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This paper considers a liquid in a finite-size cylinder in which Marangoni instability occurs. The upper boundary of the liquid is free and deformable. The problem of the occurrence of convection in a cylindrical container is solved using the method of separation of variables. A homogeneous differential equation of the sixth order with constant coefficients and complex boundary conditions is obtained. In the case of monotonic perturbations, an analytical expression for critical Marangoni numbers is derived. The case of a weightless liquid in the cylinder is considered.

Thermodynamic irreversibilities generated by the combustion process are evaluated and analyzed numerically. The numerical simulation is performed for a reference case study for which experimental data are available in the literature: diffusion flame properties in a common burner configuration are studied by the Fluent software with the standard k- e turbulence model and two-step chemical reaction. The study quantifies the contribution of each mechanism to entropy generation, i.e., friction, heat conduction, species diffusion, and chemical reaction. The chemical reaction and heat conduction are found to be the major sources of entropy production. Preheating of air reduces thermodynamic irreversibilities within the combustor.

An unsteady free convective flow of a viscous fluid past an oscillating plate is considered, and the effects of entropy generation are investigated. The governing partial differential equations are normalized by using suitable transformations, and an exact solution of the problem is obtained by using the Laplace transformation technique. The expressions for the velocity and temperature are then used to compute the skin friction, Nusselt number, local entropy generation number, and Bejan number.

The effect of a vertical alternating current, electric field, and heat transfer on a peristaltic flow of a dielectric viscoelastic Oldroyd fluid is studied. This analysis involves uniform and non-uniform annuli having a mild stenosis. The analytical solutions of equations of motion are based on the perturbation technique. This technique depends on two parameters: amplitude ratio and small wave number. Numerical calculations are performed to obtain the effects of several parameters, such as the electrical Rayleigh number, temperature gradient, Reynolds number, wave number, maximum height of stenosis, and Weissenberg numbers, on the distributions of velocity, temperature, electric potential, and wall shear stress. It is found that the above-mentioned distributions in the case of a convergent tapered tube are larger than those in the case of a non-tapered one as well as a diverging tapered tube.

A detailed comparison between the lattice Boltzmann method and the finite element method is presented for an incompressible steady laminar flow and heat transfer of a power-law fluid past a square cylinder between two parallel plates. Computations are performed for three different blockage ratios (ratios of the square side length to the channel width) and different values of the power-law index n covering both pseudo-plastic fluids (n<1) and dilatant fluids (n>1). The methodology is validated against the exact solution. The local and averaged Nusselt numbers are also presented. The results show that the relatively simple lattice Boltzmann method is a good alternative to the finite element method for analyzing non-Newtonian fluids.

This paper presents the results of experimental and numerical studies of heat transfer and swirling pulsating flows in short low-temperature heat pipes whose vapor channels have a conical nozzle shape. It has been found that as the evaporator of the heat pipe is heated, pressure pulsations occur in the vapor channel starting at a certain threshold value of the heat power, which is due to the start of boiling in the evaporator. The frequency of the pulsations was measured, and their dependence on the superheat of the evaporator was determined. It is found that in heat pipes with a conical vapor channel, pulsations occur at lower evaporator superheats and the pulsation frequency is greater than in heat pipes of the same size with a standard cylindrical vapor channel. It is shown that the curve of the heat-transfer coefficient versus heat load on the evaporator has an inflection corresponding to the start of boiling in the capillary porous evaporator of the heat pipe.

Nonlinear vibrations in a closed system of coupled nonlinear oscillators are studied using acetylene type molecules as an example. A criterion for the stable existence of long-lived vibrational states - local modes - in one of the oscillators is obtained. It is shown that the disappearance of a local mode, as well as its appearance, proceeds abruptly, and the mechanism of stabilization of these excitations is due to the presence or absence of internal resonances of an oscillatory system such as any polyatomic molecule. Energy values needed to excite vibrations in which local modes can appear are determined. It is shown that calculation results agree with experimental data.

This article presents a new asymptotic method to predict dynamic pull-in instability of nonlocal clamped-clamped carbon nanotubes (CNTs) near graphite sheets. Nonlinear governing equations of carbon nanotubes actuated by an electric field are derived. With due allowance for the van der Waals effects, the pull-in instability and the natural frequency-amplitude relationship are investigated by a powerful analytical method, namely, the parameter expansion method. It is demonstrated that retaining two terms in series expansions is sufficient to produce an acceptable solution. The obtained results from numerical methods verify the strength of the analytical procedure. The qualitative analysis of system dynamics shows that the equilibrium points of the autonomous system include center points and unstable saddle points. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits.

This papers the results of the numerical and analytical study of natural and quasinatural bending-gravitational oscillations of a circular elastic ice plate floating on the liquid surface and frozen to a cylindrical vertical support. In the framework of the theory of long waves in shallow water for limited and unlimited reservoirs, the dependence of natural and quasinatural frequencies of the geometrical parameters of the oscillation region is studied.

The model of generalized micropolar magneto-thermoelasticity for a thermally and perfectly conducting half-space is studied. The initial magnetic field is parallel to the boundary of the half-space. The formulation is applied to the generalized thermo-elasticity theories of Lord and Shulman, Green and Lindsay, as well as to the coupled dynamic theory. The normal mode analysis is used to obtain expressions for the temperature increment, the displacement, and the stress components of the model at the interface. By using potential functions, the governing equations are reduced to two fourth-order differential equations. By numerical calculation, the variation of the considered variables is given and illustrated graphically for a magnesium crystal micropolar elastic material. Comparisons are performed with the results predicted by the three theories in the presence of a magnetic field.