• Journal of Ocean Engineering and Technology
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• v.13 no.2 s.32
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• pp.129-137
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• 1999

The time of the onset of double-diffusive convection in time-dependent, nonlinear concentration fields is investigated theoretically. The initially quiescent horizontal fluid layer with a uniform temperature gradient experiences a sudden concentration change from below, but its stable thermal stratification affects concentration effects in such way to invoke convective motion. The related stability analysis, including Soret effect, is conducted on the basis of the propagation theory. Under the linear stability theory the concentration penetration depth is used as a length scaling factor, and the similarity transform for the linearized perturbation equations. The newlly obtained stability equations are solved numerically. The resulting critical time to mark the onset of regular cells are obtained as a function of the thermal Rayleigh number, the solute Rayleigh number, and the Soret effect coefficient. For a certain value of the Soret effect coefficient, the stable thermal gradient promote double-diffusive convective motion.

• Korean Chemical Engineering Research
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• v.57 no.1
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• pp.142-147
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• 2019

The onset of buoyancy-driven convection in an initially isothermal and quiescent horizontal fluid layer was analyzed theoretically. It is well-known that at the critical Rayleigh number $Ra_c=669$ convective motion sets in with a constant-heat-flux cooling through the upper boundary. Here, based on the momentary instability concept, the dimensionless critical time ${\tau}_m$ to mark the onset of convective motion for Ra > 669 was analyzed theoretically. The energy method under the momentary stability concept was used to find the critical conditions as a function of the Rayleigh number Ra and the Prandtl number Pr. The predicted critical conditions were compared with the previous theoretical and experimental results. The momentary stability criterion gives more reasonable wavenumber than the conventional energy method.

• Korean Chemical Engineering Research
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• v.57 no.5
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• pp.723-729
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• 2019

A theoretical analysis was conducted of convective instability driven by buoyancy forces under transient temperature fields in an annular porous medium bounded by coaxial vertical cylinders. Darcy's law and Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. The linear stability equations are derived in a global domain, and then cast into in a self-similar domain. Using a spectral expansion method, the stability equations are reformed as a system of ordinary differential equations and solved analytically and numerically. The critical Darcy-Rayleigh number is founded as a function of the radius ratio. Also, the onset time and corresponding wavelength are obtained for the various cases. The critical time becomes smaller with increasing the Darcy-Rayleigh number and follows the asymptotic relation derived in the infinite horizontal porous layer.

• Journal of the Korean Physical Society
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• v.73 no.12
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• pp.1840-1844
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• 2018

Working in an arbitrary Lorentz frame, we address the question of formulating the covariant variational principle for classical, single-particle, dissipative, relativistic mechanics. First, within a Minkowskian geometry, the basic properties of the proper time ${\tau}$ and the covariant velocity $u_{\mu}$ are recapitulated. Next, using a scalar function ${\psi}(x)$ and its negative derivatives ${\varphi}_{\mu}{^{\prime}}s$, we construct a covariant Lagrangian ${\Lambda}$ that generalizes the famous Bateman-Caldirola-Kanai Lagrangian of nonrelativistic frictional mechanics. Finally, we propose a deterministic model for ${\psi}$ (involving the drag coefficient A) whose explicit solution leads to relativistic damped Rayleigh motion in the rest frame of the medium.

• Computers and Concrete
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• v.29 no.3
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• pp.201-207
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• 2022

The evaluation of velocity profile for large values of buoyancy parameter and Bioconvected Rayleigh number is examined. The non-linear problem has been tackled numerically by shooting technique. Nanofluid temperature and nanoparticle concentration slightly elevates for increasing values of thermophoresis coefficient. Thickness of thermal boundary layer is significantly increased with thermophoresis coefficient whereas thickness of concentration boundary layer is more slightly enhanced. The response of temperature and nanoparticles concentration is observed due to change in Brownian motion parameter. As Brownian motion parameter increased temperature distribution is slightly enhanced. The reverse behavior is observed in case of nanoparticles concentration. Comparison of numerical technique with the extant literature is made and an acceptable agreement is attained.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.19 no.6
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• pp.447-456
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• 2007

Suspended particles behavior when they go through a vertical riser with heat transfer is of significant concern to system designers and operators in pneumatic transport, various processes such as in chemical, pharmaceutical and food industries. When it comes with the energy system, that knowledge is critical to the reliable design practices of related equipment as heat exchangers, especially in the phase of system scale-up. Without haying a good understanding of the related physics, many scale-up practices based on their pilot plant experience suffer from unexpected behaviors and problems of unstable fluidization typically associated with excessive pressure drop, pressure fluctuation and even unsuccessful particle circulation. In the present study, we try to explain the observed phenomena with related physics, which may help understanding of our unanswered experiences and to provide the designers with more reliable resources for their work. We selected hot exhaust gas with solid particle that goes through a heat exchanger riser as our model to be considered. The effect of temperature change on the gas velocity, thermodynamic properties, and eventually on the particles motion behavior is reviewed along with some heat transfer analyses. The present study presents an optimal riser length at full scale under given conditions, and also defines the theoretical limiting length of the riser. The field data from the numerical analysis was validated against our experimental results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.9
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• pp.2304-2314
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• 1993

Natural convective flow and heat transfer in a two-dimensional square enclosure fitted with a horizontal partition are investigated numerically. The enclosure was composed of the lower hot and the upper cold horizontal walls and the adiabatic vertical walls, and a partition was situated perpendicularly at the one vertical insulated wall. The governing equations are solved by using the finite element method with Galerkin method. The computations were carried out with the variations of length, position and thermal conductivity of the partition, and Rayleigh number based on the temperature difference between two horizontal walls and the enclosure height with water(Pr=4.95). As the results, an oscillatory motion of natural convection is resulted in a sudden rise of overall heat transfer, but the increase of length of partition is significantly restrained the increase of Nusselt number. The maximum heat transfer was shown just before the transition of the direction of oscillating flow. An oscillatory motion of flow was perfectly shown the stability with the decrease of the length of partition and Rayleigh number. Also, the heat transfer was raised with the increase of the thermal conductivity in proportion to the increase of the length of partition. The stability and oscillation of flow are affected by the position of partition.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.551-556
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• 2004

The theoretical method is developed to investigate the vibration characteristics of the combined cylindrical shells with an annular plate joined to the shell at any arbitrary axial position. The structural rotational coupling between shell and plate is simulated using the rotational artificial spring. For the translational coupling, the continuity conditions for the displacements of shell and plate are used. For the uncoupled annular plate, the transverse motion is considered and the in-plane motions are not. And the additional transverse and in-plane motions of the coupled annular plate by shell deformation are considered in analysis. Theoretical formulations are based on Love's thin shell theory. The frequency equation of the combined shell with an annular plate is derived using the Rayleigh-Ritz approach. The effect of inner-to-outer radius ratio, axial position and thickness of annular plate on vibration characteristics of combined cylindrical shells is studied. To demonstrate the validity of present theoretical method, the finite element analysis is performed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.8 s.101
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• pp.968-974
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• 2005

An analytical method for the hydroelastic vibration of a vessel composed of an upper annular plate and a lower circular plate is developed by the Rayleigh-Ritz method. The two plates are clamped along a rigid cylindrical vessel wall. It is assumed that the fluid bounded by a rigid cylindrical vessel is incompressible and non-viscous. The wet mode shape of the plates is assumed as a combination of the dry mode shapes of the plates. The fluid motion is described by using the fluid displacement potential and determined by using the compatibility conditions along the fluid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict well the fluid-coupled natural frequencies comparing with the finite element analysis result.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.663-673
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• 2017

We consider the multi-harmonic model for the bubble evolution in the Rayleigh-Taylor instability in two and three dimensions. We extend the multi-harmonic model in two dimensions to a high-order and present a new class of steady-state solutions of the bubble motion. The growth rate of the bubble is expressed by a continuous family of two free parameters. The critical point in the family of solutions is identified as a saddle point and is chosen as the physically significant solution. We also present the multi-harmonic model in the cylindrical geometry and find the steady-state solution of the axisymmetric bubble. Validity and limitation of the model are also discussed.