effective wavelength within the packed bed with respect to its effective penetration depth and free space wavelength, respectively and depend on the structure, dielectric properties and porosity of packing. In each regime of power absorption, the influence of microwave incidence has been analyzed based on (i) spatial nonuniformities and (ii) overall progress of reaction compared to those in corresponding conventional reactors, where entire heat equivalent to the total absorbed power is supplied from the surface. It has been shown that microwave homogenize the localized reaction rate of conventional heating and enhances overall progress of the reactor based on diffusional limitations. The enhancement of reaction gets sequentially pronounced with the increase of diffusional limitations (measured in terms of Thiele modulus for homogeneous reaction) and total amount absorbed power. The extent of enhancement has been quantified and shown to have one-to-one correlation with power absorption characteristics. The effect of various other transport related parameters are also analyzed in details, which show the enhancement of reaction due to microwave incidence to be valid in most of the cases except for reactors with much higher heat transfer limitations than mass transfer and relatively slow reaction rate compared to diffusional rate to reactant.