• Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.349-362
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• 2016

The numerical solutions of unsteady hydromagnetic natural convection Couette flow of a viscous, incompressible and electrically conducting fluid between the two vertical parallel plates in the presence of thermal radiation, thermal diffusion and diffusion thermo are obtained here. The fundamental dimensionless governing coupled linear partial differential equations for impulsive movement and uniformly accelerated movement of the plate were solved by an efficient Finite Element Method. Computations were performed for a wide range of the governing flow parameters, viz., Thermal diffusion (Soret) and Diffusion thermo (Dufour) parameters, Magnetic field parameter, Prandtl number, Thermal radiation and Schmidt number. The effects of these flow parameters on the velocity (u), temperature (${\theta}$) and Concentration (${\phi}$) are shown graphically. Also the effects of these pertinent parameters on the skin-friction, the rate of heat and mass transfer are obtained and discussed numerically through tabular forms. These are in good agreement with earlier reported studies. Analysis indicates that the fluid velocity is an increasing function of Grashof numbers for heat and mass transfer, Soret and Dufour numbers whereas the Magnetic parameter, Thermal radiation parameter, Prandtl number and Schmidt number lead to reduction of the velocity profiles. Also, it is noticed that the rate of heat transfer coefficient and temperature profiles increase with decrease in the thermal radiation parameter and Prandtl number, whereas the reverse effect is observed with increase of Dufour number. Further, the concentration profiles increase with increase in the Soret number whereas reverse effect is seen by increasing the values of the Schmidt number.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.12
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• pp.1774-1783
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• 1998

The transition from steady laminar to chaotic convection in a glass melting furnace specified by upper surface temperature distribution has been studied by the direct numerical analysis of the two and three-dimensional time dependent Navier-Stokes equations. The thermal instability of convection roll may take place when modified Rayleigh number($Ra_m$) is larger than $9.71{\times}10^4$. It is shown that the basic flows in a glass melting furnace are steady laminar, unsteady periodic, quasi-periodic or chaotic flow. The dimensionless time scale of unsteady period is about the viscous diffusion time, ${\tau}_d=H^2/{\nu}_0$. Through primary and secondary instability analyses the fundamental unsteady feature in a glass melting furnace is well defined as the unsteady periodic or weak chaotic flow.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.3
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• pp.257-268
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• 2014

The objective of the present study is to investigate thermal diffusion and radiation effects on unsteady MHD flow past a linearly accelerated vertical porous plate with variable temperature and also with variable mass diffusion in presence of heat source or sink under the influence of applied transverse magnetic field. The fluid considered here is a gray, absorbing/emitting radiation but a non-scattering medium. At time t > 0, the plate is linearly accelerated with a velocity $u=u_0t$ in its own plane. And at the same time, plate temperature and concentration levels near the plate raised linearly with time t. The dimensionless governing equations involved in the present analysis are solved using the closed analytical method. The velocity, temperature, concentration, skin-friction, the rate or heat transfer and the rate of mass transfer are studied through graphs in terms of different physical parameters like magnetic field parameter (M), radiation parameter (R), Schmidt parameter (Sc), Soret number (So), Heat source parameter (S), Prandtl number (Pr), thermal Grashof number (Gr), mass Grashof number (Gm) and time (t).

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.6
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• pp.767-776
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• 1985

Unsteady thermally stratified flow caused by two-dimensional surface discharge of warm water into a oblong channel was investigated. Experimental study was focused on the rapidly developing thermal diffusion at small Richardson number. The basic objective were to study the interfacial mixing between a flowing layer of warm water and an underlying body of cold water and to accumulate experimental data to test computational turbulence models. Mean velocity field measurements were carried out by using NMR-CT (Nuclear Magnetic Resonance-Computerized Tomography). It detects quantitative flow image of any desired section in any direction of flow in short time. Results show that at small Richardson number warm layer rapidly penetrates into the cold layer because of strong turbulent mixing and instability between the two layers. It is found that the transfer ofheat across the interface is more vigorous than that of momentum. It is also proved that the NMR-CT technique is a very valuable tool to measure unsteady three dimensional flow field.

• Journal of the Korean Society of Propulsion Engineers
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• v.23 no.3
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• pp.18-27
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• 2019

The flow mixing characteristics for the heated dual jets were numerically studied by using URANS (unsteady Reynolds-averaged Navier-Stokes). The increased turbulent diffusion was obtained for the compressible flow, and the thermal diffusion of incompressible flow increased more than that of compressible flow. From the results of FFT and phase portraits, periodic and quasi-periodic states were observed as the jet spacing increased. It was observed that linear variations of merging points and combined points were different because unsteady flow determined the flow mixing characteristics for a large jet spacing.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.31-40
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• 2009

In the present work transformation of dimensionless heat diffusion equation for the solution of moving boundary problems have been formulated. The formulation is based on 1-D, 2-D and 3-D, unsteady heat diffusion equations. These equations are rst turned int dimensionless form by using dimensionless quantities and their transformation was formulated in liquid and solid phases. The salient feature of this work is that during the transformation of dimensionless heat diffusion equation there arises a convective term $\tilde{v}$ which is responsible for the motion of interface in liquid as well as solid phase. In the transformed heat equation, a correction factor $\beta$ also arises naturally which gives the correct transformed flux at interface.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.12
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• pp.1557-1566
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• 2004

A flame extinction phenomenon is a typical unsteady process in combustion. Flame extinction is characterized by various physical phenomena, such as convection, diffusion, and the production of heat and mass. Flame extinction can be achieved by either increasing the strain rate or curvature, by diluting an inert gas or inhibitor, or by increasing the thermal or radiant energy loss. Though the extinction is an inherently transient process, steady and quasi-steady approaches have been used as useful tools for understanding the flame extinction phenomenon. Recently, unsteady characteristics of flames have been studied by many researchers, and various attempts have been made to understand unsteady flame behavior, by using various extinction processes. Representative parameters for describing flame, such as flame temperature, important species related to reactions, and chemi-luminescence of the flame have been used as criterions of flame extinction. In these works, verification of each parameter and establishing the proper criterions of the extinction has been very important. In this study, a time-dependent flame temperature and an OH radical concentration were measured using optical methods, and the instantaneous change of the flame luminosity was also measured using a high-speed ICCD (HICCD) camera. We compare the unsteady extinction points obtained by three different methods, and we discuss transient characteristics of maximum flame temperature and OH radical distribution near the extinction limit.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.607-623
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• 2024

This article studies the effects of heat generation/absorption and thermal radiation on the unsteady magnetohydrodynamic (MHD) Casson fluid flow past a vertical plate through rotating porous medium with constant temperature and mass diffusion. It is assumed that the plate temperature and concentration level are raised uniformly. For finding the exact solution, a set of non-dimensional partial differential equations is solved analytically using the Laplace transform technique. The influence of various non-dimensional parameters on the velocity are discussed, including the effects of the magnetic parameter M, heat generation/absorption Q, thermal radiation parameter R, Prandtl number Pr, Schmidt number Sc, permeability of porous medium parameter, Casson fluid parameter γ, on velocity, temperature, and concentration profiles, which are discussed through several figures. It is found that velocity, temperature, and concentration profiles in the case of heat generation parameter Q, Casson fluid parameter γ, thermal Grashof number Gr, mass Grashof number Gc, Permeability Porous medium parameter K, and time t have retarding effects. It is also seen that the magnetic field M, Thermal Radiation parameter R, Prandtl field Pr, Schmidt number Sc have reverse effects on it.