Search results for: transfer function

Authors: Lee Derk Huan, Nur Irmawati

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This paper aims to investigate the heat transfer and fluid flow characteristics of nanofluids used in spray cooling systems. The effect of spray height, type of nanofluids and concentration of nanofluids are numerically investigated. Five different nanofluids such as AgH2O, Al2O3, CuO, SiO2 and TiO2 with volume fraction range of 0.5% to 2.5% are used. The results revealed that the heat transfer performance decreases as spray height increases. It is found that TiO2 has the highest transfer coefficient among other nanofluids. In dilute spray conditions, low concentration of nanofluids is observed to be more effective in heat removal in a spray cooling system.

Keywords: numerical investigation, spray cooling, heat transfer, nanofluids

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Authors: Douglas Yeboah, Jai Singh

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It has been experimentally demonstrated that exciton diffusion length in organic solids can be improved by fine-tuning the material parameters that govern exciton transfer. Here, a theoretical study is carried out to support this finding. We have therefore derived expressions for the exciton diffusion length and diffusion coefficient of singlet and triplet excitons using Förster resonance energy transfer and Dexter carrier transfer mechanisms and are plotted as a function of photoluminescence (PL) quantum yield, spectral overlap integral, refractive index and dipole moment of the photoactive material. We found that singlet exciton diffusion length increases with PL quantum yield and spectral overlap integral, and decreases with increase in refractive index. Likewise, the triplet exciton diffusion length increases when PL quantum yield increases and dipole moment decreases. The calculated diffusion lengths in different organic materials are compared with existing experimental values and found to be in reasonable agreement. The results are expected to provide insight in developing new organic materials for fabricating bulk heterojunction (BHJ) organic solar cells (OSCs) with better photoconversion efficiency.

Keywords: Dexter carrier transfer, diffusion coefficient, exciton diffusion length, Föster resonance energy transfer, photoactive materials, photophysical parameters

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Authors: Han-Taw Chen, Chung-Hou Lai, Tzu-Hsiang Lin, Ge-Jang He

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This study applies the inverse method and three-dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a closed rectangular enclosure for various values of fin height. The inverse method with the finite difference method and the experimental temperature data is applied to determine the heat transfer coefficient. The k-ε turbulence model is used to obtain the heat transfer and fluid flow characteristics within the fins. To validate the accuracy of the results obtained, the comparison of the average heat transfer coefficient is made. The calculated temperature at selected measurement locations on the plate-fin is also compared with experimental data.

Keywords: inverse method, FLUENT, k-ε model, heat transfer characteristics, plate-fin heat sink

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Authors: Annunziata D’Orazio, Arash Karimipour, Iman Moradi

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The size and arrangement of the obstacles in the porous media has an influential effect on the fluid flow and heat transfer, even in the same porosity. Regarding to this, in the present study, several different amounts of obstacles, in both regular and stagger arrangements, in the analogous porosity have been simulated through a channel. In order to compare the effect of stagger and regular arrangements, as well as different quantity of obstacles in the same porosity, on fluid flow and heat transfer. In the present study, the Single Relaxation Time Lattice Boltzmann Method, with Bhatnagar-Gross-Ktook (BGK) approximation and D2Q9 model, is implemented for the numerical simulation. Also, the temperature field is modeled through a Double Distribution Function (DDF) approach. Results are presented in terms of velocity and temperature fields, streamlines, percentage of pressure drop and Nusselt number of the obstacles walls. Also, the correlation between tortuosity and Nusselt number of the obstacles walls, for both regular and staggered arrangements, has been proposed. On the other hand, the results illustrated that by increasing the amount of obstacles, as well as changing their arrangement from regular to staggered, in the same porosity, the rate of tortuosity and Nusselt number of the obstacles walls increased.

Keywords: lattice boltzmann method, heat transfer, porous media, pore-scale, porosity, tortuosity

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Authors: Roslinda Nazar, Ezad Hafidz Hafidzuddin, Norihan M. Arifin, Ioan Pop

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In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate, and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: boundary layer, exponentially stretching/shrinking sheet, generalized slip, heat transfer, numerical solutions

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Authors: Terence Soule, Tami Al Ghamdi

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To study how to transfer knowledge from multiple source problems to the target problem, we modeled the Transfer Learning (TL) process using Genetic Algorithms as the model solver. TL is the process that aims to transfer learned data from one problem to another problem. The TL process aims to help Machine Learning (ML) algorithms find a solution to the problems. The Genetic Algorithms (GA) give researchers access to information that we have about how the old problem is solved. In this paper, we have five different source problems, and we transfer the knowledge to the target problem. We studied different scenarios of the target problem. The results showed combined knowledge from multiple source problems improves the GA performance. Also, the process of combining knowledge from several problems results in promoting diversity of the transferred population.

