Search results for: Maxwell-Cattaneo heat transfers equations
1892 Effect of Alloying Elements and Hot Forging/Rolling Reduction Ratio on Hardness and Impact Toughness of Heat Treated Low Alloy Steels
Authors: Mahmoud M. Tash
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The present study was carried out to investigate the effect of alloying elements and thermo-mechanical treatment (TMT) i.e. hot rolling and forging with different reduction ratios on the hardness (HV) and impact toughness (J) of heat-treated low alloy steels. An understanding of the combined effect of TMT and alloying elements and by measuring hardness, impact toughness, resulting from different heat treatment following TMT of the low alloy steels, it is possible to determine which conditions yielded optimum mechanical properties and high strength to weight ratio. Experimental Correlations between hot work reduction ratio, hardness and impact toughness for thermo-mechanically heat treated low alloy steels are analyzed quantitatively, and both regression and mathematical hardness and impact toughness models are developed.Keywords: Hot Forging, hot rolling, heat treatment, hardness (hv), impact toughness (j), microstructure, low alloy steels.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 34541891 Existence of Solution for Boundary Value Problems of Differential Equations with Delay
Authors: Xiguang Li
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In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.
Keywords: Banach space, boundary value problem, differential equation, delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12311890 Coil and Jacket's Effects on Internal Flow Behavior and Heat Transfer in Stirred Tanks
Authors: B. Lakghomi, E. Kolahchian, A. Jalali, F. Farhadi
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Different approaches for heating\cooling of stirred tanks, coils and jackets, are investigated using computational fluid dynamics (CFD).A time-dependant sliding mesh approach is applied to simulate the flow in both conditions. The investigations are carried out under the turbulent flow conditions for a Rushton impeller and heating elements are considered isothermal. The flow behavior and temperature distribution are studied for each case and heat transfer coefficient is calculated. Results show different velocity profiles for each case. Unsteady temperature distribution is not similar for different cases .In the case of the coiled stirred vessel more uniform temperature and higher heat transfer coefficient is resulted.
Keywords: CFD, coil and jacket, heat transfer, stirred tank.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 49121889 Investigation of Heat Transfer by Natural Convection in an Open Channel
Authors: Mahmoud S. Ahmed, Hany A. Mohamed, Mohamed A. Omara, Mohamed F. Abdeen
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Experimental study of natural convection heat transfer inside smooth and rough surfaces of vertical and inclined equilateral triangular channels of different inclination angles with a uniformly heated surface are performed. The inclination angle is changed from 15º to 90º. Smooth and rough surface of average roughness (0.02mm) are used and their effect on the heat transfer characteristics are studied. The local and average heat transfer coefficients and Nusselt number are obtained for smooth and rough channels at different heat flux values, different inclination angles and different Rayleigh numbers (Ra) 6.48 × 105 ≤ Ra ≤ 4.78 × 106. The results show that the local Nusselt number decreases with increase of axial distance from the lower end of the triangular channel to a point near the upper end of channel, and then, it slightly increases. Higher values of local Nusselt number for rough channel along the axial distance compared with the smooth channel. The average Nusselt number of rough channel is higher than that of smooth channel by about 8.1% for inclined case at θ = 45o and 10% for vertical case. The results obtained are correlated using dimensionless groups for both rough and smooth surfaces of the inclined and vertical triangular channels.
Keywords: Natural heat transfer convection, constant heat flux, open channels, heat transfer.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23621888 Free Convection in an Infinite Porous Dusty Medium Induced by Pulsating Point Heat Source
Authors: K. Kannan, V. Venkataraman
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Free convection effects and heat transfer due to a pulsating point heat source embedded in an infinite, fluid saturated, porous dusty medium are studied analytically. Both velocity and temperature fields are discussed in the form of series expansions in the Rayleigh number, for both the fluid and particle phases based on the mean heat generation rate from source and on the permeability of the porous dusty medium. This study is carried out by assuming the Rayleigh number small and the validity of Darcy-s law. Analytical expressions for both phases are obtained for second order mean in both velocity and temperature fields and evolution of different wave patterns are observed in the fluctuating part. It has been observed that, at the vicinity of the origin, the second order mean flow is influenced only by relaxation time of dust particles and not by dust concentration.
