Search results for: thermal influence of boundary parameters
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 6965

Search results for: thermal influence of boundary parameters

6815 Influence of Number Parallels Paths of a Winding on Overvoltage in the Asynchronous Motors Fed by PWM- converters

Authors: Belassel Mohand-Tahar

Abstract:

This work is devoted to the calculation of the undulatory parameters and the study of the influence of te number parallel path of a winding on overvoltage compared to the frame and between turns (sections) in a multiturn random winding of an asynchronous motors supplied with PWM- converters.

Keywords: Asynchronous Motors, Parallel path, PWMconverters, Undulatory process, Undulatory parameters, Undulatory voltage

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6814 CFD Parametric Study of Mixers Performance

Authors: Mikhail Strongin

Abstract:

The mixing of two or more liquids is very common in many industrial applications from automotive to food processing. CFD simulations of these processes require comparison with test results. In many cases it is practically impossible. Therefore, comparison provides with scalable tests.  So, parameterization of the problem is sufficient to capture the performance of the mixer.

However, the influence of geometrical and thermo-physical parameters on the mixing is not well understood.

In this work influence of geometrical and thermal parameters was studied. It was shown that for full developed turbulent flows (Re > 104), Pet»const and concentration of secondary fluid ~ F(r/l).

In other words, the mixing is practically independent of total flow rate and scale for a given geometry and ratio of flow rates of mixing flows. This statement was proved in present work for different geometries and mixtures such as EGR and water-urea mixture.

Present study has been shown that the best way to improve the mixing is to establish geometry with the lowest Pet number possible by intensifying the turbulence in the domain. This is achievable by using step geometry, impinging flow EGR on a wall, or EGR jets, with a strong change in the flow direction, or using swirler like flow in the domain or combination all of these factors. All of these results are applicable to any mixtures of no compressible fluids.  

Keywords: CFD, mixing, fluids, parameterization, scalability.

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6813 A Large-Eddy Simulation of Vortex Cell flow with Incoming Turbulent Boundary Layer

Authors: Arpiruk Hokpunna, Michael Manhart

Abstract:

We present a Large-Eddy simulation of a vortex cell with circular shaped. The results show that the flow field can be sub divided into four important zones, the shear layer above the cavity, the stagnation zone, the vortex core in the cavity and the boundary layer along the wall of the cavity. It is shown that the vortex core consits of solid body rotation without much turbulence activity. The vortex is mainly driven by high energy packets that are driven into the cavity from the stagnation point region and by entrainment of fluid from the cavity into the shear layer. The physics in the boundary layer along the cavity-s wall seems to be far from that of a canonical boundary layer which might be a crucial point for modelling this flow.

Keywords: Turbulent flow, Large eddy simulations, boundary layer and cavity flow, vortex cell flow.

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6812 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (III)

Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using Leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferential equation, boundary value problems

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6811 A New Approach to Solve Blasius Equation using Parameter Identification of Nonlinear Functions based on the Bees Algorithm (BA)

Authors: E. Assareh, M.A. Behrang, M. Ghalambaz, A.R. Noghrehabadi, A. Ghanbarzadeh

Abstract:

In this paper, a new approach is introduced to solve Blasius equation using parameter identification of a nonlinear function which is used as approximation function. Bees Algorithm (BA) is applied in order to find the adjustable parameters of approximation function regarding minimizing a fitness function including these parameters (i.e. adjustable parameters). These parameters are determined how the approximation function has to satisfy the boundary conditions. In order to demonstrate the presented method, the obtained results are compared with another numerical method. Present method can be easily extended to solve a wide range of problems.

Keywords: Bees Algorithm (BA); Approximate Solutions; Blasius Differential Equation.