Keywords: transfer learning, genetic algorithm, evolutionary computation, source and target

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Authors: Zahir Bakiri, Saci Nacefa

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In this paper a comparison in made between two models, with and without dispersion term, and focused on the characterization of the movement of the sludge blanket in the secondary sedimentation tank using the solid flux theory and the velocity settling. This allowed us develop a one-dimensional models, with and without dispersion based on a thorough experimental study carried out in situ and the application of online data which are the mass load flow, transfer concentration, and influent characteristic. On the other hand, in the proposed model, the new settling velocity law (double-exponential function) used is based on the Vesilind function.

Keywords: wastewater, activated sludge, sedimentation, settling velocity, settling models

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Authors: Mohamed El-Sayed Mosaad

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An analytic approach is obtained for the steady heat transfer problem of two fluid systems, in thermal communication via heat conduction across a solid wall separating them. The two free convection layers created on wall sides are assumed to be in parallel flow. Fluid-solid interface temperature on wall sides is not prescribed in analysis in advance; rather, determined from conjugate solution among other unknown parameters. The analysis highlights the main conjugation parameters controlling thermal interaction process of involved heat transfer modes. Heat transfer results of engineering importance are obtained.

Keywords: conjugate heat transfer, boundary layer, convection, thermal systems

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Authors: Jagul Huma Lashari, Arabella Bhutto

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Last few years have shown increased an interest of researchers in knowledge and technology transfer. However, facts show fewer types of knowledge transfer practices in the developing countries. This article focuses on assessment transfer channels of academic research produced by highly qualified academicians working in universities in Sindh offering degrees in field of an Environment in Sindh Pakistan. The academic field has been chosen because in field of the environment there is alarming need of research into practice for sustainable development. Using case study approach; in this research qualitative interviews have been conducted from PhD faculty members working in the universities offering degrees in field of environment. Obtained data is analyzed using descriptive statistics and chi-square test with the help of statistical packages for social sciences (SPSS). Research explored 31 channels of academic knowledge transfer from detailed review of literature and exploratory interviews with participants. Identified knowledge transfer channels have been grouped together in 6 groups of knowledge transfer channels; As knowledge transfer through publications, networking, mobility of researchers, joint research, intellectual property and co-operations. Results revealed that academic knowledge have been transferred through publications, networking, and co-operation. However, less number of academic knowledge has been transferred through groups of knowledge transfer channels such as Intellectual Property and joint research.

Keywords: environment, research knowledge, transfer channels, universities

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Authors: Bader Alhumaidi Alsubaei, Zahid H. Akash, Ali Imam Sunny

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The heat transfer coefficient can be improved passively by using a dimpled surface on the tube. The contact area where heat transfer takes place can be enlarged and turbulence will be purposefully produced inside the duct; as a consequence, higher heat transfer quality will be achieved by employing an extended inner or outer surface (dimpled surface). In order to compare the rate and quality of heat transfer between a regular-shaped pipe and a dimpled pipe, a dimpled tube with a fixed dimple radius was created. Numerical analysis of the plain and dimpled pipes was performed using ANSYS. A 23% increase in Nusselt number was seen for dimpled tubes compared to plain tubes. In comparison to plain tubes, dimpled tubes' increase in thermal performance index was found to be between 8% and 10%. An increase in pressure drop of 18% was noted.

Keywords: heat transfer, dimpled tube, CFD, ANSYS

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Authors: Jorge L. Nisperuza, Wilson Sandoval, Edward. A. Gil, Johan A. Jimenez

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In orbital mechanics, an active research topic is the calculation of interplanetary trajectories efficient in terms of energy and time. In this sense, this work concerns the calculation of the orbital elements for sending interplanetary probes in the extrasolar system TRAPPIST-1. Specifically, using the mathematical expressions of the circular and elliptical trajectory parameters, expressions for the flight time and the orbital transfer rate increase between orbits, the orbital parameters and the graphs of the trajectories of Hohmann and Hohmann bi-elliptic for sending a probe from the innermost planet to all the other planets of the studied system, are obtained. The relationship between the orbital transfer rate increments and the relationship between the flight times for the two transfer types is found. The results show that, for all cases under consideration, the Hohmann transfer results to be the least energy and temporary cost, a result according to the theory associated with Hohmann and Hohmann bi-elliptic transfers. Saving in the increase of the speed reaches up to 87% was found, and it happens for the transference between the two innermost planets, whereas the time of flight increases by a factor of up to 6.6 if one makes use of the bi-elliptic transfer, this for the case of sending a probe from the innermost planet to the outermost.

