By Titus Petrila; Damian Trif
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Additional resources for Basics of fluid mechanics and introduction to computational fluid dynamics
We remark that the “equality symbols” would belong to the case and, implicitly, to the reversible (ideal) processes. Obviously for these reversible processes, using also the first law of thermodynamics under the form one obtains the so-called Gibbs equation which is fundamental in the study of ideal continua. 1 31 Specific Heats. Enthalpy The specific heat is defined as the amount of heat required to increase by unity the temperature of a mass unit of the considered medium. Correspondingly, the specific heat is Supposing that the temperature is a function of and we have where the subscript denotes the fixed variable for partial differentiation.
For any D) the fundamental lemma and the same hypothesis on the motion continuity allows us to write which is the unique general differential equation, in conservative form, associated to the studied principles. 3. 1 Constitutive Laws. Inviscid and real fluids Introductory Notions of Thermodynamics. First and Second Law of Thermodynamics Thermodynamics is concerned with the behaviour of different material systems from the point of view of certain state or thermodynamic variables parameters. The considered thermodynamic (state) variables will be the absolute temperature (the fundamental quantity for thermodynamics), the pressure the mass density the specific (per mass unity) internal energy and the specific entropy The last two state variables will be defined in what follows.
We get where the Reynolds transport theorem has been used. Backed by the same fundamental lemma, the following forms of the continuity equation can also be obtained: (the nonconservative form) or (the conservative form). We remark that if in the theoretical dynamics of fluids, the use of nonconservative or conservative form does not make a point, in the applications of computational fluid dynamics it is crucial which form is considered and that is why we insist on the difference between them.
Basics of fluid mechanics and introduction to computational fluid dynamics by Titus Petrila; Damian Trif