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6810 Optimization of Parametric Studies Using Strategies of Sampling Techniques

Authors: Lenka Ševelová, Aleš Florian

Abstract:

To improve the efficiency of parametric studies or tests planning the method is proposed, that takes into account all input parameters, but only a few simulation runs are performed to assess the relative importance of each input parameter. For K input parameters with N input values the total number of possible combinations of input values equals NK. To limit the number of runs, only some (totally N) of possible combinations are taken into account. The sampling procedure Updated Latin Hypercube Sampling is used to choose the optimal combinations. To measure the relative importance of each input parameter, the Spearman rank correlation coefficient is proposed. The sensitivity and the influence of all parameters are analyzed within one procedure and the key parameters with the largest influence are immediately identified.

Keywords: Concrete, pavement, simulation, reliability, Latin Hypercube Sampling, parametric studies.

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6809 The Design of PIP Controller for a Thermal System with Large Time Delay

Authors: Seiyed Hamid Zareh, Atabak Sarrafan, Kambiz Ghaemi Osgouie

Abstract:

This paper will first describe predictor controllers when the proportional-integral-derivative (PID) controllers are inactive for procedures that have large delay time (LDT) in transfer stage. Therefore in those states, the predictor controllers are better than the PID controllers, then compares three types of predictor controllers. The value of these controller-s parameters are obtained by trial and error method, so here an effort has been made to obtain these parameters by Ziegler-Nichols method. Eventually in this paper Ziegler-Nichols method has been described and finally, a PIP controller has been designed for a thermal system, which circulates hot air to keep the temperature of a chamber constant.

Keywords: Proportional-integral-predictive controller, Transferfunction, Delay time, Transport-lag.

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6808 MHD Boundary Layer Flow of a Nanofluid Past a Wedge Shaped Wick in Heat Pipe

Authors: Ziya Uddin

Abstract:

This paper deals with the theoretical and numerical investigation of magneto hydrodynamic boundary layer flow of a nanofluid past a wedge shaped wick in heat pipe used for the cooling of electronic components and different type of machines. To incorporate the effect of nanoparticle diameter, concentration of nanoparticles in the pure fluid, nanothermal layer formed around the nanoparticle and Brownian motion of nanoparticles etc., appropriate models are used for the effective thermal and physical properties of nanofluids. To model the rotation of nanoparticles inside the base fluid, microfluidics theory is used. In this investigation ethylene glycol (EG) based nanofluids, are taken into account. The non-linear equations governing the flow and heat transfer are solved by using a very effective particle swarm optimization technique along with Runge-Kutta method. The values of heat transfer coefficient are found for different parameters involved in the formulation viz. nanoparticle concentration, nanoparticle size, magnetic field and wedge angle etc. It is found that, the wedge angle, presence of magnetic field, nanoparticle size and nanoparticle concentration etc. have prominent effects on fluid flow and heat transfer characteristics for the considered configuration.

Keywords: Heat transfer, Heat pipe, numerical modeling, nanofluid applications, particle swarm optimization, wedge shaped wick.

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6807 Thermal Diffusivity Measurement of Cadmium Sulphide Nanoparticles Prepared by γ-Radiation Technique

Authors: Azmi Zakaria, Reza Zamiri, Parisa Vaziri, Elias Saion, M. Shahril Husin

Abstract:

In this study we applied thermal lens (TL) technique to study the effect of size on thermal diffusivity of cadmium sulphide (CdS) nanofluid prepared by using γ-radiation method containing particles with different sizes. In TL experimental set up a diode laser of wavelength 514 nm and intensity stabilized He-Ne laser were used as the excitation source and the probe beam respectively, respectively. The experimental results showed that the thermal diffusivity value of CdS nanofluid increases when the of particle size increased.

Keywords: Thermal diffusivity, nanofluids, thermal lens

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6806 Effects of Thermal Radiation on Mixed Convection in a MHD Nanofluid Flow over a Stretching Sheet Using a Spectral Relaxation Method

Authors: Nageeb A. H. Haroun, Sabyasachi Mondal, Precious Sibanda

Abstract:

The effects of thermal radiation, Soret and Dufour parameters on mixed convection and nanofluid flow over a stretching sheet in the presence of a magnetic field are investigated. The flow is subject to temperature dependent viscosity and a chemical reaction parameter. It is assumed that the nanoparticle volume fraction at the wall may be actively controlled. The physical problem is modelled using systems of nonlinear differential equations which have been solved numerically using a spectral relaxation method. In addition to the discussion on heat and mass transfer processes, the velocity, nanoparticles volume fraction profiles as well as the skin friction coefficient are determined for different important physical parameters. A comparison of current findings with previously published results for some special cases of the problem shows an excellent agreement.

