Search results for: heat exchangers modeling

Authors: David Lávicka

Abstract:

This paper looks into detailed investigation of thermal-hydraulic characteristics of the flow field in a fuel rod model, especially near the spacer. The area investigate represents a source of information on the velocity flow field, vortex, and on the amount of heat transfer into the coolant all of which are critical for the design and improvement of the fuel rod in nuclear power plants. The flow field investigation uses three-dimensional Computational Fluid Dynamics (CFD) with the Reynolds stresses turbulence model (RSM). The fuel rod model incorporates a vertical annular channel where three different shapes of spacers are used; each spacer shape is addressed individually. These spacers are mutually compared in consideration of heat transfer capabilities between the coolant and the fuel rod model. The results are complemented with the calculated heat transfer coefficient in the location of the spacer and along the stainless-steel pipe.

Keywords: CFD, fuel rod model, heat transfer, spacer

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Authors: Yehia Manawi, Ahmad Kayvani Fard

Abstract:

Membrane distillation is an emerging technology which has been used to produce freshwater and purify different types of aqueous mixtures. Qatar is an arid country where almost 100% of its freshwater demand is supplied through the energy-intensive thermal desalination process. The country’s need for water has reached an all-time high which stipulates finding an alternative way to augment freshwater without adding any drastic affect to the environment. The objective of this paper was to investigate the potential of using the industrial low grade waste heat to produce freshwater using membrane distillation. The main part of this work was conducting a heat audit on selected Qatari chemical industries to estimate the amounts of freshwater produced if such industrial waste heat were to be recovered. By the end of this work, the main objective was met and the heat audit conducted on the Qatari chemical industries enabled us to estimate both the amounts of waste heat which can be potentially recovered in addition to the amounts of freshwater which can be produced if such waste heat were to be recovered.

By the end, the heat audit showed that around 605 Mega Watts of waste heat can be recovered from the studied Qatari chemical industries which resulted in a total daily production of 5078.7 cubic meter of freshwater.

This water can be used in a wide variety of applications such as human consumption or industry. The amount of produced freshwater may look small when compared to that produced through thermal desalination plants; however, one must bear in mind that this water comes from waste and can be used to supply water for small cities or remote areas which are not connected to the water grid. The idea of producing freshwater from the two widely-available wastes (thermal rejected brine and waste heat) seems promising as less environmental and economic impacts will be associated with freshwater production which may in the near future augment the conventional way of producing freshwater currently being thermal desalination. This work has shown that low grade waste heat in the chemical industries in Qatar and perhaps the rest of the world can contribute to additional production of freshwater using membrane distillation without significantly adding to the environmental impact.

Keywords: Membrane distillation, desalination, heat recovery, environment.

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Authors: Trevor E. Davis, Isaac Cassar, Yi-Kai Lo, Wentai Liu

Abstract:

This study models the use of transcutaneous electrical nerve stimulation on skin with a disk electrode in order to simulate tissue damage. The current density distribution above a disk electrode is known to be a dynamic and non-uniform quantity that is intensified at the edges of the disk. The non-uniformity is subject to change through using various electrode geometries or stimulation methods. One of these methods known as edge-retarded stimulation has shown to reduce this edge enhancement. Though progress has been made in modeling the behavior of a disk electrode, little has been done to test the validity of these models in simulating the actual heat transfer from the electrode. This simulation uses finite element software to couple the injection of current from a disk electrode to heat transfer described by the Pennesbioheat transfer equation. An example application of this model is studying an experimental form of stimulation, known as edge-retarded stimulation. The edge-retarded stimulation method will reduce the current density at the edges of the electrode. It is hypothesized that reducing the current density edge enhancement effect will, in turn, reduce temperature change and tissue damage at the edges of these electrodes. This study tests this hypothesis as a demonstration of the capabilities of this model. The edge-retarded stimulation proved to be safer after this simulation. It is shown that temperature change and the fraction of tissue necrosis is much greater in the square wave stimulation. These results bring implications for changes of procedures in transcutaneous electrical nerve stimulation and transcutaneous spinal cord stimulation as well.

Keywords: Bioheat transfer, Electrode, Neuroprosthetics, TENS, Transcutaneous stimulation.

