THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Shuxian Deng

,

Huixu Li

,

Xinxin Ge

GLOBAL WELL-POSEDNESS OF A CLASS OF DISSIPATIVE THERMOELASTIC FLUIDS BASED ON FRACTAL THEORY AND THERMAL SCIENCE ANALYSIS

ABSTRACT
Thermodynamics and fluid mechanics are used to study the mechanical properties of a class of thermoelastic fluid materials. Using the law of thermodynamics and the law of conservation of energy, thermal science analysis of dissipative thermoelastic fluid materials is performed in a planar 2-D flow field, and a corresponding mathematical model is established. Fractal theory, operator semi-group theory and fractional calculus are used to study the overall well-posedness of a dissipative thermoelastic flow.
KEYWORDS
fractal, fractional order, thermoelastic, fluid, well-posedness
PAPER SUBMITTED: 2018-05-01
PAPER REVISED: 2018-11-23
PAPER ACCEPTED: 2018-11-23
PUBLISHED ONLINE: 2019-09-14
DOI REFERENCE: https://doi.org/10.2298/TSCI1904461D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 4, PAGES [2461 - 2469]
REFERENCES
  1. Chen, G., et al., Global Solutions of the Compressible Navier-Stokes Equations with Large Discontinu-ous Initial Data, Comm. Partial Differential Equations, 25 (2000), May, pp. 2233-2257
  2. Qin, Y., Universal Attractor in H4 for the Nonlinear One-Dimensional Compressible Navier-Stokes Equations, J. Differential Equations, 272 (2014), 1, pp. 21-72
  3. Shen, W., Zheng, S., Maximal Attractor for the Coupled Cahn-Hillard Equations, Nonlinear Anal. TMA, 49 (2002), 1, pp. 21-34
  4. Qin, Y., Global Existence and Asymptotic Behavior of Solutions to a System of Equations for a Nonlin-ear One-Dimensional Viscous, Heat-Conducting Real Gas (in Chinese), Chin. Ann. Math, 20A (2009), 3, pp. 343-354
  5. Ahmad, B., Ntouyas, S. K., Existence of Solutions for Nonlinear Fractional q-Difference Inclusions with Nonlocal Robin (Separated) Conditions, Mediterr. J. Math., 10 (2013), 3, pp. 1333-1351
  6. Zhang, X. Q., et al., Existence of Positive Solutions for a Class of Nonlinear Fractional Differential Equations with Integral Boundary Conditions and a Parameter, Appl. Math. Comput., 26 (2014), Jan., pp. 708-718
  7. Chen, G., Zheng, Y., Concentration Phenomenon for Fractional Nonlinear Schrödinger Equations, Pure Appl. Anal., 13 (2014), 6, pp. 2359-2376
  8. Qin, Y., Global Existence and Asymptotic Behavior for a Viscous, Heat-Conductive, One-Dimensional Real Gas with Fixed and Constant Temperature Boundary Conditions, Adv. Diff. Eqns., 7 (2012), 2, pp. 129-154
  9. Jiang, S., Large Time Behavior of Solutions to the Equations of a One-Dimensional Viscous Polytropic Ideal Gas in Unbounded Domains, Comm. Math. Phys., 200 (1999), 1, pp. 181-193
  10. He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, Int. J. Theor. Phys. 53 (2014), 11, pp. 3698-3718
  11. He, J.-H., et al., Geometrical Explanation of the Fractional Complex Transform and Derivative Chain Rule for Fractional Calculus, Phys. Lett. A, 376 (2012), 4, pp. 257-259
  12. He, J.-H., Fractal Calculus and Its Geometrical Explanation, Results in Physics,10 (2018), Sept., pp. 272-276
  13. Wang, Y, An, J. Y., Amplitude-Frequency Relationship to a Fractional Duffing Oscillator Arising in Mi-crophysics and Tsunami Motion, Journal of Low Frequency Noise, Vibration & Active Control, On-line first, doi.org/10.1177/1461348418795813
  14. Wang, Y., Deng, Q., Fractal Derivative Model for Tsunami Travelling, Fractals, On-line first, doi.org/10.1142/S0218348X19500178
  15. 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
  16. Sohail, A., et al., Exact Travelling Wave Solutions for Fractional Order KdV-Like Equation Using G′/G-Expansion Method, Nonlinear Science Letters A, 8 (2017), Mar., pp. 228-235
  17. Guner, O., Bekir, A., Exp-Function Method for Nonlinear Fractional Differential Equations, Nonlinear Science Letters A, 8 (2017), 1, pp. 41-49
PDF VERSION [DOWNLOAD]
Global well-posedness of a class of dissipative thermoelastic fluids based on fractal theory and thermal science analysis

© 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