THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Yi Tian

SYMMETRY REDUCTION A PROMISING METHOD FOR HEAT CONDUCTION EQUATIONS

ABSTRACT
Though there are many approximate methods, e. g., the variational iteration method and the homotopy perturbation, for non-linear heat conduction equations, exact solutions are needed in optimizing the heat problems. Here we show that the Lie symmetry and the similarity reduction provide a powerful mathematical tool to searching for the needed exact solutions. Lie algorithm is used to obtain the symmetry of the heat conduction equations and wave equations, then the studied equations are reduced by the similarity reduction method.
KEYWORDS
Lie algorithm, similarity reduction method, wave equations, heat conduction equations
PAPER SUBMITTED: 2018-03-15
PAPER REVISED: 2018-08-08
PAPER ACCEPTED: 1970-01-01
PUBLISHED ONLINE: 2019-09-14
DOI REFERENCE: https://doi.org/10.2298/TSCI1904219T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 4, PAGES [2219 - 2227]
REFERENCES
  1. Zhao, L., et al., Sudden Solvent Evaporation in Bubble Electrospinning for Fabrication of Unsmooth Nanofibers, Thermal Science, 21 (2017), 4, pp. 1827-1832
  2. Liu, L.-G., et al., Solvent Evaporation In A Binary Solvent System For Controllable Fabrication Of Po-rous Fibers By Electrospinning, Thermal Science, 21 (2017), 4, pp. 1821-1825
  3. Peng, N. B., et al., A Rachford-Rice like Equation for Solvent Evaporation in the Bubble Electrospin-ning, Thermal Science, 22 (2018), 4, pp. 1679-1683
  4. Liu, Y.-Q., et al., Nanoscale Multi-Phase Flow and its Application to Control Nanofiber Diameter, Thermal Science, 22 (2018), 1A, pp. 43-46
  5. Tian, D., et al., Self-Assembly of Macromolecules in a Long and Narrow Tube, Thermal Science, 22 (2018), 4, pp. 1659-1664
  6. Tian, D., et al., Strength of Bubble Walls and the Hall-Petch Effect in Bubble-Spinning, Textile Re-search Journal, 89 (2018), 7, pp. 1340-1344
  7. Liu, P., et al., Geometrical Potential: an Explanation on of Nanofibers Wettability, Thermal Science, 22 (2018), 1A, pp. 33-38
  8. He, J.-H., Homotopy Perturbation Method: a New Nonlinear Analytical Technique, Applied Mathemat-ics and Computation, 135 (2003), 1, pp. 73-79
  9. He, J.-H., An Elementary Introduction to the Homotopy Perturbation Method, Computers & Mathemat-ics with Applications, 57 (2009), 3, pp. 410-412
  10. He, J.-H., Comparison of Homotopy Perturbation Method and Homotopy Analysis Method, Applied Mathematics and Computation, 156 (2004), 2, pp. 527-539
  11. He, J.-H., Notes on the Optimal Variational Iteration Method, Applied Mathematics Letters, 25 (2012), 10, pp. 1579-1581
  12. He, J.-H., A Short Remark on Fractional Variational Iteration Method, Physics Letters A, 375 (2011), 38, pp. 3362-3364
  13. He, J.-H., Variational Iteration Method - Some Recent Results and New Interpretations, Journal of Computational and Applied Mathematics, 207 (2007), 1, pp. 3-17
  14. He, J.-H. Hamilton's Principle for Dynamical Elasticity, Appl. Math. Lett., 72 (2017), Oct., pp. 65-69
  15. He, J.-H. Generalized Equilibrium Equations for Shell Derived from a Generalized Variational Principle, Appl. Math. Lett., 64 (2017), Feb., pp. 94-100
  16. He, J.-H. An Alternative Approach To Establishment Of A Variational Principle For The Torsional Problem Of Piezoelastic Beams, Appl. Math. Lett., 52 (2016), Feb., pp. 1-3
  17. Wu, Y., He, J.-H. A Remark on Samuelson's Variational Principle in Economics, Applied Mathematics Letters, 84 (2018), Oct., pp. 143-147
  18. Liu, H. Z., Geng, Y. X., Symmetry Reductions and Exact Solutions to the Systems of Carbon Nanotubes Conveying Fluid, Journal of Differential Equations, 254 (2013), 5, pp. 2289-2303
  19. Wang, G. W., et al., Symmetry Reduction, Exact Solutions and Conservation Laws of a New Fifth-Order Nonlinear Integrable Equation, Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 9, pp. 2313-2320
  20. Xin, X. P., et al., Symmetry Reduction, Exact Solutions and Conservation Laws of the Sawada-Kotera-Kadomtsev-Petviashvili Equation, Applied Mathematics and Computation, 216 (2010), 4, pp. 1065-1071
  21. Wang, Y., Dong Z. Z., Symmetry of a 2+1-D system, Thermal Science, 22 (2018), 4, pp. 1811-1822
PDF VERSION [DOWNLOAD]
Symmetry reduction a promising method for heat conduction equations

© 2024 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