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SOLUTION FOR A SYSTEM OF FRACTIONAL HEAT EQUATIONS OF NANOFLUID ALONG A WEDGE

ABSTRACT
In this article, authors set a new system of fractional heat equations of nanofluid along a wedge and establish the existence and uniqueness of a solution based on the Riemann-Liouville differential operators. Sufficient conditions on the parameters of the system are imposed. A numerical solution of the system is discussed, and applications are illustrated. The technique is based on the ability of Podlubny’s matrix in Matlab to formulate the operation of fractional calculus.
KEYWORDS
PAPER SUBMITTED: 2014-10-10
PAPER REVISED: 2015-02-02
PAPER ACCEPTED: 2015-02-08
PUBLISHED ONLINE: 2015-08-02
DOI REFERENCE: https://doi.org/10.2298/TSCI15S1S51I
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S51 - S57]
REFERENCES
  1. Podlubny, I., Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, San Diego, Cal., USA, 1999
  2. Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000
  3. Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006
  4. Sabatier, J., et al., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, The Netherlands, 2007
  5. Lakshmikantham, V., et al., Theory of Fractional Dynamic Systems, Cambridge Scientific Publisher, Cambridge, UK, 2009
  6. He, J.-H., et al., Converting Fractional Differential Equations into Partial Differential Equation, Thermal Science, 16 (2012), 2 , pp. 331-334
  7. Guo, P., et al., Numerical Simulation of the Fractional Langevin Equation, Thermal Science, 16 (2012), 2, pp. 357-363
  8. Ibrahim, R. W., Jalab, H. A., Time-Space Fractional Heat Equation in the Unit Disk, Abstract and Applied Analysis, 2013 (2013), ID 364042
  9. Choi, S. U., Eastman, J. A., Enhancing Thermal Conductivity of Fluids with Nanoparticles, ASME Int. Mech. Eng. Congress Exposition, San Fancisco, Cal. USA, 1995
  10. Khan, W. A., Pop, I., Boundary Layer Flow past a Wedge Moving in a Nanofluid, Math. Probl. Eng. 2013 (2013), ID 637285
  11. Yang, X.-J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variational Iteration Method, Thermal Science, 17 (2013), 2, pp. 625-628
  12. Alsaedi, A., et al., Maximum Principle for Certain Generalized Time and Space Fractional Diffusion Equations, J. Quarterly Appl. Math., 73 (2015), 1, pp. 1552-4485
  13. Ran, H., Chong, C., The Thermodynamic Transitions of Antiferromagnetic Ising Model on the Fractional Multi-Branched Husimi Recursive Lattice, Communications in Theoretical Physics, 62 (2014), 5, pp. 1-16
  14. Toure, O., Audonnet, F., Development of a Thermodynamic Model of Aqueous Solution Suited for Foods and Biological Media, Part A: Prediction of Activity Coefficients in Aqueous Mixtures Containing Electrolytes, The Canadian Journal Chemical Engineering, 93 (2015), 2, pp. 443-450
  15. Podlubny, I., et al., Matrix Approach to Discrete Fractional Calculus II: Partial Fractional Differential Equations, Journal of Computational Physics, 228 (2009), 8, pp. 3137-3153

© 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