• Title/Summary/Keyword: heat equilibrium equation

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Exact solution of a thick walled functionally graded piezoelectric cylinder under mechanical, thermal and electrical loads in the magnetic field

  • Arefi, M.;Rahimi, G.H.;Khoshgoftar, M.J.
    • Smart Structures and Systems
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    • v.9 no.5
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    • pp.427-439
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    • 2012
  • The present paper deals with the analytical solution of a functionally graded piezoelectric (FGP) cylinder in the magnetic field under mechanical, thermal and electrical loads. All mechanical, thermal and electrical properties except Poisson ratio can be varied continuously and gradually along the thickness direction of the cylinder based on a power function. The cylinder is assumed to be axisymmetric. Steady state heat transfer equation is solved by considering the appropriate boundary conditions. Using Maxwell electro dynamic equation and assumed magnetic field along the axis of the cylinder, Lorentz's force due to magnetic field is evaluated for non homogenous state. This force can be employed as a body force in the equilibrium equation. Equilibrium and Maxwell equations are two fundamental equations for analysis of the problem. Comprehensive solution of Maxwell equation is considered in the present paper for general states of non homogeneity. Solution of governing equations may be obtained using solution of the characteristic equation of the system. Achieved results indicate that with increasing the non homogenous index, different mechanical and electrical components present different behaviors along the thickness direction. FGP can control the distribution of the mechanical and electrical components in various structures with good precision. For intelligent properties of functionally graded piezoelectric materials, these materials can be used as an actuator, sensor or a component of piezo motor in electromechanical systems.

Calculation of Mass-Heat Balance on the Iodine Crystallizer for SI Thermochemical Hydrogen Production Process (SI 열화학 수소 생산 공정 요오드 결정화기 열-물질 수지 계산)

  • Lee, Pyoung Jong;Park, Byung Heung
    • Journal of Institute of Convergence Technology
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    • v.5 no.1
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    • pp.1-5
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    • 2015
  • SI thermochemical hydrogen production process achieves water splitting into hydrogen and oxygen through three chemical reactions. The process is comprised of three sections and one of them is HI decomposition into $H_2$ and $I_2$ called as Section III. The production of $H_2$ included processes involving EED for concentrating a product stream from Section I. Additionally an $I_2$ crystallization would be considered to reduce burden on EED by removing certain amount of $I_2$ out of a process stream prior to EED. In this study, the current thermodynamic model of SI process was briefly described and the calculation results of the applied Electrolytes NRTL model for phase equilibrium calculations was illustrated for ternary systems of Section III. We calculated temperature and heat duty of an $I_2$ crystallizer and heat duty of heaters using UVa model and heat balance equation of simulation tool. The results were expected to be used as operation information in optimizing HI decomposition process and setting up material balance throughout SI process.

Determination of Optimal Austenitizing Temperature in High-Alloyed Tool Steels (고합금 공구강의 최적 오스테나이트 처리 온도 결정)

  • Park, Dongsung;Jun, Joong-Hwan;Lee, Min-Ha;Lee, Seok-Jae
    • Journal of the Korean Society for Heat Treatment
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    • v.30 no.4
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    • pp.156-163
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    • 2017
  • In the present study, we investigated the optimal austenitizing temperature of high-alloyed tool steels from an industrial point of view. Austenitizing temperatures for manufacturing 25 commercial tool steels were surveyed with their alloy compositions. The relationship between the austenitizing temperatures and the critical equilibrium temperatures by thermodynamic-based calculation was analyzed and a correlation was found. Based on the austenitizing temperatures of 25 commercial tool steels and the thermodynamic calculation results, we proposed a simple equation to predict an optimal austenitizing temperature to achieve superior mechanical properties of high-alloyed tool steels. The applicability of the proposed equation was experimentally validated with a new developed tool steel.