Keywords: Non-isothermal wedge, thermal radiation, nanofluid, magnetic field, Soret and Dufour effects.

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6805 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (I)

Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems

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6804 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (II)

Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems

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6803 The Effects of Tissue Optical Parameters and Interface Reflectivity on Light Diffusion in Biological Tissues

Authors: MA. Ansari

Abstract:

In cancer progress, the optical properties of tissues like absorption and scattering coefficient change, so by these changes, we can trace the progress of cancer, even it can be applied for pre-detection of cancer. In this paper, we investigate the effects of changes of optical properties on light penetrated into tissues. The diffusion equation is widely used to simulate light propagation into biological tissues. In this study, the boundary integral method (BIM) is used to solve the diffusion equation. We illustrate that the changes of optical properties can modified the reflectance or penetrating light.

Keywords: Diffusion equation, boundary element method, refractive index

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6802 Triggering Supersonic Boundary-Layer Instability by Small-Scale Vortex Shedding

Authors: Guohua Tu, Zhi Fu, Zhiwei Hu, Neil D Sandham, Jianqiang Chen

Abstract:

Tripping of boundary-layers from laminar to turbulent flow, which may be necessary in specific practical applications, requires high amplitude disturbances to be introduced into the boundary layers without large drag penalties. As a possible improvement on fixed trip devices, a technique based on vortex shedding for enhancing supersonic flow transition is demonstrated in the present paper for a Mach 1.5 boundary layer. The compressible Navier-Stokes equations are solved directly using a high-order (fifth-order in space and third-order in time) finite difference method for small-scale cylinders suspended transversely near the wall. For cylinders with proper diameter and mount location, asymmetry vortices shed within the boundary layer are capable of tripping laminar-turbulent transition. Full three-dimensional simulations showed that transition was enhanced. A parametric study of the size and mounting location of the cylinder is carried out to identify the most effective setup. It is also found that the vortex shedding can be suppressed by some factors such as wall effect.

Keywords: Boundary layer instability, boundary layer transition, vortex shedding, supersonic flows, flow control.

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6801 Field Study for Evaluating Winter Thermal Performance of Auckland School Buildings

Authors: Bin Su

Abstract:

Auckland has a temperate climate with comfortable warm, dry summers and mild, wet winters. An Auckland school normally does not need air conditioning for cooling during the summer and only needs heating during the winter. The Auckland school building thermal design should more focus on winter thermal performance and indoor thermal comfort for energy efficiency. This field study of testing indoor and outdoor air temperatures, relative humidity and indoor surface temperatures of three classrooms with different envelopes were carried out in the Avondale College during the winter months in 2013. According to the field study data, this study is to compare and evaluate winter thermal performance and indoor thermal conditions of school buildings with different envelopes.

Keywords: Building envelope, Building mass effect, Building thermal comfort, Building thermal performance, School building.

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6800 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem

Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

Abstract:

We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.

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6799 Estimating the Effect of Fluid in Pressing Process

Authors: A. Movaghar, R. A. Mahdavinejad

Abstract:

To analyze the effect of various parameters of fluid on the material properties such as surface and depth defects and/or cracks, it is possible to determine the affection of pressure field on these specifications. Stress tensor analysis is also able to determine the points in which the probability of defection creation is more. Besides, from pressure field, it is possible to analyze the affection of various fluid specifications such as viscosity and density on defect created in the material. In this research, the concerned boundary conditions are analyzed first. Then the solution network and stencil used are mentioned. With the determination of relevant equation on the fluid flow between notch and matrix and their discretion according to the governed boundary conditions, these equations can be solved. Finally, with the variation creations on fluid parameters such as density and viscosity, the affection of these variations can be determined on pressure field. In this direction, the flowchart and solution algorithm with their results as vortex and current function contours for two conditions with most applications in pressing process are introduced and discussed.

