THERMAL SCIENCE
International Scientific Journal
Find this paper on
A VARIATIONAL APPROACH TO A POROUS CATALYST
ABSTRACT
The convection-diffusion process in porous electrodes depends greatly upon the porous structure. A fractal model for porous catalyst in a thin-zone bed reactor is established using He’s fractal derivative, and a variational principle is also established in a fractal space, and an approximate solution is obtained. Additionally an ancient Chinese algorithm is adopted to solve an algebraic equation.
KEYWORDS
porous medium, fractal variational principle, fractal calculus, approximate solution, Nine Chapters, ancient Chinese mathematics
PAPER SUBMITTED: 2020-04-04
PAPER REVISED: 2020-06-13
PAPER ACCEPTED: 2020-06-13
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI200404044S
CITATION EXPORT: view in browser or download as text file
REFERENCES
[1] Constales, D., et al., When the Final Catalyst Activity Profile Depends only on the Total Amount of Admitted Substance: Theoretical Proof, AICHE Journal, 61 (2015), 1, pp. 31-34, 10.1002/aic.14675
[2] De Souza M. J. B., et al., Thermal and Catalytic Pyrolysis of Polyvinyl Chloride Using Micro/Mesoporous ZSM-35/MCM-41 Catalysts, Journal of Thermal Analysis and Calorimetry, 140 (2020), 1, pp. 167-175, 10.1007/s10973-019-08803-7
[3] He, J. H., The Simpler, the Better: Analytical Methods for Non-Linear Oscillators and Fractional Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1252-1260, 10.1177/1461348419844145
[4] He, J. H, Ain, Q. T., New Promises and Future Challenges of Fractal Calculus: from Two-Scale Thermodynamics to Fractal Vprinciple, Thermal Science, 24 (2020), 2A, pp. 659-681
[5] He, J. H., Thermal Science for the Real World: Reality and Challenge, Thermal Science, 24 (2020), 4, pp. 2289-2294, 10.2298/tsci191001177h
[6] He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133, 10.2298/tsci1904131h
[7] Yao, S. W., Wang, K. L., A New Approximate Analytical Method for a System of Fractional Differential Equations, Thermal Science, 23 (2019), 3, pp. S853-S858, 10.2298/tsci180613120y
[8] Yao, S. W., Wang, K. L., Local Fractional Derivative: A Powerful Tool to Model the Fractal Differential Equation, Thermal Science, 23 (2019), 3, pp. 1703-1706, 10.2298/tsci180712243y
[9] Ji, F. Y., et al., A Fractal Boussinesq Equation for Non-Linear Transverse Vibration of a Nanofiber-Reinforced Concrete Pillar, Applied Mathematical Modelling, 82 (2020), June, pp. 437-448, 10.1016/j.apm.2020.01.027
[10] Li, X. J., et al., A Fractal Two-Phase Flow Model for the Fiber Motion in a Polymer Filling Process, Fractals, 28 (2020), 05, 2050093, 10.1142/s0218348x20500930
[11] Shen, Y., He, J. H., Variational Principle for a Generalized KdV Equation in a Fractal Space, Fractals, 20 (2020), 4, 2050069, 10.1142/s0218348x20500693
[12] He, J. H., A Fractal Variational Theory for 1-D Compressible Flow in a Microgravity Space, Fractals, 28 (2020), 2050024
[13] He, J. H., Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves, Journal Appl. Comput. Mech., 6 (2020), 4, pp. 735-740, 10.22055/jacm.2019.14813
[14] He, J. H., Sun, C., A Variational Principle for a Thin Film Equation, Journal of Mathematical Chemistry, 57 (2019), 9, pp. 2075-2081, 10.1007/s10910-019-01063-8
[15] He, J. H., Variational Principle and Periodic Solution of the Kundu-Mukherjee-Naskar Equation, Results in Physics, 17 ( 2020), 103031, 10.1016/j.rinp.2020.103031
[16] He, C. H., A Simple Analytical Approach to a Non-Linear Equation Arising in Porous Catalyst, International Journal of Numerical Methods for Heat and Fluid-Flow, 27 (2017), 4, pp. 861-866, 10.1108/hff-03-2016-0129
[17] He, C. H., An Introduction an Ancient Chinese Algorithm and Its Modification, International Journal of Numerical Methods for Heat and Fluid-flow, 26 (2016), 8, pp. 2486-2491, 10.1108/hff-09-2015-0377
[18] He, J. H., A Simple Approach to 1-D Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), 113565
[19] Li, X. X., et al., A Fractal Modification of the Surface Coverage Model for an Electrochemical Arsenic Sensor, Electrochimica Acta, 296 (2019), 10, pp. 491-493, 10.1016/j.electacta.2018.11.042
PDF VERSION [DOWNLOAD]
© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence


