Transient nonsimilarity nonlinear heat diffusion solutions

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    An approximate analytical method for treating parabolic type nonlinear heat diffusion equations is descibed in this study. The method involves transformation of the partial differential equations along with their initial and boundary conditions in terms of several pseudo-similarity variables followed by numerical solution of a system of quasi-ordinary differential equations. One obvious advantage of the approach is that the solution at a particular time can be found independently of the previous history of the temperature field. The simplicity and directness of the method are illustrated by solving the problem of combined conduction and thermal radiation in a large, heat-generating, particulate bed in contact with a solid. Comparison of the present analytical results is made with available finite difference solutions and found to be good.

    Original languageEnglish (US)
    Pages (from-to)295-301
    Number of pages7
    JournalJournal of Heat Transfer
    Volume105
    Issue number2
    DOIs
    StatePublished - Jan 1 1983

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    heat
    Heat radiation
    thermal radiation
    Ordinary differential equations
    partial differential equations
    particulates
    Partial differential equations
    beds
    Temperature distribution
    temperature distribution
    differential equations
    histories
    Boundary conditions
    boundary conditions
    conduction
    radiation
    Hot Temperature

    All Science Journal Classification (ASJC) codes

    • Materials Science(all)
    • Condensed Matter Physics
    • Mechanics of Materials
    • Mechanical Engineering

    Cite this

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    title = "Transient nonsimilarity nonlinear heat diffusion solutions",
    abstract = "An approximate analytical method for treating parabolic type nonlinear heat diffusion equations is descibed in this study. The method involves transformation of the partial differential equations along with their initial and boundary conditions in terms of several pseudo-similarity variables followed by numerical solution of a system of quasi-ordinary differential equations. One obvious advantage of the approach is that the solution at a particular time can be found independently of the previous history of the temperature field. The simplicity and directness of the method are illustrated by solving the problem of combined conduction and thermal radiation in a large, heat-generating, particulate bed in contact with a solid. Comparison of the present analytical results is made with available finite difference solutions and found to be good.",
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    Transient nonsimilarity nonlinear heat diffusion solutions. / Cheung, Fan-bill B.

    In: Journal of Heat Transfer, Vol. 105, No. 2, 01.01.1983, p. 295-301.

    Research output: Contribution to journalArticle

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    AB - An approximate analytical method for treating parabolic type nonlinear heat diffusion equations is descibed in this study. The method involves transformation of the partial differential equations along with their initial and boundary conditions in terms of several pseudo-similarity variables followed by numerical solution of a system of quasi-ordinary differential equations. One obvious advantage of the approach is that the solution at a particular time can be found independently of the previous history of the temperature field. The simplicity and directness of the method are illustrated by solving the problem of combined conduction and thermal radiation in a large, heat-generating, particulate bed in contact with a solid. Comparison of the present analytical results is made with available finite difference solutions and found to be good.

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