Keywords: Pressing, notch, matrix, flow function, vortex.

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6798 Numerical Investigation of Indoor Air Quality and Thermal Comfort in a Ventilated Room

Authors: Ramy H. Mohammed

Abstract:

Understanding the behavior of airflow in a room is essential for building designers to provide the most efficient design of ventilation system, and having acceptable indoor air quality. This trend is the motive to solve the relationship between airflow parameters and thermal comfort. This paper investigates airflow characteristics, indoor air quality (IAQ), and the thermal comfort (TC) in a ventilated room with a displacement ventilation system using three dimensional CFD code [AirPak 2.0.6]. After validation of the code, a numerical study is executed for a typical room with dimensions of 5m by 3m by 3m height according to a variety of supply air velocities, supply air temperature and supply air relative humidity. The finite volume method and the indoor zero equation turbulence models are employed for solving the governing equations numerically. The temperature field and the mean age of air (MAA) in the modeled room for a displacement ventilation system are determined according to a variety of the above parameters. The variable air volume (VAV) systems with different supply air velocity are applicable to control room air temperature for a displacement ventilation system.

Keywords: Displacement ventilation, AirPak, Indoor zero equation, MAA.

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6797 Anomalous Thermal Behavior of CuxMg1-xNb2O6 (x=0,0.4,0.6,1) for LTCC Substrate

Authors: Jyotirmayee Satapathy, M. V. Ramana Reddy

Abstract:

LTCC (Low Temperature Co-fired Ceramics) being the most advantageous technology towards the multilayer substrates for various applications, demands an extensive study of its raw materials. In the present work, a series of CuxMg1-xNb2O6 (x=0,0.4,0.6,1) has been prepared using sol-gel synthesis route and sintered at a temperature of 900°C to study its applicability for LTCC technology as the firing temperature is 900°C in this technology. The phase formation has been confirmed using X-ray Diffraction. Thermal properties like thermal conductivity and thermal expansion being very important aspect as the former defines the heat flow to avoid thermal instability in layers and the later provides the dimensional congruency of the dielectric material and the conductors, are studied here over high temperature up to the firing temperature. Although the values are quite satisfactory from substrate requirement point view, results have shown anomaly over temperature. The anomalous thermal behavior has been further analyzed using TG-DTA.

Keywords: Niobates, LTCC, Thermal conductivity, Thermal expansion, TG-DTA.

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6796 Thermal Characterization of Graphene Oxide-Epoxy Nanocomposites Produced by Aqueous Emulsion

Authors: H. A. Brandão Cordeiro, M. G. Bocardo, N. C. Penteado, V. T. de Moraes, S. M. Giampietri Lebrão, G. W. Lebrão

Abstract:

The present study desired to obtain a nanocomposite of epoxy resin reinforced with graphene oxide (OG), for aerospace application, produced by aqueous emulsion. It was obtained proof bodies with 0.00 wt%, 0.10 wt%, 0.25 wt% and 0.50 wt% in weight of nanoparticles, to check the influence of it in the final quality of the obtained product. The validation of the results was done by the application thermal characterization by differential scanning calorimetry (DSC). It was seen that the nanocomposite reinforced with 0.10 wt% of OG showed the best results, the average glass transition temperature, at 2 °C, compared to the pure resin.

Keywords: Aqueous emulsion, graphene, nanocomposites, thermal characterization.