Keywords: bi-elliptic Hohmann transfer, exoplanet, extrasolar system, Hohmann transfer, TRAPPIST-1

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Authors: Ashok K. Satapathy, Prerana Nashine

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Radiative heat transfer in participating medium was anticipated using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation incorporated with transient conduction. Results have been obtained for irradiation and corresponding heat fluxes for both the cases. The solutions can be used to conclude incident energy and surface heat flux. Transient solutions were obtained for a slab of heat conducting in slab by thermal radiation. The effect of heat conduction during the transient phase is to partially equalize the internal temperature distribution. The solution procedure provides accurate temperature distributions in these regions. A finite volume procedure with variable space and time increments is used to solve the transient energy equation. The medium in the enclosure absorbs, emits, and anisotropically scatters radiative energy. The incident radiations and the radiative heat fluxes are presented in graphical forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is non-symmetric.

Keywords: participating media, finite volume method, radiation coupled with conduction, heat transfer

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Authors: Masato Sasaki, Masayoshi Yamamoto

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The majority of wireless power transfer (WPT) systems transfer power in a directional manner. This paper describes a discrete exciting voltage control technique for WPT via magnetic resonant coupling with two orthogonal transmitter coils (2D omni-directional WPT system) which can maximize the power transfer efficiency in response to the change of coupling status. The theory allows the equations of the efficiency of the system to be determined at all the rate of the mutual inductance. The calculated results are included to confirm the advantage to one directional WPT system and the validity of the theory and the equations.

Keywords: wireless power transfer, omni-directional, orthogonal, efficiency

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Authors: Ik–Tae Im, H. M. Abdelmotalib, M. A. Youssef, S. B. Young

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In this study the flow characteristics and bed-to-wall heat transfer in a gas-solid conical fluidized bed combustor were investigated using both experimental and numerical methods. The computational fluid dynamic (CFD) simulations were carried out using a commercial software, Fluent V6.3. A two-fluid Eulerian-Eulerian model was applied in order to simulate the gas–solid flow and heat transfer in a conical sand-air bed with 30o con angle and 22 cm static bed height. Effect of different fluidizing number varying in the range of 1.5 - 2.3, drag models namely (Syamlal-O’Brien and Gidaspow), and friction viscosity on flow and bed-to-wall heat transfer were analyzed. Both bed pressure drop and heat transfer coefficient increased with increasing inlet gas velocity. The Gidaspow drag model showed a better agreement with experimental results than other drag model. The friction viscosity had no clear effect on both hydrodynamics and heat transfer.

Keywords: computational fluid dynamics, heat transfer coefficient, hydrodynamics, renewable energy

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Authors: Nitin Ghule, S. G. Taji

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A mathematical model of hot-wall condensers used in refrigerators is presented. The model predicts the heat transfer characteristics of condenser and the effects of various design and operating parameters on condenser tube length and capacity. A finite element approach was used to model the condenser. The condenser tube is divided into elemental units, with each element consisting of adhesive tape, refrigerant tube and outer metal sheet. The heat transfer characteristics of each section are then analyzed by considering the heat transfer through the tube wall, tape and the outer sheet. Variations in inner heat transfer coefficient and pressure drop are considered depending on temperature, fluid phase, type of flow and orientation of tube. Variation in outer heat transfer coefficient is also taken into account. Various materials were analysed for the tube, tape and outer sheet.

Keywords: condenser, domestic refrigerator, heat transfer, mathematical model

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Authors: M. A. Akhavan-Behabadi, M. Najafi, A. Abbasi

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An empirical investigation was performed in order to study the heat transfer characteristics of R600a flow boiling inside horizontal flattened tubes and the simultaneous effect of nanoparticles on boiling heat transfer in flattened channel. Round copper tubes of 8.7 mm I.D. were deformed into flattened shapes with different inside heights of 6.9, 5.5, and 3.4 mm as test areas. The effect of different parameters such as mass flux, vapor quality and inside height on heat transfer coefficient was studied. Flattening the tube caused a significant enhancement in heat transfer performance, so that the maximum augmentation ratio of 163% was obtained in flattened channel with lowest internal height. A new correlation was developed based on the present experimental data to predict the heat transfer coefficient in flattened tubes. This correlation estimated 90% of the entire database within ±20%. The best flat channel with the point of view of heat transfer performance was selected to study the effect of nanoparticle on heat transfer enhancement. Four homogenized mixtures containing 1% weight fraction of R600a/oil with different CuO nanoparticles concentration including 0.5%, 1% and 1.5% mass fraction of R600a/oil/CuO were studied. Observations show that heat transfer was improved by adding nanoparticles, which lead to maximum enhancement of 79% compare to the pure refrigerant at the same test condition.

