Concepts

Core Conservation Module

Consider an arbitrary section of a bar lying between x and x+x. The mass in this portion of the bar can change due to three factors: flow in (through x); flow out (through x+x) and heat gain/loss throughout the section.


Balance of Mass is expressed as

where


Mass Density

where (x',t) is the mass per unit length at section x of the bar.


Gain


Fundamental Theorem of Calculus

Balance of mass becomes


Dubois-Reymond Lemma

x and x+ x are arbitrary


Boundary Conditions


Initial Conditions


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