THERMAL SCIENCE

International Scientific Journal

Hong-Yan LiuORCID

,

Zhi-Min LiORCID

,

Shao-Wen YaoORCID

,

Yan-Ju Yao

,

Juan LiuORCID

A VARIATIONAL PRINCIPLE FOR THE PHOTOCATALYTIC NOX ABATEMENT

ABSTRACT
Numerical study of NOx abatement in a photocatalytic reactor has been caught much attention recently. There are two ways for the numerical simulation, one is the CFD model, the other is the variational-based approach. The latter leads to a conservation algorithm with less requirement for the trial functions in the numerical study. In this paper we establish a variational principle for the problem, giving an alternative numerical method for NOx abatement.
KEYWORDS
CFD model, semi-inverse method, free surface, variational principle, photocatalytic NOx abatement, fractal Fick’s law, fractal derivative, fractal variational principle
PAPER SUBMITTED: 2019-04-05
PAPER REVISED: 2019-10-28
PAPER ACCEPTED: 2019-10-28
PUBLISHED ONLINE: 2020-06-21
DOI REFERENCE: https://doi.org/10.2298/TSCI2004515L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE No. 4, PAGES [2515 - 2518]
REFERENCES
[1] Lira, de O. B., et al., Photocatalytic NOx Abatement: Mathematical Modeling, CFD Validation and Reactor Analysis, Journal of Hazardous Materials, 372 (2019), June, pp. 145-153, 10.1016/j.jhazmat.2018.07.009
[2] Liu, G. L., Variable-Domain Variational Finite Element Method: A General Approach to Free/Moving Boundary Problems in Heat and Fluid Flow, Nonlinear Analysis: Theory, Methods & Applications, 30 (1997), 8, pp. 5229-5239, 10.1016/s0362-546x(96)00163-0
[3] Wu, Y., He, J. H., A Remark on Samuelson's Variational Principle in Economics, Applied Mathematics Letters, 84 (2018), Oct., pp. 143-147, 10.1016/j.aml.2018.05.008
[4] He, J. H., An Alternative Approach to Establishment of a Variational Principle for the Torsional Problem of Piezoelastic Beams, Applied Mathematics Letters, 52 (2016), Feb., pp. 1-3, 10.1016/j.aml.2015.08.001
[5] He, J. H., Generalized Equilibrium Equations for Shell Derived from a Generalized Variational Principle, Applied Mathematics Letters, 64 (2017), Feb., pp. 94-100, 10.1016/j.aml.2016.08.008
[6] He, J. H., Hamilton's Principle for Dynamical Elasticity, Applied Mathematics Letters, 72 (2017), Oct., pp. 65-69, 10.1016/j.aml.2017.04.008
[7] He, J. H., Variational Principles for Some Nonlinear Partial Differential Equations with Variable Coefficients, Chaos, Solitons & Fractals, 19 (2004), 4, pp. 847-851, 10.1016/s0960-0779(03)00265-0
[8] Li, X. W., et al., On the semi-Inverse Method and Variational Principle, Thermal Science, 17 (2013), 5, pp. 1565-1568, 10.2298/tsci1305565l
[9] He, J. H., Semi-Inverse Method and Generalized Variational Principles with Multi-Variables in Elasticity, Applied Mathematics and Mechanics, 21 (2000), 7, pp. 797-808, 10.1007/bf02428378
[10] He, J. H., A Modified Li-He's Variational Principle for Plasma, International Journal of Numerical Methods for Heat and Fluid Flow, On-line first, , 2019, 10.1108/HFF-06-2019-0523
[11] He, J. H., Lagrange Crisis and Generalized Variational Principle for 3D unsteady flow, International Journal of Numerical Methods for Heat and Fluid Flow, On-line first, , 2019, 10.1108/HFF-07-2019-0577
[12] Wang, Y., et al., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, 1950047, 10.1142/s0218348x19500476
[13] Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, ID 1950134, 10.1142/s0218348x19501342
[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., Generalized Variational Principles for Buckling Analysis of Circular Cylinders, Acta Mechanica, 231 (2019), 1-8, pp. 899-906, 10.1007/s00707-019-02569-7
[16] He, J. H., A Fractal Variational Theory for One-Dimensional Compressible Flow in a Microgravity Space, Fractals, On-line first, , 2019, 10.1142/s0218348x20500243
[17] He, J. H., Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves, J. Appl. Comput. Mech., 6 (2020), 4, pp. 735-740, 10.22055/jacm.2019.14813
[18] Li, X. J., He, J. H., Variational Multi-Scale Finite Element Method for the Twophase Flow of Polymer Melt Filling Process, International Journal of Numerical Methods for Heat & Fluid Flow, On-line first, 10.1108/HFF-07-2019-0599
[19] He, J. H., Fractal Calculus and Its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276, 10.1016/j.rinp.2018.06.011
[20] Li, X. X., et al., A Fractal Modification Of The Surface Coverage Model For An Electrochemical Arsenic Sensor, Electrochimica Acta, 296 (2019), Feb., pp. 491-493, 10.1016/j.electacta.2018.11.042
[21] 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
[22] Ain, Q. T., He, J. H., On Two-Scale Dimension and Its Applications, Thermal Science, 23 (2019), 3B, pp. 1707-1712, 10.2298/tsci190408138a
[23] He, C. H., et al., Taylor Series Solution for Fractal Bratu-Type Equation Arising in Electrospinning Pro-cess, Fractals, 28 (2019), 1, 2050011, 10.1142/s0218348x20500115
[24] Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Bear hairs, Fractals, 26 (2018), 6, 1850086, 10.1142/s0218348x1850086x
[25] Wang, Y., Deng, Q., Fractal Derivative Model for Tsunami Travelling, Fractals, 27 (2019), 1, 1950017, 10.1142/s0218348x19500178
[26] He, J. H., A Simple Approach to One-Dimensional Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), Dec., 113565, 10.1016/j.jelechem.2019.113565
[27] Wang,Y., et al., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, 1950047
[28] Zhang, J. J., et al., Some Analytical Methods for Singular Boundary Value Problem in a Fractal Space, Appl. Comput. Math., 18 (2019), 3, pp. 225-235
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A variational principle for the photocatalytic NOx abatement

© 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