Keywords: nano fluids, heat transfer, flattend tube, transport phenomena

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Authors: M. Amoura, M. Benmoussa, N. Zeraibi

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The flow and heat transfer is an important phenomenon in engineering systems due to its wide application in electronic cooling, heat exchangers, double pane windows etc.. The enhancement of heat transfer in these systems is an essential topic from an energy saving perspective. Lower heat transfer performance when conventional fluids, such as water, engine oil and ethylene glycol are used hinders improvements in performance and causes a consequent reduction in the size of such systems. The use of solid particles as an additive suspended into the base fluid is a technique for heat transfer enhancement. Therefore, the heat transfer enhancement in a horizontal circular tube that is maintained at a constant temperature under laminar regime has been investigated numerically. A computational code applied to the problem by use of the finite volume method was developed. Nanofluid was made by dispersion of Al2O3 nanoparticles in pure water and ethylene glycol. Results illustrate that the suspended nanoparticles increase the heat transfer with an increase in the nanoparticles volume fraction and for a considered range of Reynolds numbers. On the other hand, the heat transfer is very sensitive to the base fluid.

Keywords: Al2O3 nanoparticles, circular tube, heat transfert enhancement, numerical simulation

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Authors: Dawid Sołoducha, Tomasz Borowski, Marian Kordas, Rafał Rakoczy

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The magnetic field in the past few years became an important part of many studies. Magnetic field (MF) may be used to affect the process in many ways; for example, it can be used as a factor to stabilize the system. We can use MF to steer the operation, to activate or inhibit the process, or even to affect the vital activity of microorganisms. Using various types of magnetic field generators is always connected with the delivery of some heat to the system. Heat transfer is a very important phenomenon; it can influence the process positively and negatively, so it’s necessary to measure heat stream transferred from the place of generation and prevent negative influence on the operation. The aim of the presented work was to apply various types of magnetic fields and to measure heat transfer phenomena. The results were obtained by continuous measurement at several measuring points with temperature probes. Results were compilated in the form of temperature profiles. The study investigated the undetermined heat transfer in a custom system equipped with a magnetic field generator. Experimental investigations are provided for the explanation of the influence of the various type of magnetic fields on the heat transfer process. The tested processes are described by means of the criteria which defined heat transfer intensification under the action of magnetic field.

Keywords: heat transfer, magnetic field, undetermined heat transfer, temperature profile

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Authors: Ahmed H. El-Masry, Mohamed A. Dabaon, Tarek F. El-Shafiey, Abd El-Hakim A. Khalil

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An experimental study was performed to investigate the behavior and strength of proposed technique to connect reinforced concrete (RC) beam to steel or composite columns. This approach can practically be used in several types of building construction. In this technique, the main beam of the frame consists of a transfer part (part of beam; Tr.P) and a common reinforcement concrete beam. The transfer part of the beam is connected to the column, whereas the rest of the beam is connected to the transfer part from each side. Four full-scale beam-column connections were tested under static loading. The test parameters were the length of the transfer part and the column properties. The test results show that using of the transfer part technique leads to modify the deformation capabilities for the RC beam and hence it increases its resistance against failure. Increase in length of the transfer part did not necessarily indicate an enhanced behavior. The test results contribute to the characterization of the connection behavior between RC beam - steel column and can be used to calibrate numerical models for the simulation of this type of connection.

