The Oberbeck–Boussinesq approximation as a constitutive limit

Abstract

We derive the usual Oberbeck-Boussinesq approximation as a constitutive limit of the full system describing the motion of an compressible linearly viscous fluid. To this end the starting system is written, using the Gibbs free energy, in the variables v, θ and p. The Oberbeck-Boussinesq system is then obtained as the thermal expansion coefficient α and the isothermal compressibility coefficient β tend to zero.2000 Mathematics Subject Classification. 35Q35, 76M45, 76A, 76E, 74A.

Bread staling prediction with a multiobjective particle swarm optimization‐based bread constitutive modeling method

“…The Buchniask assumption is needed when utilizing the FE when normal pressure is acting on the boundary of a semi‐infinite medium. However, the test settings are very different from theory testing, so the FE results cannot accurately represent the actual viscoelastic properties of the agricultural products (Kagei & Růžička, 2016; Rumsey & Fridley, 1977). Other constitutive modeling techniques, however, such as partial least squares (PLS) (Córdoba, 2010), regression analyses (Li et al, 2018), and nonlinear analysis (Rao et al, 1987), depend heavily on a particular piece of software and have issues with both poor program portability and poor fitting precision.…”

The Bénard Problem for Slightly Compressible Materials: Existence and Linear Instability

“…(1.4) Since condition (1.3) proves to be too strong in the light of the so-called Müller's paradox [9,10], it was recently proposed to assume at least α 0 = α(T 0 , p 0 ), see [11].…”

“…As we mentioned above, such an approximation is suited for fluids which can be assumed thermally compressible but mechanically incompressible; a theoretical justification can be found in [2,11]. More precisely, the papers [11] aim at identifying the most suitable range, as far as the dimensionless parameters are concerned, for the O-B approximation to hold.…”

“…As we mentioned above, such an approximation is suited for fluids which can be assumed thermally compressible but mechanically incompressible; a theoretical justification can be found in [2,11]. More precisely, the papers [11] aim at identifying the most suitable range, as far as the dimensionless parameters are concerned, for the O-B approximation to hold. In particular, these papers show how the O-B approximation can be derived from the balance equations of a slightly compressible fluid with a buoyancy term in the momentum balance which does not depend on the pressure.…”