THERMAL SCIENCE

International Scientific Journal

Thermal Science - Online First

Authors of this Paper

External Links

online first only

New Laplace-type integral transform for solving steady heat-transfer problem

ABSTRACT
The fundamental purpose of this paper is to propose a new Laplace-type integral transform (NL-TIT) for solving steady heat-transfer problems. The proposed integral transform is a generalization of the Sumudu, and the Laplace transforms and its visualization is more comfortable than the Sumudu transform, the natural transform, and the Elzaki transform. The suggested integral transform is used to solve the steady heat-transfer problems, and results are compared with the results of the existing techniques.
KEYWORDS
PAPER SUBMITTED: 2018-01-10
PAPER REVISED: 2019-04-02
PAPER ACCEPTED: 2019-04-24
PUBLISHED ONLINE: 2019-05-12
DOI REFERENCE: https://doi.org/10.2298/TSCI180110160M
REFERENCES
  1. Lokenath D., Bhatta, D., Integral Transform and Their Applications, CRC Press, Boca Raton, Fla., USA., 2014.
  2. Srivastava, H.M., Luo, M., Raina, R.K., A New Integral Transform and Its Applications, Acta Mathematica Scientia, 35 (2015), 6, pp. 1386-1400.
  3. Yang, X.J., New Integral Transforms for Solving a Steady Heat-Transfer Problem, Thermal Science, 21 (2017), pp. S79-S87.
  4. Yang, X.J., A New Integral Transform with an Application in Heat-Transfer Problem, Thermal Science, 20 (2016), pp. S677-S681.
  5. Goodwine, B., Engineering Differential Equations: Theory and Applications, Springer, New York, USA, 2010.
  6. Yan, L.M., Modified Homotopy perturbation Method Coupled with Laplace Transform for Fractional Heat Transfer and Porous Media Equations, Thermal Science, 17 (2013), 5, pp. 1409-1414.
  7. Pamuk, S.,Solution of the Porous Media Equation by Adomian's Decomposition Method, Physics Letters A, 344 (2005), pp. 184-188.
  8. Elzaki, T.M., The New Integral Transform "Elzaki transform", Glob. J. of Pur. And Appl. Math., 7 (2011), 1, pp. 57-64.
  9. Spiegel, M.R., Theory and Problems of Laplace Transforms, Schaum's Outline Series, McGraw-Hill, New York, USA., 1965.
  10. Bracewell, R.N., The Fourier Transform and Its Applications, McGraw-Hill, Boston, Mass, USA., 2000.
  11. Boyadjiev, L., Luchko, Y., Mellin Integral Transform Approach to Analyze the Multidimensional Diffusion-Wave Equations, Chaos Solitons Fractals,, 102 (2017), pp. 127-134.
  12. Dattoli, G., Martinelli, M.R., Ricci, P.E., On New Families of Integral Transforms for the Solution of Partial Differential Equations, Integral Transforms and Special Functions, 8 (2005), pp. 661-667.
  13. Lévesque, M., et al., Numerical Inversion of the Laplace-Carson Transform Applied to Homogenization of Randomly Reinforced Linear Viscoelastic Media, Comput Mech., 40 (2007), pp. 771-789.
  14. Cui, Y.L., et al., Application of the Z-Transform Technique to Modeling the Linear Lumped Networks in the HIE-FDTD Method, Journal of Electromagnetic Waves and Applications, 27 (2013), 4, pp. 529-538.
  15. Watugala, G.K., Sumudu Transform-A New Integral Transform to Solve Differential Equations and Control Engineering Problems, Math Eng in Indust., 6 (1998), 1, pp. 319-329.
  16. Shah, P.C., Thambynayagam, R.K.M., Application of the Finite Hankel Transform to a Diffusion Problem Without Azimuthal Symmetry, Transport in Porous Media, 14 (1994), 3, pp. 247-264.
  17. Karunakaran, V.,Venugopal, T., The Weierstrass Transform for a Class of Generalized Functions, Journal of Mathematical Analysis and Applications, 220 (1998), 2, pp. 508-527.
  18. Belgacem, F.B.M., Silambarasan, R., Theory of Natural Transform. Math. in Eng. Sci., and Aeros., 3 (2012), 1, pp. 99-124.
  19. Yang, X.J., A New Integral Transform Operator for Solving the Heat-Diffusion Problem, Applied Mathematics Letters, 64 (2017), pp. 193-197.
  20. Yang, X.J., A New Integral Transform Method for Solving Steady Heat-Transfer Problem, Thermal Science, 20 (2016), pp. S639-S642.