Keywords: composite column, reinforced concrete beam, steel column, transfer part

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

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The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: curved stretching sheet, finite difference method, MHD, variable thermal conductivity

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Authors: Dong Il Shim, Geehong Choi, Donghwi Lee, Namkyu Lee, Hyung Hee Cho

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Effective cooling technology is required to secure thermal stability in extreme heat generated systems such as integrated electronic devices and power generated systems. Pool boiling heat transfer is one of the powerful cooling mechanisms using phase change phenomena. Critical heat flux (CHF) and heat transfer coefficient (HTC) are main factors to evaluate the performance of boiling heat transfer. CHF is the limitation of boiling heat transfer before film boiling which occurs thermal failure. Surface wettability is an important surface characteristic of boiling heat transfer. A hydrophilic surface has higher CHF through effective working fluid supply to local hot spots. A hydrophobic surface promotes the onset of nucleate boiling (ONB) to enhance HTC. In this study, superbiphilic surfaces, which is combined with superhydrophillic and superhydrophobic, are applied on boiling experiments to maximize boiling performance. We conducted pool boiling heat transfer using DI water at a saturated temperature and recorded bubble dynamics using a high-speed camera with 2000 fps. As a result, superbiphilic patterned surfaces promote ONB and enhance both CHF and HTC. This study demonstrates the enhanced boiling performance using superbiphilic surfaces by effective nucleation and separation of liquid/vapor pathway. We expect that further enhancement of heat transfer could be achieved in future work using optimized patterned surfaces.

Keywords: boiling heat transfer, wettability, critical heat flux, heat transfer coefficient

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Authors: Assaad Ghazouani, Hedia Teraoui

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The purpose of this article is to try to see if the FDI actually contributes to technology transfer in Tunisia or are there other sources that can guarantee this transfer? The answer to this problem was gradual as we followed an approach using economic theory, the reality of Tunisia and econometric and statistical tools. We examined the relationship between technology transfer and FDI in Tunisia over a period of 40 years from 1970 to 2010. We estimated in two stages: first, a growth equation, then we have learned from this regression residue (proxy technology), secondly, we regressed on European FDI, exports of manufactures, imports of goods from the European Union in addition to other variables to test the robustness of the results and describing the level of infrastructure in the country. It follows from our study that technology transfer does not originate primarily and exclusively in the FDI and the latter is econometrically weakly with technology transfer and spill over effect of FDI does not seem to occur according to our results. However, the relationship between technology transfer and imports is negative and significant. Although this result is cons-intuitive, is recurrent in the literature of panel data. It has also given rise to intense debate on the microeconomic modelling as well as on the empirical applications. Technology transfer through trade or foreign investment has become a catalyst for growth recognized by numerous empirical studies in particular. However, the relationship technology transfer FDI is more complex than it appears. This complexity is due, primarily, but not exclusively to the close link between FDI and the characteristics of the host country. This is essentially the host's responsibility to establish general conditions, transparent and conducive to investment, and to strengthen human and institutional capacity necessary for foreign capital flows that can have real effects on growth.

Keywords: technology transfer, foreign direct investment, economics, finance

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Authors: V. D. Thi, M. Li, M. Khelifa, M. El Ganaoui, Y. Rogaume

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This paper presents a two-dimensional model to study the heat and moisture transfer through porous building materials. Dynamic and static coupled models of heat and moisture transfer in porous material under low temperature are presented and the coupled models together with variable initial and boundary conditions have been considered in an analytical way and using the finite element method. The resulting coupled model is converted to two nonlinear partial differential equations, which is then numerically solved by an implicit iterative scheme. The numerical results of temperature and moisture potential changes are compared with the experimental measurements available in the literature. Predicted results demonstrate validation of the theoretical model and effectiveness of the developed numerical algorithms. It is expected to provide useful information for the porous building material design based on heat and moisture transfer model.

Keywords: finite element method, heat transfer, moisture transfer, porous materials, wood

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Authors: Ali Reza Tahavvor, Saeed Hosseini, Nazli Jowkar, Behnam Amiri

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Heat transfer of leaves is a crucial factor in optimal operation of metabolic functions in plants. In order to quantify this phenomenon in different leaves and investigate the influence of leaf shape on heat transfer, natural convection for pine, orange and olive leaves was simulated as representatives of different groups of leaf shapes. CFD techniques were used in this simulation with the purpose to calculate heat transfer of leaves in similar environmental conditions. The problem was simulated for steady state and three-dimensional conditions. From obtained results, it was concluded that heat fluxes of all three different leaves are almost identical, however, total rate of heat transfer have highest and lowest values for orange leaves and pine leaves, respectively.