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6795 Mechanical and Thermal Stresses in Functionally Graded Cylinders

Authors: A. Kurşun, E. Kara, E. Çetin, Ş. Aksoy, A. Kesimli

Abstract:

In this study, thermal elastic stress distribution occurred on long hollow cylinders made of functionally graded material (FGM) was analytically defined under thermal, mechanical and thermo mechanical loads. In closed form solutions for elastic stresses and displacements are obtained analytically by using the infinitesimal deformation theory of elasticity. It was assumed that elasticity modulus, thermal expansion coefficient and density of cylinder materials could change in terms of an exponential function as for that Poisson’s ratio was constant. A gradient parameter n is chosen between - 1 and 1. When n equals to zero, the disc becomes isotropic. Circumferential, radial and longitudinal stresses in the FGMs cylinders are depicted in the figures. As a result, the gradient parameters have great effects on the stress systems of FGMs cylinders.

Keywords: Functionally graded materials, hollow cylinder, thermoelasticity, thermomechanical load.

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6794 Development of Thermal Insulation Materials Based On Silicate Using Non-Traditional Binders and Fillers

Authors: J. Hroudova, J. Zach, L. Vodova

Abstract:

When insulation and rehabilitation of structures is important to use quality building materials with high utility value. One potentially interesting and promising groups of construction materials in this area are advanced, thermally insulating plaster silicate based. With the present trend reduction of energy consumption of building structures and reducing CO2 emissions to be developed capillary-active materials that are characterized by their low density, low thermal conductivity while maintaining good mechanical properties.

The paper describes the results of research activities aimed at the development of thermal insulating and rehabilitation material ongoing at the Technical University in Brno, Faculty of Civil Engineering. The achieved results of this development will be the basis for subsequent experimental analysis of the influence of thermal and moisture loads developed on these materials.

Keywords: Insulation materials, rehabilitation materials, lightweight aggregate, fly ash, slag, hemp fibers, glass fibers, metakaolin.

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6793 Thermal Fatigue Behavior of Austenitic Stainless Steels

Authors: Jung-Ho Moon, Tae Kwon Ha

Abstract:

Continually increasing working temperature and growing need for greater efficiency and reliability of automotive exhaust require systematic investigation into the thermal fatigue properties especially of high temperature stainless steels. In this study, thermal fatigue properties of 300 series austenitic stainless steels have been evaluated in the temperature ranges of 200-800oC and 200-900oC. Systematic methods for control of temperatures within the predetermined range and measurement of load applied to specimens as a function of temperature during thermal cycles have been established. Thermal fatigue tests were conducted under fully constrained condition, where both ends of specimens were completely fixed. Load relaxation behavior at the temperatures of thermal cycle was closely related with the thermal fatigue property.

Keywords: Austenitic stainless steel, automotive exhaust, thermal fatigue, microstructure, load relaxation.

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6792 Clamped-clamped Boundary Conditions for Analysis Free Vibration of Functionally Graded Cylindrical Shell with a Ring based on Third Order Shear Deformation Theory

Authors: M.Pourmahmoud, M.Salmanzadeh, M.Mehrani, M.R.Isvandzibaei

Abstract:

In this paper a study on the vibration of thin cylindrical shells with ring supports and made of functionally graded materials (FGMs) composed of stainless steel and nickel is presented. Material properties vary along the thickness direction of the shell according to volume fraction power law. The cylindrical shells have ring supports which are arbitrarily placed along the shell and impose zero lateral deflections. The study is carried out based on third order shear deformation shell theory (T.S.D.T). The analysis is carried out using Hamilton-s principle. The governing equations of motion of FGM cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.

Keywords: Vibration, FGM, Cylindrical shell, Hamilton'sprinciple, Ring support.

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6791 Quartic Nonpolynomial Spline Solutions for Third Order Two-Point Boundary Value Problem

Authors: Talaat S. El-Danaf

Abstract:

In this paper, we develop quartic nonpolynomial spline method for the numerical solution of third order two point boundary value problems. It is shown that the new method gives approximations, which are better than those produced by other spline methods. Convergence analysis of the method is discussed through standard procedures. Two numerical examples are given to illustrate the applicability and efficiency of the novel method.

Keywords: Quartic nonpolynomial spline, Two-point boundary value problem.

