Article
Physics, Multidisciplinary
Asia Yasmin, Kashif Ali, Muhammad Ashraf
Summary: This study investigates the flow and thermal characteristics of MHD Casson nanofluid in a square enclosure with non-uniform heat source using the Brinkman model. The impact of governing parameters on local Nusselt number, streamlines and isotherms is demonstrated, showing the increase in Raleigh number results in sharp temperature rise in the middle of the enclosure with steeper thermal distribution near the walls. High values of the Rayleigh number also highlight the effect of the magnetic field as a force of retardation.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Thermodynamics
Shantanu Dutta, Navneet Goswami, Sukumar Pati, Arup Kumar Biswas
Summary: This study investigates the natural convection heat transfer and entropy generation characteristics in a rhombic enclosure filled with a porous medium and inclined at 30 degrees. Results show significant influence of phase shift angle, Rayleigh number, and Darcy number on heat transfer rate, with entropy generation primarily induced by heat transfer and maximum entropy values varying with phase angle.
JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY
(2021)
Article
Chemistry, Analytical
Vemula Rajesh, Mikhail Sheremet
Summary: This paper investigates the natural convection of a ternary hybrid nanosuspension in a closed cavity with a linearly warming side border. The motion and energy transfer of the hybrid nanosuspension are modeled using partial differential equations and the Boussinesq approximation. The impact of different factors on the flow and thermal patterns, as well as the Nusselt number, is analyzed using streamlines, isotherms, and other suitable patterns. The study shows that the addition of a third kind of nanomaterial enhances the energy transport within the closed cavity.
Article
Engineering, Multidisciplinary
Subramanian Muthukumar, Selvaraj Sureshkumar, Arthanari Malleswaran, Murugan Muthtamilselvan, Eswari Prem
Summary: The study investigates the effects of heating patterns on mixed convective heat transfer in a square porous chamber filled with nanofluid. Results show that overall heat transfer rate is lower in the positive lid movement direction, while average Nusselt number decreases in the negative direction. Increasing solid volume fraction can enhance heat transfer rate.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Physics, Multidisciplinary
A. Sumithra, R. Sivaraj
Summary: In this study, the characteristics of mixed convection nanofluid flow inside a square enclosure saturated with porous medium are numerically investigated, taking into account the impact of chemical reaction, Joule heating, magnetic field, and viscous dissipation. The results show that free convection is more dominant than forced and mixed convection, and the increase in the chemical reaction parameter has a significant effect on fluid flow and mass transfer.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Thermodynamics
Laith M. Jasim, Hudhaifa Hamzah, Cetin Canpolat, Besir Sahin
Summary: This study presents a numerical solution for the influence of an inner rotating adiabatic cylinder on mixed convection of hybrid nanofluid inside a vented cavity. The study explores the effects of various parameters on energy transport and presents the results through qualitative and quantitative figures.
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER
(2021)
Article
Physics, Multidisciplinary
Amna Yasin, Naeem Ullah, S. Saleem, Sohail Nadeem, A. Al-Zubaidi
Summary: This article presents a numerical study on laminar natural convective flow in a porous rectangular cavity with two heated rods. The finite element method is used to obtain solutions for the partial differential equations, and the results show that non-uniform heating suppresses heat transfer rate compared to uniform heating, an increase in heated rod length strengthens the flow field, and greater permeability of the porous medium enhances velocity distribution and Nusselt number.
Article
Physics, Multidisciplinary
Dipak Kumar Mandal, Nirmalendu Biswas, Nirmal K. Manna, Rama Subba Reddy Gorla, Ali J. Chamkha
Summary: This study investigates the hydrothermal characteristics of an Al2O3-Cu-H2O hybrid nanofluid saturated in a non-Darcian porous complex wavy enclosure under a uniform magnetic field. Numerical simulations show that increasing the amplitude of the undulation enhances heat transfer, but does not always promote the growth of flow strength. Flow intensity and heat transfer increase with the modified-Rayleigh number, while they decrease with the Darcy number and Hartmann number. The local distribution of heat transfer characteristics exhibits complex behavior depending on the amplitude of the undulations and dimensionless numbers.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2022)
Article
Thermodynamics
Khaled Al-Farhany, Kadhim K. Al-Chlaihawi, Mohamed F. Al-dawody, Nirmalendu Biswas, Ali J. Chamkha
Summary: This study numerically investigates the magnetohydrodynamic conjugate heat transfer characteristics of a ferrofluid-filled porous inclined enclosure, with a focus on the influence of parameters such as fins length, gap between fins, modified Rayleigh number, Darcy number, and Hartmann number on the average Nusselt number. The results suggest that the fins length and gap between fins play a significant role in heat transfer enhancement, while the modified Rayleigh number, Darcy number, and Hartmann number also have notable effects.
