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Heat equation 1 dimensional meaning of thin rod?

A thin rod is used to model the heat equation, what is the meaning of this?

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  • 2 months ago
    Favorite Answer

    A "thin rod" has a "small" cross sectional area, so that diffusion doesn't need to be modeled throughout the cross-section and at the boundary around the rod. That is, heat only varies with the x and t variables.

    If you want to model a wire-like rod, you would have to use different assumptions than if you wanted to model a very thick rod.

    Simplifying assumptions and experimental physical laws are used in deriving different PDEs.

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  • Vaman
    Lv 7
    2 months ago

    It is Q dT/dx= - K T. T is the temperature. K and Q are constants. Make it dT/dx = - m T. This gives the temperature distribution at a given time. Any mathematical method will have such equation.

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  • 2 months ago

    which heat equation? can you provide a reference or example?

    edit:

    partial differential equations are beyond my knowledge.

    the thin rod is an attempt to show a simple example of the equation. 

    • Kevin2 months agoReport

      https://en.wikipedia.org/wiki/Heat_equation

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