Open AccessApproximations for the Concentration and Effectiveness Factor in Porous Catalysts of Arbitrary Shape: Taylor Series and Akbari-Ganji’s Methods
Author(s) -
Ramu UshaRani,
L. Rajendran,
Marwan Abukhaled
Publication year - 2021
Publication title -
mathematical modelling and engineering problems/mathematical modelling of engineering problems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.26
H-Index - 11
eISSN - 2369-0747
pISSN - 2369-0739
DOI - 10.18280/mmep.080405
Subject(s) - thiele modulus , taylor series , michaelis–menten kinetics , series (stratigraphy) , diffusion , thermodynamics , substrate (aquarium) , mathematics , simple (philosophy) , catalysis , constant (computer programming) , mathematical analysis , chemistry , physics , computer science , organic chemistry , paleontology , philosophy , oceanography , programming language , epistemology , biology , enzyme assay , enzyme , geology
A mathematical model of reaction-diffusion problem with Michaelis-Menten kinetics in catalyst particles of arbitrary shape is investigated. Analytical expressions of the concentration of substrates are derived as functions of the Thiele modulus, the modified Sherwood number, and the Michaelis constant. A Taylor series approach and the Akbari-Ganji's method are utilized to determine the substrate concentration and the effectiveness factor. The effects of the shape factor on the concentration profiles and the effectiveness factor are discussed. In addition to their simple implementations, the proposed analytical approaches are reliable and highly accurate, as it will be shown when compared with numerical simulations.