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER
(2021)
Article
Thermodynamics
Tahar Tayebi, Fatima Dahmane, Wasim Jamshed, Ali J. Chamkha, Sayed M. El Din, Zehba Raizah
Summary: The study focuses on the numerical analysis of magneto-natural convection induced by double-diffusion of a nanofluid using the finite volume method. A wavy porous cylinder in a enclosure is considered, where the local thermal non-equilibrium (LTNE) is modeled by the Darcy-Brinkman-Forchheimer design. Controlling variables such as Rayleigh number (Ra), Lewis number (Le), Hartman number (Ha), buoyancy ratio parameter (N), Darcy number (Da), and medium's porosity (epsilon) are evaluated, showing that heat and mass transfers can be improved with certain augmentations and diminutions of these variables.
CASE STUDIES IN THERMAL ENGINEERING
(2023)
Article
Nuclear Science & Technology
Aissa Abderrahmane, Umar F. Alqsair, Kamel Guedri, Wasim Jamshed, Nor Ain AzeanyMohd Nasir, Hasan Sh. Majdi, Shaghayegh Baghaei, Abed Mourad, Riadh Marzouki
Summary: This paper investigates the impact of an inner adiabatic rotating cylinder within a vented cavity on the mixed convection of a hybrid nanofluid using numerical solution. The effects of various parameters on convective heat transfer are studied and the findings suggest that counterclockwise rotation of the cylinder enhances heat transfer. Additionally, when the cylinder is rotated counterclockwise, the heat transfer improves as the cylinder approaches the hot wall.
ANNALS OF NUCLEAR ENERGY
(2022)
Article
Thermodynamics
R. Hemalatha, Peri K. Kameswaran, P. V. S. N. Murthy
Summary: The current article discusses the mixed convective flow of Graphene oxide and Clay nanoparticles suspended in a nanofluid in a non-Darcy porous medium, taking into account the shape of the nanoparticles. The findings indicate that spherical nanoparticles exhibit an enhanced temperature distribution and have a higher settling rate in the base fluid.
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER
(2022)
Article
Engineering, Multidisciplinary
Arif Ullah Khan, Naeem Ullah, Abdou Al-Zubaidi, Sohail Nadeem
Summary: This article investigates the natural convection nanofluid flow in a hexagon shaped enclosure with a heated cylinder, considering the influence of a porous medium and inclined magnetic field. The finite element method is used to solve the physical model, and the results are presented using contour plots and line graphs to show the effects of flow controlling parameters.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Thermodynamics
Hudhaifa Hamzah, Ahmed Albojamal, Besir Sahin, Kambiz Vafai
Summary: This study numerically investigates the thermal transport of nanofluid natural convection in a wavy porous enclosure exposed to an external and uniform magnetic source. Various factors such as Darcy, Hartmann, Rayleigh, Prandtl, undulation numbers, wave amplitudes, and particle volume concentration have been examined. The results show that the magnetic field may not have a substantial role in convective thermal energy under certain conditions, and heat conduction intensity increases with high Hartmann and low Rayleigh values.
JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY
(2021)
Article
Computer Science, Information Systems
Zehba A. S. Raizah, Abdelraheem M. Aly
Summary: This study simulated natural convection flow in an H-shaped enclosure filled with a nanofluid using ISPH method. The research found that increasing the length of the heated partitions enhances the velocity field and temperature distributions, while a higher Rayleigh number increases fluid velocity and heat transfer. The presence of a porous layer on the right side causes a high resistance force.
CMC-COMPUTERS MATERIALS & CONTINUA
(2021)
Article
Thermodynamics
Syed Saqib Shah, Hakan F. Oztop, Rizwan Ul-Haq, Nidal Abu-Hamdeh
Summary: This paper analyzes the buoyancy flow, mass and heat transfer in a coaxial duct under the Soret and Dufour effect. The combined effects of various parameters on natural convection are studied using a numerical approach. The results show that the Lewis number has a significant impact on mass transfer, while the buoyancy ratio parameter decreases the average rate of heat flow and increases mass transfer.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2023)
Article
Thermodynamics
Ahmad H. Milyani, Mohammed N. Ajour, Hesham A. Alhumade, Nidal H. Abu-Hamdeh
Summary: This article numerically simulates the heat transfer between air and a battery pack in a duct using Comsol software. The results show that the battery temperature in the duct changes over time and eventually stabilizes. Calculations indicate that 13.83% of the required thermal energy can be supplied by the batteries.
JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY
(2023)
Article
Engineering, Multidisciplinary
Ammar A. Melaibari, Ahmad S. Alamoudi, Mohamed E. Mostafa, Nidal H. Abu-Hamdeh
Summary: The treatment of industrial wastewaters, especially petroleum wastewaters, is of high environmental importance. Recycling wastewater is doubly important in water scarce countries. Refineries, being heavy water consumers, can cause surface and underground water contamination if environmental preservation is not prioritized. Therefore, it is necessary to use appropriate methods to remove toxic substances like phenol from wastewater.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Green & Sustainable Science & Technology
Ceylin Sirin, Fatih Selimefendigil, Hakan Fehmi Oztop
Summary: In this study, thermal energy storage unit-integrated photovoltaic thermal (PVT) air collectors with and without nanoparticles were designed, fabricated, and tested. The integration of aluminum oxide nanoparticles into the thermal storage unit improved the performance of the PVT collector, reducing drying time by approximately 15-22%. The use of nanoparticles in the thermal energy storage unit also improved the overall energy and exergy efficiencies of the PVT air collectors, with an increase of 6.91-6.97% and 9.20-9.47%, respectively. The combination of increasing the flow rate and integrating nanoparticles into the storage unit further improved the overall exergetic efficiency of the PVT air collector by 28.58%.
Review
Multidisciplinary Sciences
Fatih Selimefendigil, Gurel Senol, Hakan F. Oztop, Nidal H. Abu-Hamdeh
Summary: This review discusses the applications of non-Newtonian nanofluids for convection in cavities under a magnetic field. Convection in cavities is of great significance in thermal energy systems, with various applications in different processes. The review provides information on nanofluids and non-Newtonian fluids, and focuses on the thermal conductivity/viscosity, as well as the magnetohydrodynamic effects of non-Newtonian nanofluids. Different applications of vented cavities using nanofluid and magnetic field are explored. The review points out the gaps in current literature and discusses future trends.
Article
Multidisciplinary Sciences
Hakan F. Oztop, Omer Akbal, Fatih Selimefendigil, Nidal H. Abu-Hamdeh
Summary: Three-dimensional computational analysis investigates the melting time of PCM in a sinusoidal pipe inserted into another pipe. The study aims to control melting time through passive techniques by adjusting the geometrical parameter without extra energy consumption.
Review
Chemistry, Multidisciplinary
Muhammad Mohsin, Tehmeena Ishaq, Ijaz Ahmad Bhatti, Maryam, Asim Jilani, Ammar A. Melaibari, Nidal H. Abu-Hamdeh
Summary: This article discusses the application of nanomaterials in photocatalytic hydrogen production. Nanomaterials are attractive due to their high specific surface area, morphology, and light absorption. Hydrogen, as a clean and green energy source, can help mitigate the existing energy crisis and environmental pollution caused by fossil fuels. The article summarizes various techniques to enhance hydrogen production, including the thermochemical process, electrocatalytic process, and direct solar water splitting. It also reviews modification strategies such as band gap engineering, semiconductor alloys, and multiphoton photocatalysts. This review can serve as a reference for researchers and encourage the development of new materials for hydrogen generation.
Article
Thermodynamics
Hakan F. Oztop, Fatih Selimefendigil, Hakan Cosanay, Nidal Abu-Hamdeh
Summary: In this study, the phase change process and convection inside an open cavity equipped with two different phase change materials (PCMs) were analyzed using the finite volume method with ANSYS Fluent. The analysis was conducted for different Grashof number values and it was found that the PC becomes faster when the object is closer to the exit in the fully open case. The partly open case results in higher thermal performance improvements, with a 94.5% increase in the average Nusselt number for PCM-18.
NUMERICAL HEAT TRANSFER PART A-APPLICATIONS
(2023)
Article
Green & Sustainable Science & Technology
Fatih Selimefendigil, Damla Okulu, Hakan F. Öztop
Summary: Two different cooling systems were developed for the thermal management of a photovoltaic module. The PV/TEG and PV/TEG-mini-channel cooling systems used water and Al2O3 nanofluids in the cooling channel. Higher-loading nanoparticles in the base fluid achieved effective cooling, and the nanofluid showed non-Newtonian behavior. The PV/TEG-cooling channel with the lowest fluid inlet temperature and the highest particle loading resulted in significantly increased PV efficiency and TEG output power compared to PV/TEG and conventional PV systems without cooling.
