By Alastair H. Fitter, Robert K.M. Hay
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G. by the limits Δx → 0 and Δt → 0. 3) which is a differential formulation for the principle of mass conservation. The presumption for the differentiation procedure is that the functions c and jx , are sufficiently smooth, mathematically speaking differentiable, which is usually taken for granted. 3) is valid for one-dimensional transport and is the basis for the mathematical analysis of transport processes. The unit of the equation is [M/(L3 ·T)]. 3) is valid if there are no internal sources or sinks for the concerned biogeochemical species.
As velocity is a vector, the momentum also is a vector, with one vector component for each space dimension of the model. Conservation of Energy The kinetic energy of a fluid is expressed as 1/2ρv 2 with the physical unit [M/(LT2 )]. If energy is measured in Joule, the given expression measures Joule per volume. In problems, which include heat transfer, thermal energy is expressed in terms of temperature T . The energy content per volume is given by the product ρCT , where the new factor C is the specific heat capacity.
In order to use the functionality of a single M-file for the example from the preceding sub-chapter, the programming technique of loops has to be applied. How loops work, is best explained by an example. 1:1]; figure; hold on; for lambda = 1:1:5 f = c0*exp(-lambda*t); plot (t,f); end legend (‘1’,‘2’,‘3’,‘4’,‘5’); for is a MATLAB R keyword, which is indicated by a different color. MATLAB R keywords may not be used as variable names. The statement, starting with the for keyword, starts a loop, which ends at the line with the end keyword.