Enhanced and reduced natural convection using magnetic fluid in a square cavity

Natural convection using a magnetic fluid was studied in a square cavity under the influence of a permanent magnet. The aim was to explore the degree by which heat transfer may be controlled, enhanced or reduced, by investigating a set of different distances of a permanent magnet to the cavity. These distances of the magnet were set such that the cavity was in some cases fully dominated by buoyancy or by the magnetic body force and in other cases partly dominated by either of both body forces in different parts of the fluid. The effect on heat transfer was characterised by an averaged Nusselt number, Rayleigh and magnetic Rayleigh number. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The self-propulsion of a body with moving internal masses in a viscous fluid

An investigation of the characteristics of motion of a rigid body with variable internal mass distribution in a viscous fluid is carried out on the basis of a joint numerical solution of the Navier — Stokes equations and equations of motion for a rigid body. A nonstationary three-dimensional solution to the problem is found. The motion of a sphere and a drop-shaped body in a viscous fluid in a gravitational field, which is caused by the motion of internal material points, is explored. The possibility of self-propulsion of a body in an arbitrary given direction is shown.     

Global nonlinear stability of convection in a heat generating fluid filled channel with a moving boundary

The energy method is employed to investigate the stability of a steady convective flow in a heat generating fluid arising due to the combined effect of buoyancy, shear and pressure gradient. By introducing a suitable generalized energy functional and using energy inequalities sufficient conditions for the existence of such a flow are found. An analysis through the variational principles is then made to find sharper limits for nonlinear stability. Comparisons are made with linear results in the literature and it is shown that the linear theory fails to capture the physics of the onset of secondary flow.     

The motion in a perfect fluid of a body containing a moving point mass

The motion of a system (a rigid body, symmetrical about three mutually perpendicular planes, plus a point mass situated inside the body) in an unbounded volume of a perfect fluid, which executes vortex-free motion and is at rest at infinity, is considered. The motion of the body occurs due to displacement of the point mass with respect to the body. Two cases are investigated: (a) there are no external forces, and (b) the system moves in a uniform gravity field. An analytical investigation of the dynamic equations under conditions when the point performs a specified plane periodic motion inside the body showed that in case (a) the system can be displaced as far as desired from the initial position. In case (b) it is proved that, due to the permanent addition of energy of the corresponding relative motion of the point, the body may float upwards. On the other hand, if the velocity of relative motion of the point is limited, the body will sink. The results of numerical calculations, when the point mass performs random walks along the sides of a plane square grid rigidly connected with the body, are presented.     

On the linear stability analysis of a Maxwell fluid with double-diffusive convection

The problem of double-diffusive convection and cross-diffusion in a Maxwell fluid in a horizontal layer in porous media is re-examined using the modified Darcy–Brinkman model. The effect of Dufour and Soret parameters on the critical Darcy–Rayleigh numbers is investigated. Analytical expressions of the critical Darcy–Rayleigh numbers for the onset of stationary and oscillatory convection are derived. Numerical simulations show that the presence of Dufour and Soret parameters has a significant effect on the critical Darcy–Rayleigh number for over-stability. In the limiting case some previously published results are recovered.     

Estimates of the solutions to the equations of motion for viscous fluid in a moving cavity with a porous damper

Estimates are obtained for theL ₂-norms of the solutions to the equations of motion for viscous incompressible fluid in a moving ellipsoidal cavity with a porous damper.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 1039–1044, July, 1993.     

Effects of Reynolds and Prandtl number on mixed convection in a ventilated cavity with a heat-generating solid circular block

A numerical study has been executed to analyze the effects of Reynolds and Prandtl number on mixed convective flow and heat transfer characteristics inside a ventilated cavity in presence of a heat-generating solid circular obstacle placed at the center. The inlet opening is at the bottom of the left wall, while the outlet one is at the top of the right wall and all the walls of the cavity are considered to be adiabatic. Galerkin weighted residual finite element method is used to solve the governing equations of mass, momentum and energy. Results are presented in terms of streamlines, isotherms, the average Nusselt number, the Drag force and the average fluid temperature in the cavity for different combinations of controlling parameters namely, Reynolds number, Prandtl number and Richardson number. The results indicate that the flow and thermal fields as well as the heat transfer rate, the Drag force and the average fluid temperature in the cavity depend significantly on the mentioned parameters.     

Effect of variable density on hydromagnetic mixed convection flow of a non-Newtonian fluid past a moving vertical plate

The effect of temperature-dependent density on MHD mixed convection flow of power-law fluid past a moving semi-infinite vertical plate for high temperature differences between the plate and the ambient fluid is studied. The fluid density is assumed to decrease exponentially with temperature. The usual Boussinesq approximations are not considered due to the large temperature differences. The surface temperature of the moving plate was assumed to vary according to a power-law form, that is, T_w(x) = T_∞ + Ax^γ. The fluid is permeated by a uniform magnetic field imposed perpendicularly to the plate on the assumption of small magnetic Reynolds number. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge–Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. The effects of various parameters on the velocity and temperature profiles as well as the local skin-friction coefficient and the local Nusselt number are presented graphically and in the tabular form. The results show that application of Boussinesq approximations in a non-Newtonian fluid subjected to high temperature differences gives a significant error in the values of the skin-friction coefficient and the application of an external magnetic field reduces this error markedly in the case of shear-thickening fluid.     

On convection with nearly insulating boundaries in a low Prandtl number fluid

Summary For the Prandtl numberP in the rangeP ^1/3 1 ( is the ratio between the thermal conductivities of the boundary and of the fluid) two-dimensional rolls are preferred in contrast to square-pattern convection that represents the preferred stable convection in the rangeP ^1/3.

---

Zussammenfasung Für PrandtlzahlenP, die der RelationP ^1/3 1 genügen (\ ist das Verhältnis zwischen den thermischen Leitfähigkeiten der Wand und des Fluid), sind zweidimensionale Rollen bevorzugt im Gegensatz zur quadratartigen Konvektion, welche die bevorzugte stabile Konvektionsform im BereichP ^1/3 darstellt.

     

On the fall of a heavy rigid body in an ideal fluid

We consider a problem about the motion of a heavy rigid body in an unbounded volume of an ideal irrotational incompressible fluid. This problem generalizes a classical Kirchhoff problem describing the inertial motion of a rigid body in a fluid. We study different special statements of the problem: the plane motion and the motion of an axially symmetric body. In the general case of motion of a rigid body, we study the stability of partial solutions and point out limiting behaviors of the motion when the time increases infinitely. Using numerical computations on the plane of initial conditions, we construct domains corresponding to different types of the asymptotic behavior. We establish the fractal nature of the boundary separating these domains.     

Nonsimilar aiding mixed convection along a moving cylinder

The work of Mahmood and Merkin (ZAMP 39:186–203, 1988) concerns the mixed convection flow along a stationary cylinder in a constant free stream. In the present note, we extend the above work to general situations involving a moving cylinder.     

Nonsimilar aiding mixed convection along a moving cylinder

The work of Mahmood and Merkin (ZAMP 39:186–203, 1988) concerns the mixed convection flow along a stationary cylinder in a constant free stream. In the present note, we extend the above work to general situations involving a moving cylinder.     

On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid

We consider the motion of a rigid body immersed in a bidimensional incompressible perfect fluid. The motion of the fluid is governed by the Euler equations and the conservation laws of linear and angular momentum rule the dynamics of the rigid body. We prove the existence and uniqueness of a global classical solution for this fluid–structure interaction problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid–structure interaction problem obtained by incorporating some viscosity.