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Heat Conduction in a Finite Bar with a Linear Source

In: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences

Author

Listed:
  • David J. Wollkind

    (Washington State University, Department of Mathematics)

  • Bonni J. Dichone

    (Gonzaga University, Department of Mathematics)

Abstract

This chapter considers heat conduction in a laterally insulated finite bar with a linear source term. That requires a derivation of the heat equation in a nonmoving continua from a conservation of energy balance law, which involves source and flux terms by using both the divergence theorem and the DuBois–Reymond Lemma. Then an equation of state and constitutive relations must be introduced. Finally, for appropriate boundary conditions, the partial differential heat equation is solved by a separation of variables eigenvalue approach and initial conditions satisfied by a Fourier series methodology, which is introduced as a pastoral interlude. This allows for an examination of the long-time behavior of that heat conduction situation and a deduction of a stability criterion.

Suggested Citation

  • David J. Wollkind & Bonni J. Dichone, 2017. "Heat Conduction in a Finite Bar with a Linear Source," Springer Books, in: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences, chapter 0, pages 99-113, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-73518-4_5
    DOI: 10.1007/978-3-319-73518-4_5
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