Keywords: Pulsating point heat source, azimuthal velocity, porous dusty medium, Darcy's law.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13631887 Study on Cross-flow Heat Transfer in Fixed Bed
Authors: Hong-fang Ma, Hai-tao Zhang, Wei-yong Ying, Ding-ye Fang
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Radial flow reactor was focused for large scale methanol synthesis and in which the heat transfer type was cross-flow. The effects of operating conditions including the reactor inlet air temperature, the heating pipe temperature and the air flow rate on the cross-flow heat transfer was investigated and the results showed that the temperature profile of the area in front of the heating pipe was slightly affected by all the operating conditions. The main area whose temperature profile was influenced was the area behind the heating pipe. The heat transfer direction according to the air flow directions. In order to provide the basis for radial flow reactor design calculation, the dimensionless number group method was used for data fitting of the bed effective thermal conductivity and the wall heat transfer coefficient which was calculated by the mathematical model with the product of Reynolds number and Prandtl number. The comparison of experimental data and calculated value showed that the calculated value fit the experimental data very well and the formulas could be used for reactor designing calculation.Keywords: Cross-flow, Heat transfer, Fixed bed, Mathematical model
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18741886 Investigations of Natural Convective Heat Transfer in Rectangular Thermal Passages
Authors: Hussain H. Al-Kayiem, Ahmed K. Hussein, Toh Seng Peow
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The evaluation of the convective heat transfer of flow in passages with rectangular cross section is still of interest for the heat transfer investigators, as in the air heater solar collectors. The aim of this paper is to present investigation results on the natural convection heat transfer in a solar air heater. The effect of the channel length as heat transfer surface and the inclination of the passage were investigated. The results were obtained experimentally and theoretically. For that, an experimental test rig was fabricated with channel lengths of 1m, 1.5m, and 2m. For each length, the air outlet and inlet temperatures, absorber and cover temperatures, solar radiation intensity and air flow rate were measured at 10o, 30o, 50o, 70o, and 90o tilt angles. Measurements were recorded every 2 hours interval to investigate the transient behavior of the system. The experimental and theoretical results are presented in terms of Nu number versus Ra number and discussed. The percentages of differences between experimental and theoretical results are within the margin of 6% to 13%, effectively. It is recommended to extend the investigation to study the same configurations with different artificial surface roughing by ribs or pins.
Keywords: Convective heat transfer, Flat plate, Natural convection, Passage flow, Solar energy.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20661885 Design of a Compact Herriott Cell for Heat Flux Measurement Applications
Authors: R. G. Ramírez-Chavarría, C. Sánchez-Pérez, V. Argueta-Díaz
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In this paper we present the design of an optical device based on a Herriott multi-pass cell fabricated on a small sized acrylic slab for heat flux measurements using the deflection of a laser beam propagating inside the cell. The beam deflection is produced by the heat flux conducted to the acrylic slab due to a gradient in the refractive index. The use of a long path cell as the sensitive element in this measurement device, gives the possibility of high sensitivity within a small size device. We present the optical design as well as some experimental results in order to validate the device’s operation principle.Keywords: Heat flux, herriott cell, optical beam deflection, thermal conductivity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 28181884 Comparison of Two Types of Preconditioners for Stokes and Linearized Navier-Stokes Equations
Authors: Ze-Jun Hu, Ting-Zhu Huang, Ning-Bo Tan
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To solve saddle point systems efficiently, several preconditioners have been published. There are many methods for constructing preconditioners for linear systems from saddle point problems, for instance, the relaxed dimensional factorization (RDF) preconditioner and the augmented Lagrangian (AL) preconditioner are used for both steady and unsteady Navier-Stokes equations. In this paper we compare the RDF preconditioner with the modified AL (MAL) preconditioner to show which is more effective to solve Navier-Stokes equations. Numerical experiments indicate that the MAL preconditioner is more efficient and robust, especially, for moderate viscosities and stretched grids in steady problems. For unsteady cases, the convergence rate of the RDF preconditioner is slightly faster than the MAL perconditioner in some circumstances, but the parameter of the RDF preconditioner is more sensitive than the MAL preconditioner. Moreover the convergence rate of the MAL preconditioner is still quite acceptable. Therefore we conclude that the MAL preconditioner is more competitive than the RDF preconditioner. These experiments are implemented with IFISS package.