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Authors: Chih-Chieh Chen, Chih-Hao Chen, Guan-Wei Wu, Sih-Li Chen

Abstract:

A high thermal dissipation performance polyethylene terephthalate heat pipe has been fabricated and tested in this research. Polyethylene terephthalate (PET) is used as the container material instead of copper. Copper mesh and methanol are sealed in the middle of two PET films as the wick structure and working fluid. Although the thermal conductivity of PET (0.15-0.24 W/m·K) is much smaller than copper (401 W/m·K), the experiment results reveal that the PET heat pipe can reach a minimum thermal resistance of 0.146 (^oC/W) and maximum effective thermal conductivity of 18,310 (W/m·K) with 36.9 vol% at 26 W input power. However, when the input power is larger than 30 W, the laminated PET will debond due to the high vapor pressure of methanol.

Keywords: PET, heat pipe, thermal resistance, effective thermal conductivity.

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Authors: Ibrahim A. Aref, Tarek A. El-Mihoub

Abstract:

This paper shows how we can integrate communication modeling into the design modeling at early stages of the design flow. We consider effect of incorporating noise such as impulsive noise on system stability. We show that with change of the system model and investigate the system performance under the different communication effects. We modeled a unmanned aerial vehicle (UAV) as a demonstration using SystemC methodology. Moreover the system is modeled by joining the capabilities of UML and SystemC to operate at system level.

Keywords: Modelling, SoC, SystemC, UAV, Simulation, SoC.

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Authors: Sina Babadi, K. M. Ebrahimi

Abstract:

The aim of this paper is to determine the stress levels at the end of a long slender shaft such as a drilling assembly used in the oil or gas industry using a mathematical model in real-time. The torsional deflection experienced by this type of drilling shaft (about 4 KM length and 20 cm diameter hollow shaft with a thickness of 1 cm) can only be determined using a distributed modeling technique. The main objective of this project is to calculate angular velocity and torque at the end of the shaft by TLM method and also analyzing of the behavior of the system by transient response. The obtained result is compared with lumped modeling technique the importance of these results will be evident only after the mentioned comparison. Two systems have different transient responses and in this project because of the length of the shaft transient response is very important.

Keywords: Distributed Lumped modeling, Lumped modeling, Drill string, Angular Velocity, Torque.

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Authors: A. Chatterjee, A. Sarkar, N. Gayathri, P. Mukherjee, P. Barat

Abstract:

An experimental study is presented on the effect of microstructural change on the Portevin-Le Chatelier effect behaviour of Al-2.5%Mg alloy. Tensile tests are performed on the as received and heat treated (at 400 ºC for 16 hours) samples for a wide range of strain rates. The serrations observed in the stress-time curve are investigated from statistical analysis point of view. Microstructures of the samples are characterized by optical metallography and X-ray diffraction. It is found that the excess vacancy generated due to heat treatment leads to decrease in the strain rate sensitivity and the increase in the number of stress drop occurrences per unit time during the PLC effect. The microstructural parameters like domain size, dislocation density have no appreciable effect on the PLC effect as far as the statistical behavior of the serrations is considered.

Keywords: Dynamic strain ageing, Heat treatment, Portevin-LeChatelier effect

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Authors: V. Nikkhah Rashidabad, M. Manteghian, M. Masoumi, S. Mousavian

Abstract:

In this research, the changes in bubbles diameter and  number that may occur due to the change in heat flux of pure water  during pool boiling process. For this purpose, test equipment was  designed and developed to collect test data. The bubbles were graded  using Caliper Screen software. To calculate the growth and  nucleation rates of bubbles under different fluxes, population balance  model was employed. The results show that the increase in heat flux  from q=20 kw/m2 to q= 102 kw/m2 raised the growth and nucleation  rates of bubbles.

 

Keywords: Heat flux, bubble growth, bubble nucleation, population balance model.

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Authors: O. S. Pradeep, S. Vigneshwaran, K. Praveen Kumar, K. Jeyendran, V. R. Sanal Kumar

Abstract:

The influence of injector attitude on wall heat flux plays an important role in predicting the start-up transient and also determining the combustion chamber wall durability of liquid rockets. In this paper comprehensive numerical studies have been carried out on an idealized liquid rocket combustion chamber to examine the transient wall heat flux during its start-up transient at different injector attitude. Numerical simulations have been carried out with the help of a validated 2d axisymmetric, double precision, pressure-based, transient, species transport, SST k-omega model with laminar finite rate model for governing turbulent-chemistry interaction for four cases with different jet intersection angles, viz., 0^o, 30^o, 45^o, and 60^o. We concluded that the jets intersection angle is having a bearing on the time and location of the maximum wall-heat flux zone of the liquid rocket combustion chamber during the start-up transient. We also concluded that the wall heat flux mapping in liquid rocket combustion chamber during the start-up transient is a meaningful objective for the chamber wall material selection and the lucrative design optimization of the combustion chamber for improving the payload capability of the rocket.  