Numerical Analysis of Turbulent Flow and Heat Transfer in a Rectangular Duct with a 180° Bend Degree (직사각단면을 갖는 180°곡관내의 난류 유동및 열전달에 관한 수치해석적 연구)

  • Choi, Y.D.;Moon, C.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.6 no.4
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    • pp.325-336
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    • 1994
  • A numerical simulation of velocity and temperature fields and Nusselt number distributions is performed by using the algebraic stress model (ASM) for the velocity profiles and low Reynolds number ${\kappa}-{\varepsilon}$ model and the algebraic heat flux model(AHFM) for turbulent heat transfer in a $180^{\circ}$ bend with a constant wall heat flux. In the low Reynolds number ${\kappa}-{\varepsilon}$ model, turbulent Prandtl number is modified by considering the streamline curvature effect and the non-equilibrium effect between turbulent kinetic energy production and dissipation rate. Every heat flux term presented in the transport equation of turbulent heat flux is reduced to algebraic expressions in a way similar to algebraic stress model. Also. in the wall region, low Reynods number algebraic heat flux model(AHFM) is applied.

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Passive Control of the Condensation Shock Wave Oscillation in a Supersonic Nozzle (초음속 노즐에서 발생하는 응축충격파 진동의 피동제어)

  • Baek, Seung-Cheol;Kwon, Soon-Bum;Kim, Heuy-Dong
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.26 no.7
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    • pp.951-958
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    • 2002
  • Rapid expansion of a moist air or a stream through a supersonic nozzle often leads to non-equilibrium condensation shock wave, causing a considerable energy loss in flow field. Depending on amount of latent heat released due to non-equilibrium condensation, the flow is highly unstable or a periodical oscillation accompanying the condensation shock wave in the nozzle. The unsteadiness of the condensation shock wave is always associated with several kinds of instabilities as well as noise and vibration of flow devices. In the current study, a passive control technique using a porous wall with a plenum cavity underneath is applied for the purpose of alleviation of the condensation shock oscillations in a transonic nozzle. A droplet growth equation is coupled with two-dimensional Navier-Stokes equation system. Computations are carried out using a third-order MUSCL type TVD finite-difference scheme with a second-order fractional time step. An experiment using an indraft wind tunnel is made to validate the present computational results. The results show that the oscillations of the condensation shock wave are completely suppressed by the current passive control method.

Development of four-equation turbulence model for prediction of mixed convective heat transfer on a flat plate (수평평판위 의 혼합대류 열전말 계산 을 위한 4-방정식 모델 의 개발)

  • 성형진;정명균
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.7 no.2
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    • pp.193-203
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    • 1983
  • The mixed convective heat transfer problems are characterized by the relatively significant contribution of buoyancy force to the transport processes of momentum and heat. Past analytical studies on this kind of problems have been carried out by employing either the conventional R-.epsilon. turbulence model which includes constant turbulent Prandtl number .sigma.$_{+}$ 1 or an extended R-.epsilon. turbulence model which takes account of the buoyancy effect in appropriate length scale equations. But in the latter case, the temperature variance .the+a.$^{2}$ over bar is approximated by a model under local equilibrium condition and the time scale ratio between velocity and temperature is assumed to be constant. These approximation is known to break down when the buoyancy effect is dominant. The present study is aimed at development of new computational turbulence closure level which can be applied to this rather complex turbulent process. The temperature variance is obtained directly by solving its dynamic transport equation and the time scale ratio which is variable in space is computed by a solution of a dynamic equation for the rate of scalar dissipation .epsilon.$_{\thetod}$ It was found that the computational results are in good agreement with available experimental data of wide range of unstable conditions.

Comparative Study on the Properties Estimation of the Constituents of the Natural Gas and Refrigerant Mixtures Between GERG-2004 Model and Peng-Robinson Equation of State (GERG-2004 모델식과 Peng-Robinson 상태방정식을 이용한 천연가스 및 냉매 구성성분들의 물성 비교연구)

  • Kim, Mi-Jin;Rho, Jae-Hyun;Kim, Dong-Sun;Cho, Jung-Ho
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.13 no.2
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    • pp.906-918
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    • 2012
  • In this study, we compared with results simulated by EOS(Equation of State) using Peng-Robinson model and GERG-2004 model for estimating vapor pressure, latent heat of vaporation, liquid density, and binary isotherm vapor-liquid equilibrium on pure components composing natural gases. We obtained the simulated results that while EOS using GERG-2004 model is more accurate than EOS using Peng-Robinson model for estimating liquid density, but rather it is less accurate for estimating binary isotherm vapor-liquid equilibrium. On the other hand, the use of Costald model in EOS using Peng-Robinson model for increasing more accuracy to calculate liquid density is almost same as EOS using GERG-2004 model within the error of 1 % compared with experimental data. Also, we confirmed that on the estimation of binary isotherm vapor-liquid equilibrium, EOS using GERG-2004 model is more accurate than EOS using Peng-Robinson model, but they are almost same.