Keywords: Navier-Stokes equations, Krylov subspace method, preconditioner, dimensional splitting, augmented Lagrangian preconditioner.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18771883 Quantitative Changes in Biofilms of a Seawater Tubular Heat Exchanger Subjected to Electromagnetic Fields Treatment
Authors: Sergio Garcia, Alfredo Trueba, Luis M. Vega, Ernesto Madariaga
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Biofilms adhesion is one of the more important cost of industries plants on wide world, which use to water for cooling heat exchangers or are in contact with water. This study evaluated the effect of Electromagnetic Fields on biofilms in tubular heat exchangers using seawater cooling. The results showed an up to 40% reduction of the biofilm thickness compared to the untreated control tubes. The presence of organic matter was reduced by 75%, the inorganic mater was reduced by 87%, and 53% of the dissolved solids were eliminated. The biofilm thermal conductivity in the treated tube was reduced by 53% as compared to the control tube. The hardness in the effluent during the experimental period was decreased by 18% in the treated tubes compared with control tubes. Our results show that the electromagnetic fields treatment has a great potential in the process of removing biofilms in heat exchanger.Keywords: Biofilm, heat exchanger, electromagnetic fields, seawater.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6571882 Experimental Investigation of Gas Bubble Behaviours in a Domestic Heat Pump Water Heating System
Authors: J. B. Qin, X. H. Jiang, Y. T. Ge
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The growing awareness of global warming potential has internationally aroused interest and demand in reducing greenhouse gas emissions produced by human activity. Much national energy in the UK had been consumed in the residential sector mainly for space heating and domestic hot water production. Currently, gas boilers are mostly applied in the domestic water heating which contribute significantly to excessive CO2 emissions and consumption of primary energy resources. The issues can be solved by popularizing heat pump systems that are attributable to higher performance efficiency than those of traditional gas boilers. Even so, the heat pump system performance can be further enhanced if the dissolved gases in its hot water circuit can be efficiently discharged. To achieve this target, the bubble behaviors in the heat pump water heating system need to be extensively investigated. In this paper, by varying different experimental conditions, the effects of various heat pump hot water side parameters on gas microbubble diameters were measured and analyzed. Correspondingly, the effect of each parameter has been investigated. These include varied system pressures, water flow rates, saturation ratios and heat outputs. The results measurement showed that the water flow rate is the most significant parameter to influence on gas microbubble productions. The research outcomes can significantly contribute to the understanding of gas bubble behaviors at domestic heat pump water heating systems and thus the efficient way for the discharging of the associated dissolved gases.
Keywords: Dissolved gases in water, heat pump, domestic water heating system, microbubble formation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8411881 Uniform Solution on the Effect of Internal Heat Generation on Rayleigh-Benard Convection in Micropolar Fluid
Authors: Izzati K. Khalid, Nor Fadzillah M. Mokhtar, Norihan Md. Arifin
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The effect of internal heat generation is applied to the Rayleigh-Benard convection in a horizontal micropolar fluid layer. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid and free-free with the combination of isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is shown that the critical Rayleigh number decreases as the value of internal heat generation increase and hence destabilize the system.
Keywords: Internal heat generation, micropolar fluid, rayleighbenard convection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24321880 Unsteady Temperature Distribution in a Finite Functionally Graded Cylinder
Authors: A. Amiri Delouei
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In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.
Keywords: Functionally graded materials, unsteady heat conduction, cylinder, Temperature distribution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12051879 Modeling of a Small Unmanned Aerial Vehicle
Authors: A. Elsayed Ahmed, A. Hafez, A. N. Ouda, H. Eldin Hussein Ahmed, H. Mohamed Abd-Elkader
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Unmanned aircraft systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. Simulating a small unmanned aerial vehicle (SUAV) dynamics and analyzing its behavior at the preflight stage is too important and more efficient. The first step in the UAV design is the mathematical modeling of the nonlinear equations of motion. . In this paper, a survey with a standard method to obtain the full non-linear equations of motion is utilized, and then the linearization of the equations according to a steady state flight condition (trimming) is derived. This modeling technique is applied to an Ultrastick-25e fixed wing UAV to obtain the valued linear longitudinal and lateral models. At the end the model is checked by matching between the behavior of the states of the nonlinear UAV and the resulted linear model with doublet at the control surfaces.