Keywords: Combustion chamber, injector, liquid rocket, rocket engine wall heat flux.

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Authors: Bhausaheb L. Pangarkar, M. G. Sane, Saroj B. Parjane, Rajendra M. Abhang, Mahendra Guddad

Abstract:

Vacuum membrane distillation (VMD) process can be used for water purification or the desalination of salt water. The process simply consists of a flat sheet hydrophobic micro porous PTFE membrane and diaphragm vacuum pump without a condenser for the water recovery or trap. The feed was used aqueous NaCl solution. The VMD experiments were performed to evaluate the heat and mass transfer coefficient of the boundary layer in a membrane module. The only operating parameters are feed inlet temperature, and feed flow rate were investigated. The permeate flux was strongly affected by the feed inlet temperature, feed flow rate, and boundary layer heat transfer coefficient. Since lowering the temperature polarization coefficient is essential enhance the process performance considerable and maximizing the heat transfer coefficient for maximizes the mass flux of distillate water. In this paper, the results of VMD experiments are used to measure the boundary layer heat transfer coefficient, and the experimental results are used to reevaluate the empirical constants in the Dittus- Boelter equation.

Keywords: Desalination, heat and mass transfer coefficient, temperature polarization, membrane distillation

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Authors: I. D. Arroyo

Abstract:

This article seeks to integrate different concepts from contemporary software engineering with an agile development approach. We seek to clarify some definitions and uses, we make a difference between the Systems Development Life Cycle (SDLC) and the methodologies, we differentiate the types of frameworks such as methodological, philosophical and behavioral, standards and documentation. We define relationships based on the documentation of the development process through formal and ad hoc models, and we define the usefulness of using DevOps and Agile Modeling as integrative methodologies of principles and best practices.

Keywords: Methodologies, SDLC, modeling languages, agile modeling, DevOps, UML, agile software development.

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Authors: Man Young Kim

Abstract:

In this work, the effects of scale on thermal behavior of the slab in a walking-beam type reheating furnace is studied by considering scale formation and growth in a furnace environment. Also, mathematical heat transfer model to predict the thermal radiation in a complex shaped reheating furnace with slab and skid buttons is developed with combined nongray WSGGM and blocked-off solution procedure. The model can attack the heat flux distribution within the furnace and the temperature distribution in the slab throughout the reheating furnace process by considering the heat exchange between the slab and its surroundings, including the radiant heat transfer among the slabs, the skids, the hot combustion gases and the furnace wall as well as the gas convective heat transfer in the furnace. With the introduction of the mathematical formulations validation of the present numerical model is conducted by calculating two example problems of blocked-off and nongray gas radiative heat transfer. After discussing the formation and growth of the scale on the slab surface, slab heating characteristics with scale is investigated in terms of temperature rise with time. 

Keywords: Reheating Furnace, Scale, Steel Slab, Radiative Heat Transfer, WSGGM.

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Authors: Hamid. Gholami, Mohammad. Chamani, Armin. Towhidi, Mohammad. H. Fazeli

Abstract:

The aim of current study was to investigate the changes in the quality parameters of Holstein bull semen during the heat stress and the effect of feeding a source of omega-3 fatty acids in this period. Samples were obtained from 19 Holstein bulls during the expected time of heat stress in Iran (June to September 2009). Control group (n=10) were fed a standard concentrate feed while treatment group (n=9) had this feed top dressed with 100 g of an omega-3 enriched nutriceutical. Semen quality was assessed on ejaculates collected after 1, 5, 9 and 12 weeks of supplementation. Computer-assisted assessment of sperm motility, viability (eosinnigrosin) and hypo-osmotic swelling test (HOST) were conducted. Heat stress affected sperm quality parameters by week 5 and 9 (p<0.05). Supplementation has significantly increased total motility, progressive motility, HOST and average path velocity in the fresh semen of bulls (P<0.05).

Keywords: Bull, heat stress, omega-3 fatty acids, spermatozoa.

