TY - JOUR
T1 - Dead-core solutions for slightly non-isothermal diffusion-reaction problems with power-law kinetics
AU - Golman, Boris
AU - Andreev, Vsevolod V.
AU - Skrzypacz, Piotr
N1 - Funding Information:
This work was supported by the Nazarbayev University under Grant 090118FD5347 .
Publisher Copyright:
© 2020
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/7
Y1 - 2020/7
N2 - The paper deals with dead-core solutions to a non-isothermal reaction- diffusion problem with power-law kinetics for a single reaction that takes place in a catalyst pellet along with mass and heat transfer from the bulk phase to the outer pellet surface. The model boundary value problem for two coupled non-linear diffusion-reaction equations is solved using the semi-analytical method. The exact solutions are established under the assumption of a small temperature gradient in the pellet. The nonlinear algebraic expressions are derived for the critical Thiele modulus, dead-zone length, reactant concentration, and temperature profiles in catalyst pellets of planar geometry. The effects of the reaction order, Arrhenius number, energy generation function, Thiele modulus, and Biot numbers are investigated on the concentration and temperature profiles, dead-zone length, and critical Thiele modulus.
AB - The paper deals with dead-core solutions to a non-isothermal reaction- diffusion problem with power-law kinetics for a single reaction that takes place in a catalyst pellet along with mass and heat transfer from the bulk phase to the outer pellet surface. The model boundary value problem for two coupled non-linear diffusion-reaction equations is solved using the semi-analytical method. The exact solutions are established under the assumption of a small temperature gradient in the pellet. The nonlinear algebraic expressions are derived for the critical Thiele modulus, dead-zone length, reactant concentration, and temperature profiles in catalyst pellets of planar geometry. The effects of the reaction order, Arrhenius number, energy generation function, Thiele modulus, and Biot numbers are investigated on the concentration and temperature profiles, dead-zone length, and critical Thiele modulus.
KW - Catalytic pellet
KW - Dead zone
KW - Diffusion and reaction
KW - Non-isothermal reaction
KW - Power-law kinetics
KW - Semi-analytical solutions
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U2 - 10.1016/j.apm.2020.03.016
DO - 10.1016/j.apm.2020.03.016
M3 - Article
AN - SCOPUS:85082726119
SN - 0307-904X
VL - 83
SP - 576
EP - 589
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
ER -