Keywords: Equations of motion, linearization, modeling, nonlinear model, UAV.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 56111878 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
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21551877 Influence of Flash Temperature on Exergetical Performance of Organic Flash Cycle
Authors: Kyoung Hoon Kim, Chul Ho Han
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Organic Flash Cycle (OFC) has potential of improving efficiency for recovery of low temperature heat sources mainly due to reducing temperature mismatch in the heat exchanger. In this work exergetical performance analysis of ORC is conducted for recovery of low grade heat source. Effects of system parameters such as flash evaporation temperature or heating temperature are theoretically investigated on the exergy destructions (anergies) at various components of the system as well as exergy efficiency. Results show that exergy efficiency has a peak with respect to the flash temperature, and the optimum flash temperature increases with the heating temperature. The component where the largest exergy destruction occurs varies with the flash temperature or heating temperature.
Keywords: Organic flash cycle (OFC), low grade heat source, exergy, anergy, flash temperature.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19091876 A Theoretical Model for a Humidification Dehumidification (HD) Solar Desalination Unit
Authors: Yasser Elhenawy, M. Abd Elkader, Gamal H. Moustafa
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A theoretical study of a humidification dehumidification solar desalination unit has been carried out to increase understanding the effect of weather conditions on the unit productivity. A humidification-dehumidification (HD) solar desalination unit has been designed to provide fresh water for population in remote arid areas. It consists of solar water collector and air collector; to provide the hot water and air to the desalination chamber. The desalination chamber is divided into humidification and dehumidification towers. The circulation of air between the two towers is maintained by the forced convection. A mathematical model has been formulated, in which the thermodynamic relations were used to study the flow, heat and mass transfer inside the humidifier and dehumidifier. The present technique is performed in order to increase the unit performance. Heat and mass balance has been done and a set of governing equations has been solved using the finite difference technique. The unit productivity has been calculated along the working day during the summer and winter sessions and has compared with the available experimental results. The average accumulative productivity of the system in winter has been ranged between 2.5 to 4 (kg/m2)/day, while the average summer productivity has been found between 8 to 12 (kg/m2)/day.
Keywords: Finite difference, Dehumidification, Humidification, Solar desalination, Solar collector, Simulation, Water productivity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16811875 Two-dimensional Heat Conduction of Direct Cooling in the Rotor of an Electrical Generator(Numerical Analysis)
Authors: A. Kargar, A. Kianifar, H. Mohammadiun
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Two-dimensional heat conduction within a composed solid material with a constant internal heat generation has been investigated numerically in a sector of the rotor a generator. The heat transfer between two adjacent materials is assumed to be purely conduction. Boundary conditions are assumed to be forced convection on the fluid side and adiabatic on symmetry lines. The control volume method is applied for the diffusion energy equation. Physical coordinates are transformed to the general curvilinear coordinates. Then by using a line-by-line method, the temperature distribution in a sector of the rotor has been determined. Finally, the results are normalized and the effect of cooling fluid on the maximum temperature of insulation is investigated.
Keywords: general curvilinear coordinates , jacobian, controlvolume.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18151874 Strict Stability of Fuzzy Differential Equations by Lyapunov Functions
Authors: Mustafa Bayram Gücen, Coşkun Yakar
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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.Keywords: Fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11271873 On Some Properties of Interval Matrices
Authors: K. Ganesan
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By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations.Keywords: Interval arithmetic, Interval matrix, linear equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20551872 Study of Heat Transfer of Nanofluids in a Circular Tube
Authors: M. Amoura, M. Alloti, A. Mouassi, N. Zeraibi
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Heat transfer behavior of three different types of nanofluids flowing through a horizontal tube under laminar regime has been investigated numerically. The wall of tube is maintained at constant temperature. Al2O3-water, CuO-water and TiO2-water are used with different Reynolds number and different volume fraction. The numerical results of heat transfer indicate that the Nusselt number of nanofluids is larger than that of the base fluid. The Pressure loss coefficient decreases by increasing Reynolds number for all types of nanofluids. Results of Nusselt number enhancement and pressure loss coefficient enhancement indicate that Al2O3 nanoparticules give the best results in term of thermal-hydrolic properties.
