By H. Versteeg, W. Malalasekera

This complete textual content provides the basics of computing device Fluid Dynamics easily and obviously.

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**Additional resources for An Introduction to Computational Fluid Dynamics: The Finite Volume Method (2nd Edition) **

**Sample text**

Smaller eddies are themselves stretched strongly by somewhat larger eddies and more weakly with the mean ﬂow. In this way the kinetic energy is handed down from large eddies to progressively smaller and smaller eddies in what is termed the energy cascade. All the ﬂuctuating properties of a turbulent ﬂow contain energy across a wide range of frequencies or wavenumbers (= 2πf/U where f is the frequency). 3, which gives the energy spectrum of turbulence downstream of a grid. The spectral energy E(κ) is shown as a function of the wavenumber κ = 2π/λ, where λ is the wavelength of the eddies.

16a–c) divided by the volume δxδyδz. 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.

E. along direction −grad φ. For instance, heat is conducted in the direction of negative temperature gradients. Thus, the product n . (−Γ grad φ) is the component of diffusion ﬂux along the outward normal vector, so out of the ﬂuid element. Similarly, the product n . ( Γ grad φ), which is also equal to Γ(−n . e. into the ﬂuid element. 42), the diffusive term, is thus associated with a ﬂux into the element and represents the net rate of increase of fluid property φ of the fluid element due to diffusion.