By H. Versteeg, W. Malalasekera
This entire textual content provides the basics of machine Fluid Dynamics easily and obviously.
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Additional info for An Introduction to Computational Fluid Dynamics: The Finite Volume Method (2nd Edition)
5). 19) Fourier’s law of heat conduction relates the heat ﬂux to the local temperature gradient. 21) Energy equation Thus far we have not deﬁned the speciﬁc energy E of a ﬂuid. Often the energy of a ﬂuid is deﬁned as the sum of internal (thermal) energy i, kinetic energy –12 (u2 + v2 + w2) and gravitational potential energy. 1 GOVERNING EQUATIONS OF FLUID FLOW AND HEAT TRANSFER 19 takes the view that the ﬂuid element is storing gravitational potential energy. It is also possible to regard the gravitational force as a body force, which does work on the ﬂuid element as it moves through the gravity ﬁeld.
If the initial amplitude is given by a, the solution of this problem is A πct D A πx D y(x, t) = a cos B E sin B E C LF C LF The solution shows that the vibration amplitude remains constant, which demonstrates the lack of damping in the system. This absence of damping has a further important consequence. Consider, for example, initial conditions corresponding to a near-triangular initial shape whose apex is a section of a circle with very small radius of curvature. This initial shape has a sharp discontinuity at the apex, but it can be represented by means of a Fourier series as a combination of sine waves.
The Kolmogorov microscales can be expressed in terms of the rate of energy dissipation of a turbulent ﬂow and the ﬂuid viscosity, which uses the notion that in every turbulent ﬂow the rate of production of turbulent energy has to be broadly in balance with its rate of dissipation to prevent unlimited growth of turbulence energy.