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Authors: Tusharkanta Das, Tumbanath Samantara, Sukanta Kumar Sahoo

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Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.

Keywords: Heat transfer, radiation, MHD, free convection, porous medium, suction.

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Authors: E. Danso-Boateng

Abstract:

The effects of enzyme action and heat pretreatment on oil extraction yield from sunflower kernels were analysed using hexane extraction with Soxhlet, and aqueous extraction with incubator shaker. Ground kernels of raw and heat treated kernels, each with and without Viscozyme treatment were used. Microscopic images of the kernels were taken to analyse the visible effects of each treatment on the cotyledon cell structure of the kernels. Heat pretreated kernels before both extraction processes produced enhanced oil extraction yields than the control, with steam explosion the most efficient. In hexane extraction, applying a combination of steam explosion and Viscozyme treatments to the kernels before the extraction gave the maximum oil extractable in 1 hour; while for aqueous extraction, raw kernels treated with Viscozyme gave the highest oil extraction yield. Remarkable cotyledon cell disruption was evident in kernels treated with Viscozyme; whereas steam explosion and conventional heat treated kernels had similar effects.

Keywords: Enzyme-assisted aqueous and hexane extraction, heatpretreatment, sunflower cotyledon structure, sunflower oil extraction

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Authors: Abderrahmane Diaf, Kamel Benabdellaziz

Abstract:

Remote arid areas of the vast expanses of the African deserts hold huge subterranean reserves of brackish water resources waiting for economic development. This work presents design guidelines as well as initial performance data of new autonomous solar desalination equipment which could help local communities produce their own fresh water using solar energy only and, why not, contribute to transforming desert lands into lush gardens. The output of solar distillation equipments are typically low and in the range of 3 l/m2/day on the average. This new design with an integrated, water based, environmentally-friendly solar heat storage system produced 5 l/m2/day in early spring weather. Equipment output during summer exceeded 9 liters per m2 per day.

Keywords: Multiple trough distillation, solar desalination, solar distillation with heat storage, water based heat storage system.

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Authors: Ahmed Helal, Sherif Zain Elabideen, Ahmed Lotfy

Abstract:

In this paper the modeling and analysis of Space Vector Pulse Width Modulation (SVPWM) based Dynamic Voltage Restorer (DVR) using PSCAD/EMTDC software will be presented in details. The simulation includes full modeling of the SVPWM technique used to control the DVR inverter. A test power system composed of three phase voltage source, sag generator, DVR and three phase resistive load is used to demonstrate restoration capability of the DVR. The simulation results of the presented DVR proved excellent voltage sag mitigation to protect sensitive loads.

Keywords: Dynamic voltage restorer, power quality, simulationand modeling, voltage sag.

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Authors: Aman Agarwal, Georg Klepp

Abstract:

Impinging jets are used in various industrial areas as a cooling and drying technique. The current research is concerned with the means of improving the heat transfer for configurations with a minimum distance of the nozzle to the impingement surface. The impingement heat transfer is described using numerical methods over a wide range of parameters for an array of planar jets. These parameters include varying jet flow speed, width of nozzle, distance of nozzle, angle of the jet flow, velocity and geometry of the impingement surface. Normal pressure and shear stress are computed as additional parameters. Using dimensionless characteristic numbers the parameters and the results are correlated to gain generalized equations. The results demonstrate the effect of the investigated parameters on the flow.

Keywords: Heat Transfer Coefficient, Minimum distance jet impingement, Numerical simulation, Dimensionless coefficients.

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Authors: Sen-Yung Lee, Li-Kuo Chou, Chao-Kuang Chen

Abstract:

In this study, the problem of temperature transient response of a spiral fin, with its end insulated, is analyzed with base end subjected to a variation of fluid temperature. The hybrid method of Laplace transforms/Adomian decomposed method-Padé, is applied to the temperature transient response of the fin, the result of the temperature distribution and the heat flux at the base of the spiral fin are obtained, show a good agreement in the physical phenomenon.

Keywords: Laplace transforms/Adomian decomposed method- Padé, transient response, heat transfer.

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Authors: J. Fernandez de Canete

Abstract:

Object-oriented modeling is spreading in current simulation of physiological systems through the use of the individual components of the model and its interconnections to define the underlying dynamic equations. In this paper we describe the use of both the SIMSCAPE and MODELICA simulation environments in the object-oriented modeling of the closed loop cardiovascular system. The performance of the controlled system was analyzed by simulation in light of the existing hypothesis and validation tests previously performed with physiological data. The described approach represents a valuable tool in the teaching of physiology for graduate medical students.

