Abstract The one-dimensional diffusion equation can be written as $$\begin{aligned} \frac{\partial \phi }{\partial t}=\alpha \frac{\partial ^{2}\phi }{\partial x^{2}}\,. \end{aligned}$$ The dependent variable $$\phi $$ (such as temperature, species, momentum) diffuses in an infinite medium in both directions (to the left and right, $$x^{+}$$ and $$x^{-}$$ ) without any preference due to molecular activity. On the macroscopic scale, the rate of diffusion depends on the parameter $$\alpha $$ , where $$\alpha $$ stands for the thermal diffusion coefficient, mass diffusion coefficient, or kinematics viscosity, for energy, species, and momentum diffusion, respectively. The diffusion process becomes faster as the parameter $$\alpha $$ increases. An order of magnitude analysis of the above equation yields $$\begin{aligned} \frac{1}{\tau }\approx \alpha \frac{1}{\ell ^{2}}\,, \end{aligned}$$ where $$\tau $$ and l are time and length scales, respectively.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    The Diffusion Equation


    Beteiligte:
    Mohamad, A. A. (Autor:in)

    Erschienen in:

    Ausgabe :

    2nd ed. 2019


    Erscheinungsdatum :

    2019-01-01


    Format / Umfang :

    28 pages




    Medientyp :

    Aufsatz/Kapitel (Buch)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch




    Indirect adaptive control of unknown diffusion equation

    Airimitoaie, Tudor-Bogdan / Collewet, Christophe | AIAA | 2014



    Effective diffusion equation in a random velocity field

    VINALS, JORGE / SEKERKA, ROBERT | AIAA | 1992