THERMAL SCIENCE

International Scientific Journal

AN INTEGRAL TRANSFORM APPLIED TO SOLVE THE STEADY HEAT TRANSFER PROBLEM IN THE HALF-PLANE

ABSTRACT
An integral transform operator U[П(t)= 1/λ ∞∫−∞ П(t)е-iλt dt is considered to solve the steady heat transfer problem in this paper. The analytic technique is illustrated to be applicable in the solution of a 1-D Laplace equation in the half-plane. The results are interesting as well as potentially useful in the linear heat transfer problems.
KEYWORDS
PAPER SUBMITTED: 2017-03-10
PAPER REVISED: 2017-05-01
PAPER ACCEPTED: 2017-06-27
PUBLISHED ONLINE: 2017-12-02
DOI REFERENCE: https://doi.org/10.2298/TSCI17S1105X
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S105 - S111]
REFERENCES
  1. Pletcher, R. H., et al., Computational Fluid Mechanics and Heat Transfer, CRC Press, Boca Raton, Fla., USA, 2012
  2. Yang, X. J., A New Integral Transform Operator for Solving the Heat-Diffusion Problem, Applied Mathematics Letters, 64 (2017), Feb., pp. 193-197
  3. Yang, X. J., Gao, F., A New Technology for Solving Diffusion and Heat Equations, Thermal Science, 21 (2017), 1A, pp. 133-140
  4. Liang, X, et al., Applications of a Novel Integral Transform to Partial Differential Equations, Journal of Nonlinear Science and Applications, 10 (2017), 2, pp. 528-534
  5. Sommerfeld, A., Partial Differential Equations in Physics, Academic Press, New York, USA, 1949
  6. Sangani, A. S., Acrivos, A., Slow Flow Past Periodic Arrays of Cylinders with Application to Heat Transfer, International Journal of Multiphase Flow, 8 (1982), 3, pp. 193-206
  7. Domenico, P. A., Palciauskas, V. V., Theoretical Analysis of Forced Convective Heat Transfer in Regional Ground-Water Flow, Geological Society of America Bulletin, 84 (1973), 12, pp. 3803-3814
  8. Yang, X. J., A New Integral Transform Method for Solving Steady Heat Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S639-S642
  9. Yang, X. J., A New Integral Transform with an Application in Heat Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S677-S681
  10. Servadei, R., Valdinoci, E., Fractional Laplacian Equations with Critical Sobolev Exponent, Revista Matemática Complutense, 28 (2015), 3, pp. 655-676
  11. Servadei, R., Valdinoci, E., Weak and Viscosity Solutions of the Fractional Laplace Equation, Publicacions Matematiques, 58 (2014), 1, pp. 133-154
  12. Acosta, G., Borthagaray, J. P., A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations, SIAM Journal on Numerical Analysis, 55 (2017), 2, pp. 472-495
  13. Yang, X. J., et al., Local Fractional Integral Transforms and their Applications, Academic Press, New York, USA, 2015
  14. Yang, X. J., et al., A New Family of the Local Fractional PDE, Fundamenta Informaticae, 151 (2017), 1-4, pp. 63-75
  15. Debnath, L., Bhatta, D., Integral Transforms and their Applications, CRC Press, Boca Raton, Fla., USA, 2014
  16. Yang, X. J., A New Integral Transform Method for Soliving a Steady Heat Transfer Problem, Thermal Science, 20 (2016), Suppl. 2, pp. S639-S642

© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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