Keywords: Object-Oriented Modeling, SIMSCAPE Simulation Language, MODELICA Simulation Language, Cardiovascular System.

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Authors: Arash Mir Abdolah Lavasani, Hamidreza Bayat

Abstract:

Heat transfer from two cam shape cylinder in side-byside arrangement had been studied numerically. The transverse gap between the centers of cylinders (T) is allowed to vary to change the pitch ratio (T/Deq). The equivalent diameter of the cylinder (Deq) is 27.6 mm and pitch ratio varies in range of 1≤T/Deq≤3. The Reynolds numbers based on equivalent circular cylinder are within 50≤ Reeq≤150. Results show that Nusselt number of cylinders increases about 1 to 36 percent when pitch ratio increases from 1 to 3.

Keywords: Cam shaped, side-by-side cylinders, numerical, heat Transfer.

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Authors: Y. El Kaissi, M. Allam, A. Koulou, M. Galai, M. Ebn Touhami

Abstract:

The aim of our work is to develop an industrial bath of nickel alloy deposit on mild steel. The optimization of the operating parameters made it possible to obtain a stable Ni-P alloy deposition formulation. To understand the reaction mechanism of the deposition process, a kinetic study was performed by cyclic voltammetry and by electrochemical impedance spectroscopy (EIS). The coatings obtained have a very high corrosion resistance in a very aggressive acid medium which increases with the heat treatment.

Keywords: Ni–P coating, electrochemical impedance spectroscopy, heat treatment, cyclic voltammetry, potentiodynamic polarization.

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Authors: S. Ali, M. Baccar

Abstract:

In this work, numerical simulations were carried out using a specific CFD code in order to study the performance of an innovative Scraped Surface Heat Exchanger (SSHE) with helical ribbons for Bingham fluids (threshold fluids). The resolution of three-dimensional form of the conservation equations (continuity, momentum and energy equations) was carried out basing on the finite volume method (FVM). After studying the effect of dimensionless numbers (axial Reynolds, rotational Reynolds and Oldroyd numbers) on the hydrodynamic and thermal behaviors within SSHE, a parametric study was developed, by varying the width of the helical ribbon, the clearance between the stator wall and the tip of the ribbon and the number of turns of the helical ribbon, in order to improve the heat transfer inside the exchanger. The effect of these geometrical numbers on the hydrodynamic and thermal behaviors was discussed.

Keywords: Heat transfer, helical ribbons, hydrodynamic behavior, parametric study, scraped surface heat exchanger, thermal behavior.

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Authors: Sandipkumar Sonawane, Upendra Bhandarkar, Bhalchandra Puranik, S. Sunil Kumar

Abstract:

The effect of Alumina nanoparticle size on thermophysical properties, heat transfer performance and pressure loss characteristics of Aviation Turbine Fuel (ATF)-Al2O3 nanofluids is studied experimentally for the proposed application of regenerative cooling of semi-cryogenic rocket engine thrust chambers. Al2O3 particles with mean diameters of 50 nm or 150 nm are dispersed in ATF. At 500C and 0.3% particle volume concentration, the bigger particles show increases of 17% in thermal conductivity and 55% in viscosity, whereas the smaller particles show corresponding increases of 21% and 22% for thermal conductivity and viscosity respectively. Contrary to these results, experiments to study the heat transfer performance and pressure loss characteristics show that at the same pumping power, the maximum enhancement in heat transfer coefficient at 500C and 0.3% concentration is approximately 47% using bigger particles, whereas it is only 36% using smaller particles.

Keywords: Heat transfer performance, Nanofluids, Thermalconductivity, Viscosity

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Authors: Zanariah Mohd Yusof, Siti Khuzaimah Soid, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

Abstract:

Unsteady magnetohydrodynamics (MHD) boundary layer flow and heat transfer over a continuously stretching surface in the presence of radiation is examined. By similarity transformation, the governing partial differential equations are transformed to a set of ordinary differential equations. Numerical solutions are obtained by employing the Runge-Kutta-Fehlberg method scheme with shooting technique in Maple software environment. The effects of unsteadiness parameter, radiation parameter, magnetic parameter and Prandtl number on the heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases as the Prandtl number and unsteadiness parameter increase but decreases with magnetic and radiation parameter.

