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Boussinesq-type approximation for second-grade fluids
International Journal of Non-Linear Mechanics, 2005 We derive the equivalent of the Oberbeck-Boussinesq approximation for second-grade fluids. We find that two new nondimensional numbers (in comparison to the Newtonian model) have to be taken into account in order to arrive at the approximation.
Arianna Passerini, Gudrun Thäter
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ON THE OBERBECK-BOUSSINESQ APPROXIMATION
Mathematical Models and Methods in Applied Sciences, 1996This paper deals with a derivation (using a perturbation technique) of an approximation, due to Oberbeck8,9 and Boussinesq,1 to describe the thermal response of linearly viscous fluids that are mechanically incompressible but thermally compressible. The present approach uses a nondimensionalization suggested by Chandrasekhar2 and utilizing the ratio ...
Rajagopal, Kumbakonam Ramamani +2 more
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Approximate Symmetries of the Boussinesq Equation
Quaestiones Mathematicae, 2003In this paper we show that all exact symmetries of the linear wave equation are inherited by the Boussinesq type equation with a small parameter as approximate symmetries in any order of precision. We find an approximate integral differential transformation of any order of precision, which transforms the Boussinesq type equation into the linear wave ...
Baikov, V.A., Kordyukova, S.A.
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The validity of the boussinesq approximation for liquids and gases
International Journal of Heat and Mass Transfer, 1976Abstract A new method for obtaining approximate equations for natural convection flows is presented. The systematic application of this method leads to explicit conditions for the neglect of various terms. It is shown that this method allows the specification of the conditions under which the traditional Boussinesq approximation applies to a given ...
Gray, Donald D., Giorgini, Aldo
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Magnetic buoyancy and the Boussinesq approximation
Geophysical & Astrophysical Fluid Dynamics, 1982Abstract The full Boussinesq equations for hydromagnetic convection are derived and shown to include the effects of magnetic buoyancy. Instabilities caused by magnetic buoyancy are analyzed and their roles in double convection are brought out.
E. A. Spiegel, N. O. Weiss
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Boussinesq-Approximation (Boussinesq approximation)
2000Es handelt sich um eine mathematische Naherung bei der Beschreibung von Stromungen, die durch Auftriebseffekte hervorgerufen oder beeinflust werden (naturliche bzw. gemischte Konvektion). Dabei wird unterstellt, das die Temperaturabhangigkeit der beteiligten Stoffwerte und hier insbesondere die der Dichte ϱ* bis auf eine einzige Ausnahme vernachlassigt
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1990
In the analysis of atmospheric flows, it is usual to consider the atmosphere as an incompressible fluid medium but which is stratified in altitude. We will see that this is the consequence of the characteristic velocity U0 being always very small compared to the characteristic speed of sound c ∞ 0 = [γRT∞(0)]1/2 (flows also called “hyposonic”).
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In the analysis of atmospheric flows, it is usual to consider the atmosphere as an incompressible fluid medium but which is stratified in altitude. We will see that this is the consequence of the characteristic velocity U0 being always very small compared to the characteristic speed of sound c ∞ 0 = [γRT∞(0)]1/2 (flows also called “hyposonic”).
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Approximate Inertial Manifolds to the Newton-Boussinesq Equations
Journal of Partial Differential Equations, 1996The authors construct two approximate inertial manifolds for the following two-dimensional Newton-Boussinesq equations: \[ {\partial\over\partial t} \Delta\psi+J(\psi,\Delta\psi)=\Delta^2\psi-{R_a\over P_r} {\partial\theta\over\partial x},\quad {\partial\theta\over\partial t}+J(\psi,\theta)={1\over P_r} \Delta\theta, \] where \(J(u,v)=u_yv_x-u_xv_y\), \
Guo, Boling, Wang, Bixiang
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Boussinesq approximation in the Rayleigh-Benard problem
Fluid Dynamics, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Approximation methods for boundary control of the Boussinesq equations
52nd IEEE Conference on Decision and Control, 2013In this paper we discuss an approximation method for dealing with Dirichlet boundary control of thermal-fluid systems. The physics of displacement ventilation and buoyancy-driven flows are described by the Boussinesq equations. We first develop a computational algorithm for solving the corresponding LQR control problem for the Boussinesq equations with
John A. Burns, Weiwei Hu
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