Flat diffuser: steady state flow of a viscous incompressible fluid

The article analyzes the evolution of the main single-mode stationary flow of a viscous incompressible fluid in a flat diffuser (with a constant sign in the flow velocity depending on the aperture angle of the diffuser) in the classical formulation of the Jeffrey — Hamel problem. Depending on the determining parameters (the diffuser angle and the Reynolds number), a complete solution of the problem is given. The transition of main single-mode flow at a fixed angle of the diffuser to the multimode modes (where the velocity of flow changes sign depending on the angle of the diffuser) when the Reynolds number has been changed is shown. It is found that starting from a certain critical value of the Reynolds number, the existence of a stationary single-mode flow is impossible. The corresponding bifurcation diagram is constructed and the dependence of this critical value vs. the aperture angle of diffuser is found. The possibility of realization of both single-mode and multimode flows at the same Reynolds number is shown. The parameters of the second and third bifurcation domains are also calculated.

One-Electron Conical Nanotube in External Electric and Magnetic Fields

The effects of variation of the aperture angle on spectral and magnetic properties of one-electron nanotube of the axially symmetrical conical shape in the presence of the electric and magnetic fields have been investigated based on a numerical solution of the Schrödinger equation in the effective mass approximation. We show that the energy spectrum and the magnetic dipole moment of the structure are changed dramatically with increase of the cone’s aperture angle due to the interplay between the diamagnetic and centrifugal forces, which push the electron at opposite directions. Particularly, the energy levels close to the ground state become quasi-degenerate, owing to a change of the hidden symmetry, induced by the magnetic field in this structure, when its morphology is converted from the cylindrical type to the conical one and the Aharonov-Bohm oscillations of the ground state energy and of the magnetic dipole moment are quenched. We found additionally that any weak electric field breaks this hidden symmetry, splits quasi-degenerate state, and restores the Aharonov-Bohm oscillations.

Natural convection air flow in vertical upright-angled triangular cavities under realistic thermal boundary conditions

This paper presents an analytical and numerical computation of laminar natural convection in a collection of vertical upright-angled triangular cavities filled with air. The vertical wall is heated with a uniform heat flux; the inclined wall is cooled with a uniform temperature; while the upper horizontal wall is assumed thermally insulated. The defining aperture angle ? is located at the lower vertex between the vertical and inclined walls. The finite element method is implemented to perform the computational analysis of the conservation equations for three aperture angles ? (= 15?, 30? and 45?) and height-based modified Rayleigh numbers ranging from a low Ra = 0 (pure conduction) to a high 109. Numerical results are reported for the velocity and temperature fields as well as the Nusselt numbers at the heated vertical wall. The numerical computations are also focused on the determination of the value of the maximum or critical temperature along the hot vertical wall and its dependence with the modified Rayleigh number and the aperture angle.