Keywords: Heat transfer, magnetohydrodynamics, radiation, unsteadiness.

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Authors: A. Jamal, M. A. I. El-Shaarawi, E. M. A. Mokheimer

Abstract:

Combined conduction-free convection heat transfer in vertical eccentric annuli is numerically investigated using a finitedifference technique. Numerical results, representing the heat transfer parameters such as annulus walls temperature, heat flux, and heat absorbed in the developing region of the annulus, are presented for a Newtonian fluid of Prandtl number 0.7, fluid-annulus radius ratio 0.5, solid-fluid thermal conductivity ratio 10, inner and outer wall dimensionless thicknesses 0.1 and 0.2, respectively, and dimensionless eccentricities 0.1, 0.3, 0.5, and 0.7. The annulus walls are subjected to thermal boundary conditions, which are obtained by heating one wall isothermally whereas keeping the other wall at inlet fluid temperature. In the present paper, the annulus heights required to achieve thermal full development for prescribed eccentricities are obtained. Furthermore, the variation in the height of thermal full development as function of the geometrical parameter, i.e., eccentricity is also investigated.

Keywords: Conjugate natural convection, eccentricity, heat transfer, vertical eccentric annuli.

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Authors: Hanan Rizk

Abstract:

Heat exchanger is a device used to mix liquids having different temperatures. In this case, the temperature control becomes a critical objective. This research work presents the temperature control of the double-pipe heat exchanger (multi-input multi-output (MIMO) system), which is modeled as first-order coupled hyperbolic partial differential equations (PDEs), using conventional and advanced control techniques, and develops appropriate robust control strategy to meet stability requirements and performance objectives. We designed the proportional–integral–derivative (PID) controller and H-infinity controller for a heat exchanger (HE) system. Frequency characteristics of sensitivity functions and open-loop and closed-loop time responses are simulated using MATLAB software and the stability of the system is analyzed using Kalman's test. The simulation results have demonstrated that the H-infinity controller is more efficient than PID in terms of robustness and performance.

Keywords: heat exchanger, multi-input multi-output system, MATLAB simulation, partial differential equations, PID controller, robust control

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Authors: Zhang Lei, Liu Gaotong

Abstract:

The atomization effect is an important factor of the heat transfer of liquid nitrogen spray. In this paper, two kinds of internal-mixing twin-fluid atomizers were design. According to the fracture theory and fluid mechanics, the model is established to simulate atomization effect. The results showed that: Internal-mixing atomizers, with the liquid nitrogen atomization size from 20um to 40um, have superior performance. Y-jet atomizer spray speed is greater than Multi-jet atomizer, and it can improve the efficiency of heat transfer between the liquid nitrogen and its spray object. Multi-jet atomizer atomization cone angle is about 30°, Y-jet atomizer atomization cone angle is about 20°. During atomizer selection, the size of the heat transfer area should be considered.

Keywords: Atomization, two-phase flow, atomizer, heat transfer.

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Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

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In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.

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Authors: A. Rong, P. B. Luh, R. Lahdelma

Abstract:

High penetration of intermittent renewable energy sources (RES) such as solar power and wind power into the energy system has caused temporal and spatial imbalance between electric power supply and demand for some countries and regions. This brings about the critical need for coordinating power production and power exchange for different regions. As compared with the power-only systems, the combined heat and power (CHP) systems can provide additional flexibility of utilizing RES by exploiting the interdependence of power and heat production in the CHP plant. In the CHP system, power production can be influenced by adjusting heat production level and electric power can be used to satisfy heat demand by electric boiler or heat pump in conjunction with heat storage, which is much cheaper than electric storage. This paper addresses multi-site CHP systems without considering RES, which lay foundation for handling penetration of RES. The problem under study is the unit commitment (UC) of the transmission-constrained multi-site CHP systems. We solve the problem by combining linear relaxation of ON/OFF states and sequential dynamic programming (DP) techniques, where relaxed states are used to reduce the dimension of the UC problem and DP for improving the solution quality. Numerical results for daily scheduling with realistic models and data show that DP-based algorithm is from a few to a few hundred times faster than CPLEX (standard commercial optimization software) with good solution accuracy (less than 1% relative gap from the optimal solution on the average).

Keywords: Dynamic programming, multi-site combined heat and power system, relaxed states, transmission-constrained generation unit commitment.

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