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Understanding time scales of diffusive fluxes and the implication for steady state and steady shape conditions
Author(s) -
Jazaei Farhad,
Simpson Matthew J.,
Clement T. Prabhakar
Publication year - 2017
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/2016gl071914
Subject(s) - steady state (chemistry) , transient (computer programming) , variable (mathematics) , mechanics , diffusion , steady state theory , scale (ratio) , thermodynamics , statistical physics , environmental science , physics , mathematics , chemistry , computer science , mathematical analysis , universe , operating system , de sitter universe , quantum mechanics , astrophysics
The diffusion equation is one of the most commonly used models for describing environmental problems involving heat, solute, and water transport. A diffusive system can be either transient or steady state . When a system is transient, the dependent variable (e.g., temperature, concentration, or hydraulic head) varies with time; whereas at steady state, the temporal variations are negligible. Here we consider an intermediate state, called steady shape , corresponding to the situation where temporal variations in diffusive fluxes are negligible but the dependent variable may remain transient. We present a general theoretical framework for identifying steady shape conditions and propose a novel method for evaluating the time scale needed for a diffusive system to approach both steady shape and steady state conditions.