By H. Versteeg, W. Malalasekra
This article goals to supply info for amateur CFD clients who, while constructing CFD abilities through the use of software program, want a reader that covers the basics of the fluid dynamics at the back of complicated engineering flows and of the numerical resolution algorithms on which CFD codes are dependent.
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Extra info for An Introduction to Computational Fluid Dynamics: The Finite Volume Method Approach
5. 69) shows the domination in pores of rather complex (and most probably organic) molecules with a large number of degrees of freedom (the isochoric heat capacity per one gaseous-phase molecule must, in any case, exceed three). 69) it is therefore seen that the larger is c2v , the more abruptly the right-hand side of the dependence CM (T ) will decrease. 61) obtained a little earlier qualitatively describe the analytical dependence of the speciﬁc heat capacity of a unit volume of a porous dielectric on the temperature, to which Figs.
Denoted as [a, a+ ]), then after elementary calculations we obtain aa+ − a+ a = 1 . 35) + As we know, the so-called Bose operators of creation (a ) and annihilation (a) of quasi-particles satisfy this commutation condition. It would be so if only one oscillator were concerned. 4 Temperature-Behavior Estimation of Porous Media Heat Capacity 43 atomic oscillators. e. we should introduce the sum over all oscillators. Hence we represent the Hamiltonian as N − H= i=1 2 2M ∂2 ∂x2i 1 + M ω 2 x2i . 37) where the law of phonon dispersion is ωk = cs k, where cs is the average velocity of a sound quantum, which may be introduced, for example, according to the formula 3/c3s = 2/c3t + 1/c3l , where cl and ct are longitudinal and transverse sound velocities respectively, and k is the wave vector.
5 Comparison with Experiment In order to clear up the agreement of the theoretical description of the heat capacity CV (T ), whose behavior is illustrated in Fig. 5, with reality, a simple but labor-consuming experiment was conducted with the purpose of studying the behavior of CVP (T ) for diﬀerent types of cellulose and paper in the temperature range from 50◦ C up to 275◦ C (see Figs. 5). 2 with the measured values of the heat capacity. 6 Mechanical Strength of the Porous Structure: Calculation of the Break Force and Its Dependence on the Substance Density If the model representation of the porous dielectric structure is available, the task to calculate the break force does not seem to be too complicated.