Keywords: computational fluid dynamic, heat flux, heat transfer, natural convection

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Authors: K. Bourouni, M. Chacha, T. Jaber, A. Tchantchane

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In Multi-Effect Distillation (MED) desalination evaporators, the scale deposit outside the tubes presents a barrier to heat transfers reducing the global heat transfer coefficient and causing a decrease in water production; hence a loss of efficiency and an increase in operating and maintenance costs. Scale removal (by acid cleaning) is the main maintenance operation and constitutes the major reason for periodic plant shutdowns. A better understanding of scale deposition mechanisms will lead to an accurate determination of the variation of scale thickness around the tubes and an improved accuracy of the overall heat transfer coefficient calculation. In this paper, a coupled heat transfer-calcium carbonate scale deposition model on a horizontal tube bundle is presented. The developed tool is used to determine precisely the heat transfer area leading to a significant cost reduction for a given water production capacity. Simulations are carried to investigate the influence of different parameters such as water salinity, temperature, etc. on the heat transfer.

Keywords: multi-effect-evaporator, scale deposition, water desalination, heat transfer coefficient

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Authors: M. Tarawneh

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This work is an experimental study on the heat transfer characteristics and pressure drop of different refrigerants during the condensation and evaporation processes in porous media. Four different refrigerants (R134a, R407C, 600a, R290), with different porosities were used to reach a real understanding of the actual heat transfer characteristics and pressure drop when using porous material inside the condenser and evaporator. Steel balls were used as porous media with different porosities (38%, 43%, 48%). The main goal of this project is to enhance the heat transfer coefficient during the condensation and evaporation processes when using different refrigerants and different porosities. Different correlations for the heat transfer coefficient and the pressure drop of the different refrigerants were developed. Also a generalized empirical correlation was developed for the different refrigerants. The experimental and predicted heat transfer coefficients and pressure drops were compared. It was found that, the Absolute standard deviation for the heat transfer coefficient and the pressure drop not exceeded values of 15% and 20%, respectively.

Keywords: condensation, evaporation, porous media, horizontal tubes, heat transfer coefficient, propane, butane

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Han-Taw Chen, Tzu-Hsiang Lin, Chung-Hou Lai

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This study applies the inverse method and three-dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a rectangular closed enclosure. The inverse method with the finite difference method and the experimental temperature data is applied to determine the approximate heat transfer coefficient. Later, based on the obtained results, the zero-equation turbulence model is used to obtain the heat transfer and fluid flow characteristics between two fins. To validate the accuracy of the results obtained, the comparison of the heat transfer coefficient is made. The obtained temperature at selected measurement locations of the fin is also compared with experimental data. The effect of the height of the rectangular enclosure on the obtained results is discussed.

Keywords: inverse method, fluent, heat transfer characteristics, plate-fin heat sink

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Authors: Badache Messaoud

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Geothermal thermosyphons (GTs) are increasingly used in many heating and cooling geothermal applications owing to their high heat transfer performance. This paper proposes a response surface methodology (RSM) to investigate and optimize the performance of a CO2 geothermal thermosyphon. The filling ratio (FR), temperature, and flow rate of the heat transfer fluid are selected as the designing parameters, and heat transfer rate and effectiveness are adopted as response parameters (objective functions). First, a dedicated experimental GT test bench filled with CO2 was built and subjected to different test conditions. An RSM was used to establish corresponding models between the input parameters and responses. Various diagnostic tests were used to assess evaluate the quality and validity of the best-fit models, which explain respectively 98.9% and 99.2% of the output result’s variability. Overall, it is concluded from the RSM analysis that the heat transfer fluid inlet temperatures and the flow rate are the factors that have the greatest impact on heat transfer (Q) rate and effectiveness (εff), while the FR has only a slight effect on Q and no effect on εff. The maximal heat transfer rate and effectiveness achieved are 1.86 kW and 47.81%, respectively. Moreover, these optimal values are associated with different flow rate levels (mc level = 1 for Q and -1 for εff), indicating distinct operating regions for maximizing Q and εff within the GT system. Therefore, a multilevel optimization approach is necessary to optimize both the heat transfer rate and effectiveness simultaneously.

Keywords: geothermal thermosiphon, co2, Response surface methodology, heat transfer performance

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Authors: Hari Mohan Kushwaha, Santosh Kumar Sahu

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In the present study, analysis of heat transfer is carried out in the slip flow region for the fluid flowing between two parallel plates by employing the asymmetric heat fluxes at surface of the plates. The flow is assumed to be hydrodynamically and thermally fully developed for the analysis. The second order velocity slip and viscous dissipation effects are considered for the analysis. Closed form expressions are obtained for the Nusselt number as a function of Knudsen number and modified Brinkman number. The limiting condition of the present prediction for Kn = 0, Kn2 = 0, and Brq1 = 0 is considered and found to agree well with other analytical results.

Keywords: Knudsen number, modified Brinkman number, slip flow, velocity slip

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