Article
Thermodynamics
Burak Kiyak, Hakan F. Oztop, I. Gokhan Aksoy
Summary: This study investigated the melting performance of phase change materials in a disk-shaped container with partial circular heating. The results showed that in partial heating cases, increasing the aspect ratio extended the melting time and decreased the liquid fraction.
NUMERICAL HEAT TRANSFER PART A-APPLICATIONS
(2023)
Article
Thermodynamics
Sudhanshu Kumar, Krunal M. Gangawane, Hakan F. Oztop, Sibasish Panda
Summary: This research work presents a numerical investigation of magnetohydrodynamics (MHD) characteristics near-wall blockage due to double-diffusive convection (DDC) in a rectangular cavity. The results show that as the separation distance increases, heat and mass transfer rates enhance, while the increase in Hartmann number (Ha) results in a monotonic decrease in heat and mass transfer rates.
NUMERICAL HEAT TRANSFER PART A-APPLICATIONS
(2023)
Article
Thermodynamics
Ahmad H. Milyani, Nidal H. Abu-Hamdeh, Abdullah A. Azhari, Hussein A. Z. AL-bonsrulah, Amira M. Hussin
Summary: This article achieved improvement in the rate of freezing by utilizing porous containers and hybrid nanomaterials. The effects of different factors on the freezing process were analyzed through numerical simulations.
CASE STUDIES IN THERMAL ENGINEERING
(2023)
Article
Thermodynamics
Khalid H. Almitani, Nidal H. Abu-Hamdeh, Abdullah M. Abusorrah, Hussein A. Z. AL-bonsrulah, Nasrin B. M. Elbashir
Summary: By dispersing nanomaterials and altering the container shape and additive properties, the speed of solidification can be increased significantly. The mathematical models show that the longest freezing time occurs for pure water, and the optimal performance is achieved with a moderate diameter and a certain fraction of added particles, resulting in a significant reduction in freezing time.
CASE STUDIES IN THERMAL ENGINEERING
(2023)
Article
Thermodynamics
Mahsa Taghavi, Swapnil Sharma, Vemuri Balakotaiah
Summary: This study investigates the natural convection effects in the insulation layers of spherical storage tanks and their impact on the tanks' performance. The permeability and Rayleigh number of the insulation material are considered as key factors. The results show that as the Rayleigh number increases, new convective cells emerge and cause the cold boundary to approach the external hot boundary. In the case of large temperature differences, multiple solutions may coexist.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Jinyang Xu, Fangjun Hong, Chaoyang Zhang
Summary: This study introduces a self-induced jet impingement device for enhancing pool boiling performance in high power electronic cooling. Through visualization and parametric investigations, the effects of this device on pool boiling performance are studied, revealing the promotion of additional liquid supply and vapor exhausting. The flow rate of the liquid jet is found to positively impact boiling performance.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Wenchao Ke, Yuan Liu, Fissha Biruke Teshome, Zhi Zeng
Summary: Underwater wet laser welding (UWLW) is a promising and labor-saving repair technique. A thermal multi-phase flow model was developed to study the heat transfer, fluid dynamics, and phase transitions during UWLW. The results show that UWLW creates a water keyhole, making the welding environment similar to in air laser welding.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Xingrong Lian, Lin Tian, Zengyao Li, Xinpeng Zhao
Summary: This study investigates the heat transfer mechanisms in natural fiber-derived porous structures and finds that thermal radiation has a significant impact on the thermal conductivity in low-density regions, while natural convection rarely occurs. Insulation materials derived from micron-sized natural fibers can achieve minimum thermal conductivity at specific densities. Strategies to lower the thermal conductivity include increasing porosity and incorporating nanoscale pores using nanosize fibers.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Yasir A. Malik, Kilian Koebschall, Stephan Bansmer, Cameron Tropea, Jeanette Hussong, Philippe Villedieu
Summary: Ice crystal icing is a significant hazard in aviation, and accurate modeling of sticking efficiency is essential. In this study, icing wind tunnel experiments were conducted to quantify the volumetric liquid water fraction, sticking efficiency, and maximum thickness of ice layers. Two measurement techniques, calorimetry and capacitive measurements, were used to measure the liquid water content and distribution in the ice layers. The experiments showed that increasing wet bulb temperatures and substrate heat flux significantly increased sticking efficiency and maximum ice layer thickness.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Jinqi Hu, Tongtong Geng, Kun Wang, Yuanhong Fan, Chunhua Min, Hsien Chin Su
