International Scientific Journal

Thermal Science - Online First

External Links

online first only

Exact traveling-wave solutions for linear and nonlinear heat-transfer equations

The exact traveling-wave solutions for the linear and nonlinear heat-transfer equations at several different excess temperatures are addressed and investigated in this paper.
PAPER REVISED: 2016-12-19
PAPER ACCEPTED: 2016-12-19
  1. Rohsenow, W. M., Choi, H. Y., Heat, Mass, and Momentum Transfer, Prentice- Hall, New York, NY, 1961
  2. Carslaw, H. S., Introduction to the Mathematical Theory of the Conduction of Heat in Solids, Macmillan, London, UK, 2010.
  3. Wazwaz, A. M., The Tanh Method for Generalized Forms of Nonlinear Heat Conduction and Burgers-Fisher equations, Applied Mathematics and Computation, 169(2005), 1, pp. 321-338
  4. Wen, Y.-X., Zhou, X.-W., Exact Solutions for the Generalized Nonlinear Heat Conduction Equations Using the Exp-function Method, Computers and Mathematics with Applications, 58(2009), 11-12, pp. 2464-2467
  5. Kabir, M. M., Analytic Solutions for Generalized Forms of the Nonlinear Heat Conduction Equation, Nonlinear Analysis: Real World Applications, 12(2011), 5, pp. 2681-2691
  6. Hristov, J., Integral Solutions to Transient Nonlinear Heat (mass) Diffusion with a Power-law Diffusivity: a Semi-infinite Medium with Fixed Boundary Conditions, Heat Mass Transfer, 52(2016), 3, pp. 635-655
  7. Schiesser, W. E., Griffiths, G. W., A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab, Cambridge University Press, Cambridge, UK, 2009
  8. Nikitin, A. G., Barannyk, T. A., Solitary Wave and Other Solutions for Nonlinear Heat Equations, Central European Journal of Mathematics, 2(2004), 5, pp. 840-858
  9. Yang, X.-J., A New Integral Transform Operator for Solving the Heat-diffusion Problem, Applied Mathematics Letters, 64(2017), February, pp. 193-197
  10. Yang, X.-J., A New Integral Transform Method for Solving Steady Heat-transfer Problem, Thermal Science, 20 (2016), Suppl.3, pp. 639-642
  11. Yang, X.-J., A New Integral Transform with an Application in Heat-transfer Problem, Thermal Science, 20(2016), Suppl.3, pp. 677-681
  12. He, J.-H., Maximal Thermo-geometric Parameter in a Nonlinear Heat Conduction Equation, Bulletin of the Malaysian Mathematical Sciences Society, 39 (2016), 2, pp. 605-608
  13. Robinson, J. C., An Introduction to Ordinary Differential Equations, Cambridge University Press, Cambridge, UK, 2004
  14. Carslaw, H. S., Jaeger, J. C., Conduction of Heat in Solids, Oxford University Press, Oxford, UK,1959