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Green’s functions for non-self-adjoint problems in heat conduction with steady motion

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Abstract

Heat conduction in a rectangular parallelepiped that is in steady motion relative to a fluid is studied in this paper. The governing equation consists of the standard heat equation plus lower-order derivative terms with the space variables that represent the effects of the solid flow. The presence of the first-order-derivative terms with the space variables renders the spatial part of the governing differenial equation non-self-adjoint and care must be exercised in defining the new Green’s functions to be used in representing the solutions of initial- and boundary-value problems. It is illustrated how the Green’s functions may be constructed and how solutions of initial- and boundary-value problems may be obtained that lead to numerical results. Convergence properties of the solutions are also discussed.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    David H. Y. Yen

  2. Department of Mechanical Engineering, Michigan State University, East Lansing, MI, 48824, USA

    James V. Beck

Authors
  1. David H. Y. Yen
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  2. James V. Beck
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Correspondence to James V. Beck.

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Yen, D.H.Y., Beck, J.V. Green’s functions for non-self-adjoint problems in heat conduction with steady motion. J Eng Math 57, 115–132 (2007). https://doi.org/10.1007/s10665-006-9067-9

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  • DOI: https://doi.org/10.1007/s10665-006-9067-9

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