Effects of Soil and Air Flow Characteristics on the Soil-Air Heat Exchanger Performances (토양과 공기유동특성이 토양-공기 열교환기 성능에 미치는 영향)

  • 김영복;김기영
    • Journal of Biosystems Engineering
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    • v.23 no.1
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    • pp.21-30
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    • 1998
  • A theoretical model was developed to evaluate the effects of soil and airflow characteristics on the soil-air heat exchanger performances. The model, which includes three-dimensional transient energy and mass equilibrium-equation, was solved by using a computer program that uses Finite Difference Methods and Gauss-Seidel iteration computation. Energy gains, heat exchange efficiencies, and outlet air temperature are presented including the effects of soil moisture content, soil conductivity, soil thermal diffusivity, and soil initial temperature. Also, data related to the effects of airflow rate and inlet air temperature on the thermal performance of the system are presented. The results indicated that energy gains depend on soil conductivity, soil thermal diffusivity, and soil initial temperature. Heat exchange efficiencies relied on air mass flow rate and soil moisture content.

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Simulation and Optimization Study on the Pressure-Swing Distillation of Ethanol-Benzene Azeotrope (Ethanol-Benzene 공비혼합물의 분리를 위한 압력변환 증류공정의 전산모사)

  • Park, Hoey Kyung;Kim, Dong Sun;Cho, JungHo
    • Korean Chemical Engineering Research
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    • v.53 no.4
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    • pp.450-456
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    • 2015
  • In the present study, modelling and optimization of ethanol-benzene separation process were performed using pressure-swing distillation. Order to obtain a reliable results, vapour-liquid equilibrium (VLE) experiments of ethanol-benzene binary system were performed. The parameters of thermodynamic equation were determined using experimental data and the regression. The pressure-swing distillation process optimization was performed to obtain high purity ethanol and high purity benzene into a low-high pressure columns configuration and a high-low pressure columns configuration. The heat duty values of the reboiler from simulation were compared, and the process was optimized to minimize the heat duty.

Magneto-thermo-elastic response of a rotating functionally graded cylinder

  • Hosseini, Mohammad;Dini, Ali
    • Structural Engineering and Mechanics
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    • v.56 no.1
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    • pp.137-156
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    • 2015
  • In this paper, an analytical solution of displacement, strain and stress field for rotating thick-walled cylinder made of functionally graded material subjected to the uniform external magnetic field and thermal field in plane strain state has been studied. Stress, strain and displacement field as a function of radial coordinates considering magneto-thermo-elasticity are derived analytically. According to the Maxwell electro-dynamic equations, Lorentz force in term of displacement is obtained in cylindrical coordinates. Also, symmetric temperature distribution along the thickness of hollow cylinder is obtained by solving Fourier heat transfer equation in cylindrical coordinates. Using equation of equilibrium and thermo-mechanical constitutive equations associated with Lorentz force, a second-order inhomogeneous differential equation in term of displacement is obtained and will be solved analytically. Except Poisson's ratio, other mechanical properties such as elasticity modulus, density, magnetic permeability coefficient, heat conduction coefficient and thermal expansion coefficient are assumed to vary through the thickness according to a power law. In results analysis, non-homogeneity parameter has been chosen arbitrary and inner and outer surface of cylinder are assumed to be rich metal and rich ceramic, respectively. The effect of rotation, thermal, magnetic field and non-homogeneity parameter of functionally graded material which indicates percentages of cylinder's constituents are studied on displacement, Von Mises equivalent stress and Von Mises equivalent strain fields.