The formation of dead zones in nonisothermal porous catalyst with temperature-dependent diffusion coefficient |
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Authors: | Vsevolod V. Andreev Piotr Skrzypacz Boris Golman |
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Affiliation: | 1. Department of Heat Power Setups, Faculty of Energy and Electrical Engineering, Chuvash State University, Cheboksary, Russia;2. Department of Mathematics, School of Science and Technology, Nazarbayev University, Nur-Sultan, Kazakhstan;3. Department of Chemical and Materials Engineering, School of Engineering, Nazarbayev University, Nur-Sultan, Kazakhstan |
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Abstract: | This paper considers the formation of dead zones in the porous catalyst pellets due to the chemical reaction and diffusion. We established and investigated the model with nonisothermal reaction of fractional order and activated temperature-dependent diffusivity. The effects of process parameters, catalyst shape, and reaction and diffusion parameters on the formation of the dead zone are studied numerically and characterized by the critical Thiele modulus. The lower bounds for the critical Thiele modulus are derived analytically in terms of process parameters for exothermic and endothermic reactions and verified numerically. The critical Thiele modulus increases with increasing Arrhenius number for diffusion and decreasing Arrhenius number for reaction in the case of exothermic reactions, whereas the opposite trends hold for the endothermic reactions. The critical Thiele modulus also increases with increasing fractional reaction order as well as with decreasing energy generation function, and increasing Biot numbers for heat and mass transfer. Moreover, the critical Thiele modulus is the highest for spherical pellets and the lowest for pellets with planar shape. |
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Keywords: | catalyst pellet critical Thiele modulus dead zone power-law kinetics temperature-dependent diffusion |
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