Keywords: Heat transfer, Laminar flow, Nanofluid, Numerical study.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 30671871 Approximate Solution to Non-Linear Schrödinger Equation with Harmonic Oscillator by Elzaki Decomposition Method
Authors: Emad K. Jaradat, Ala’a Al-Faqih
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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.
Keywords: Non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two- dimensional Schrodinger equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9041870 Combined Effect of Cold Rolling and Heat Treatment on the Mechanical Properties of Al-Ti Alloy
Authors: Adeosun S. Oluropo, Sekunowo O. Israel, Talabi S. Isaac
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This study investigated the combined effect of cold rolling and heat treatment on the mechanical properties of Al-Ti alloy. Samples of the alloy are cast in metal mould to obtain 0.94-2.19wt% mixes of titanium. These samples are grouped into untreated (as-cast) and those that are cold rolled to fifty percent reduction, homogenized at 5000C and soaked for one hour. The cold rolled and heat treated samples are normalized (RTn) and quench-tempered (RTq-t) at 1000C. All these samples are subjected to tensile, micro-hardness and microstructural evaluation. Results show remarkable improvement in the mechanical properties of the cold rolled and heat treated samples compared to the as-cast. In particular, the RTq-t samples containing titanium in the range of 1.7-2.2% demonstrates improve tensile strength by 24.7%, yield strength, 28%, elastic modulus, 38.3% and micro-hardness, 20.5%. The Al3Ti phase being the most stable precipitate in the α-Al matrix appears to have been responsible for the significant improvement in the alloy’s mechanical properties. It is concluded that quench and temper heat treatment is an effective method of improving the strength-strain ratio of cold rolled Al-.0.9-2.2%Ti alloy.
Keywords: Aluminum-titanium alloy, heat treatment, mechanical properties, precipitate.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27591869 Comparing the Efficiency of Simpson’s 1/3 and 3/8 Rules for the Numerical Solution of First Order Volterra Integro-Differential Equations
Authors: N. M. Kamoh, D. G. Gyemang, M. C. Soomiyol
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This paper compared the efficiency of Simpson’s 1/3 and 3/8 rules for the numerical solution of first order Volterra integro-differential equations. In developing the solution, collocation approximation method was adopted using the shifted Legendre polynomial as basis function. A block method approach is preferred to the predictor corrector method for being self-starting. Experimental results confirmed that the Simpson’s 3/8 rule is more efficient than the Simpson’s 1/3 rule.
Keywords: Collocation shifted Legendre polynomials, Simpson’s rule and Volterra integro-differential equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9751868 Numerical Study of the Influence of the Primary Stream Pressure on the Performance of the Ejector Refrigeration System Based on Heat Exchanger Modeling
Authors: Elhameh Narimani, Mikhail Sorin, Philippe Micheau, Hakim Nesreddine
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Numerical models of the heat exchangers in ejector refrigeration system (ERS) were developed and validated with the experimental data. The models were based on the switched heat exchangers model using the moving boundary method, which were capable of estimating the zones’ lengths, the outlet temperatures of both sides and the heat loads at various experimental points. The developed models were utilized to investigate the influence of the primary flow pressure on the performance of an R245fa ERS based on its coefficient of performance (COP) and exergy efficiency. It was illustrated numerically and proved experimentally that increasing the primary flow pressure slightly reduces the COP while the exergy efficiency goes through a maximum before decreasing.
Keywords: Coefficient of performance, ejector refrigeration system, exergy efficiency, heat exchangers modeling, moving boundary method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5511867 Exact Solutions of Steady Plane Flows of an Incompressible Fluid of Variable Viscosity Using (ξ, ψ)- Or (η, ψ)- Coordinates
Authors: Rana Khalid Naeem, Asif Mansoor, Waseem Ahmed Khan, Aurangzaib
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The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating that the flow equations possess an infinite set of solutions.