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6790 Effect of Linear Thermal Gradient on Steady-State Creep Behavior of Isotropic Rotating Disc

Authors: Minto Rattan, Tania Bose, Neeraj Chamoli

Abstract:

The present paper investigates the effect of linear thermal gradient on the steady-state creep behavior of rotating isotropic disc using threshold stress based Sherby’s creep law. The composite discs made of aluminum matrix reinforced with silicon carbide particulate has been taken for analysis. The stress and strain rate distributions have been calculated for discs rotating at linear thermal gradation using von Mises’ yield criterion. The material parameters have been estimated by regression fit of the available experimental data. The results are displayed and compared graphically in designer friendly format for the above said temperature profile with the disc operating under uniform temperature profile. It is observed that radial and tangential stresses show minor variation and the strain rates vary significantly in the presence of thermal gradation as compared to disc having uniform temperature.

Keywords: Creep, isotropic, steady-state, thermal gradient.

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6789 Evaluation of Optimal Residence Time in a Hot Rolled Reheating Furnace

Authors: Dong-Eun Lee

Abstract:

To calculate the temperature distribution of the slab in a hot rolled reheating furnace a mathematical model has been developed by considering the thermal radiation in the furnace and transient conduction in the slab. The furnace is modeled as radiating medium with spatially varying temperature. Radiative heat flux within the furnace including the effect of furnace walls, combustion gases, skid beams and buttons is calculated using the FVM and is applied as the boundary condition of the transient conduction equation of the slab. After determining the slab emissivity by comparison between simulation and experimental work, variation of heating characteristics in the slab is investigated in the case of changing furnace temperature with various time and the slab residence time is optimized with this evaluation.

Keywords: Reheating Furnace, Thermal Radiation, ResidenceTime, FVM for Radiation

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6788 Thermal and Mechanical Buckling of Short and Long Functionally Graded Cylindrical Shells Using First Order Shear Deformation Theory

Authors: O. Miraliyari, M.M. Najafizadeh, A.R. Rahmani, A. Momeni Hezaveh

Abstract:

This paper presents the buckling analysis of short and long functionally graded cylindrical shells under thermal and mechanical loads. The shell properties are assumed to vary continuously from the inner surface to the outer surface of the shell. The equilibrium and stability equations are derived using the total potential energy equations, Euler equations and first order shear deformation theory assumptions. The resulting equations are solved for simply supported boundary conditions. The critical temperature and pressure loads are calculated for both short and long cylindrical shells. Comparison studies show the effects of functionally graded index, loading type and shell geometry on critical buckling loads of short and long functionally graded cylindrical shells.

Keywords: Buckling, Functionally graded materials, Short and long cylindrical shell, Thermal and mechanical loads.

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6787 Experimental Investigation the Effectiveness of Using Heat Pipe on the Spacecraft Mockup Panel

Authors: M. Abdou, M. K. Khalil

Abstract:

The heat pipe is a thermal device which allows efficient transport of thermal energy. The experimental work of this research was split into two phases; phase 1 is the development of the facilities, material and test rig preparation. Phase 2 is the actual experiments and measurements of the thermal control mockup inside the modified vacuum chamber (MVC). Due to limited funds, the development on the thermal control subsystem was delayed and the experimental facilities such as suitable thermal vacuum chamber with space standard specifications were not available from the beginning of the research and had to be procured over a period of time. In all, these delays extended the project by one and a half year. Thermal control subsystem needs a special facility and equipment to be tested. The available vacuum chamber is not suitable for the thermal tests. Consequently, the modification of the chamber was a must. A vacuum chamber has been modified to be used as a Thermal Vaccum Chamber (TVC). A MVC is a vacuum chamber modified by using a stainless mirror box with perfect reflectability and the infrared lamp connected with the voltage regulator to vary the lamp intensity as it will be illustrated through the paper.

Keywords: Heat pipe, thermal control, thermal vacuum chamber, satellite.

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6786 A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation

Authors: Aziz Sezgin

Abstract:

We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: Backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems.

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