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Analytic solutions of a two-dimensional rectangular heat equation with a heat source

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Abstract

The method of separation of variables is applied in order to investigate the analytical solutions of a certain two-dimensional rectangular heat equation. In the analysis presented here, the partial differential equation is directly transformed into ordinary differential equations. The closed-form transient temperature distributions and heat transfer rates are generalized for a linear combination of the products of Fourier-Bessel series of the exponential type. Relevant connections with some other closely-related recent works are also indicated.

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References

  1. V. S. Arpaci, Conduction Heat Transfer (Addition-Wesley, Reading, 1966).

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  2. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford University Press, Oxford and New York, 1959).

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  3. K. Y. Kung and H.M. Srivastava, “Analytic Transient Solutions of a Cylindrical Heat Equation with Oscillating Heat Flux,” Appl. Math. Comput. 195, 745–753 (2008).

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  4. H. M. Srivastava, K.Y. Kung, and K.-J. Wang, “Analytic Solutions of a Two-Dimensional Rectangular Heat Equation,” Russ. J. Math. Phys. 14(1), 115–119 (2007).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3R4, Canada

    H. M. Srivastava

  2. Department of Mechanical Engineering, Nan-Ya Institute of Technology, Chung-Li, 32034, Taiwan, Republic of China

    K. Y. Kung

  3. Department of Industrial Management, National Taiwan University of Science and Technology, Taipei, 10673, Taiwan, Republic of China

    K. -J. Wang

Authors
  1. H. M. Srivastava
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  2. K. Y. Kung
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  3. K. -J. Wang
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Correspondence to H. M. Srivastava.

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Srivastava, H.M., Kung, K.Y. & Wang, K.J. Analytic solutions of a two-dimensional rectangular heat equation with a heat source. Russ. J. Math. Phys. 15, 542–547 (2008). https://doi.org/10.1134/S1061920808040110

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  • DOI: https://doi.org/10.1134/S1061920808040110

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