Keywords: Exact solutions, Fluid of variable viscosity, Navier-Stokes equations, Steady plane flows
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 34481866 Thermo-mechanical Behavior of Pressure Tube of Indian PHWR at 20 bar Pressure
Authors: Gopal Nandan, P. K. Sahooa, Ravi Kumara, B Chatterjeeb, D. Mukhopadhyayb, H. G. Leleb
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In a nuclear reactor Loss of Coolant accident (LOCA) considers wide range of postulated damage or rupture of pipe in the heat transport piping system. In the case of LOCA with/without failure of emergency core cooling system in a Pressurised Heavy water Reactor, the Pressure Tube (PT) temperature could rise significantly due to fuel heat up and gross mismatch of the heat generation and heat removal in the affected channel. The extent and nature of deformation is important from reactor safety point of view. Experimental set-ups have been designed and fabricated to simulate ballooning (radial deformation) of PT for 220 MWe IPHWRs. Experiments have been conducted by covering the CT by ceramic fibers and then by submerging CT in water of voided PTs. In both the experiments, it is observed that ballooning initiates at a temperature around 665´┐¢C and complete contact between PT and Caldaria Tube (CT) occurs at around 700´┐¢C approximately. The strain rate is found to be 0.116% per second. The structural integrity of PT is retained (no breach) for all the experiments. The PT heatup is found to be arrested after the contact between PT and CT, thus establishing moderator acting as an efficient heat sink for IPHWRs.Keywords: Pressure Tube, Calandria Tube, Thermo-mechanicaldeformation, Boiling heat transfer, Reactor safety
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22241865 Tuning of Thermal FEA Using Krylov Parametric MOR for Subsea Application
Authors: A. Suleng, T. Jelstad Olsen, J. Šindler, P. Bárta
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A dead leg is a typical subsea production system component. CFD is required to model heat transfer within the dead leg. Unfortunately its solution is time demanding and thus not suitable for fast prediction or repeated simulations. Therefore there is a need to create a thermal FEA model, mimicking the heat flows and temperatures seen in CFD cool down simulations. This paper describes the conventional way of tuning and a new automated way using parametric model order reduction (PMOR) together with an optimization algorithm. The tuned FE analyses replicate the steady state CFD parameters within a maximum error in heat flow of 6 % and 3 % using manual and PMOR method respectively. During cool down, the relative error of the tuned FEA models with respect to temperature is below 5% comparing to the CFD. In addition, the PMOR method obtained the correct FEA setup five times faster than the manually tuned FEA.Keywords: CFD, convective heat, FEA, model tuning, subseaproduction
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17241864 Solitary Wave Solutions for Burgers-Fisher type Equations with Variable Coefficients
Authors: Amit Goyal, Alka, Rama Gupta, C. Nagaraja Kumar
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We have solved the Burgers-Fisher (BF) type equations, with time-dependent coefficients of convection and reaction terms, by using the auxiliary equation method. A class of solitary wave solutions are obtained, and some of which are derived for the first time. We have studied the effect of variable coefficients on physical parameters (amplitude and velocity) of solitary wave solutions. In some cases, the BF equations could be solved for arbitrary timedependent coefficient of convection term.Keywords: Solitary wave solution, Variable coefficient Burgers- Fisher equation, Auxiliary equation method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16271863 Modelling of Organic Rankine Cycle for Waste Heat Recovery Process in Supercritical Condition
Authors: Jahedul Islam Chowdhury, Bao Kha Nguyen, David Thornhill, Roy Douglas, Stephen Glover
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Organic Rankine Cycle (ORC) is the most commonly used method for recovering energy from small sources of heat. The investigation of the ORC in supercritical condition is a new research area as it has a potential to generate high power and thermal efficiency in a waste heat recovery system. This paper presents a steady state ORC model in supercritical condition and its simulations with a real engine’s exhaust data. The key component of ORC, evaporator, is modelled using finite volume method, modelling of all other components of the waste heat recovery system such as pump, expander and condenser are also presented. The aim of this paper is to investigate the effects of mass flow rate and evaporator outlet temperature on the efficiency of the waste heat recovery process. Additionally, the necessity of maintaining an optimum evaporator outlet temperature is also investigated. Simulation results show that modification of mass flow rate is the key to changing the operating temperature at the evaporator outlet.
Keywords: Organic Rankine cycle, supercritical condition, steady state model, waste heat recovery.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3073