Summary: This study experimentally examined the heat dissipation of vibrating fans and demonstrated its inherent mechanism through numerical simulation. The results showed that the flow fields induced by the vibrating blades exhibited pulsating features and formed large-scale and small-scale vortical structures, significantly improving heat dissipation. The study also identified the impacts of different blade structures and developed a trapezoidal-folding blade, which effectively reduced the maximum temperature of the heat source and alleviated high-temperature failure crisis.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Dan-Dan Su, Xiao-Bin Li, Hong-Na Zhang, Feng-Chen Li
Summary: The boiling heat transfer of low-boiling-point working fluid is a common heat dissipation technology in electronic equipment cooling. This study analyzed the interfacial boiling behavior of R134a under different conditions and found that factors such as the initial thickness of the liquid film, solid-liquid interaction force, and initial temperature significantly affect the boiling mode and thermal resistance.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Jinyi Wu, Dongke Sun, Wei Chen, Zhenhua Chai
Summary: A unified lattice Boltzmann-phase field scheme is proposed to simulate dendrite growth of binary alloys in the presence of melt convection. The effects of various factors on the growth are investigated numerically, and the model is validated through comparisons and examinations.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Shaokun Ge, Ya Ni, Fubao Zhou, Wangzhaonan Shen, Jia Li, Fengqi Guo, Bobo Shi
Summary: This study investigated the temperature distribution of main cables in a suspension bridge during fire scenarios and proposed a prediction model for the maximum temperature of cables in different lane fires. The results showed that vehicle fires in the emergency lane posed a greater thermal threat to the cables.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Shuang-Ying Wu, Shi-Yao Zhou, Lan Xiao, Jia Luo
Summary: This paper investigates the two-phase flow and heat transfer characteristics of low-velocity jet impacting on a cylindrical surface. The study reveals that the heat transfer regimes are non-phase transition and nucleate boiling with the increase of heat transfer rate. The effects of jet impact height and outlet velocity on local surface temperatures are pronounced at the non-phase transition stage. The growth rates of heat transfer rate and liquid loss rate increase significantly from the non-phase transition to nucleate boiling stage.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Emad Hasani Malekshah, Wlodzimierz Wlodzimierz, Miros law Majkut
Summary: Cavitation has significant practical importance and can be controlled by air injection. This study investigates the natural to ventilated cavitation process around a hydrofoil through numerical and experimental methods. The results show that the location and rate of air injection have a meaningful impact on the characteristics of cavitation.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Feriel Yahiat, Pascale Bouvier, Antoine Beauvillier, Serge Russeil, Christophe Andre, Daniel Bougeard
Summary: This study explores the enhancement of mixing performance in laminar flow equipment by investigating the generation of chaotic advection using wall deformations in annular geometries. The findings demonstrate that the combined geometry can achieve perfect mixing at various Reynolds numbers.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Hui He, Ning Lyu, Caihua Liang, Feng Wang, Xiaosong Zhang
Summary: This study investigates the condensation, frosting, and defrosting processes on superhydrophobic surfaces with millimeter-scale structures. The results reveal that the structures can influence the growth and removal of frost crystals, with the bottom grooves creating a frost-free zone and conical edges promoting higher frost crystal heights. Two effective methods for defrosting are observed: hand-lifting the groove and airfoil retraction contraction on protruding structures. This research provides valuable insights into frost formation and defrosting on millimeter-structured superhydrophobic surfaces, with potential applications in anti-frost engineering.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Thiwanka Arepolage, Christophe Verdy, Thibaut Sylvestre, Aymeric Leray, Sebastien Euphrasie
Summary: This study developed two thermal concentrators, one with a 2D design of uniform thickness and another with a 3D design, using the coordinate transformation technique and metamaterials. By structuring the thermal conductor, the desired local density-heat capacity product and anisotropic thermal conductivities were achieved. The homogenized thermal conductivities were obtained from finite element simulations and cylindrical symmetry consideration. A 3D concentrator was fabricated using 3D metal printing and characterized using a thermal camera. Compared to devices that solely consider anisotropic conductivities, the time evolution characteristics of the metadevice designed with coordinate transformation were closer to those of an ideal concentrator.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Article
Thermodynamics
Liangyuan Cheng, Qingyang Wang, Jinliang Xu
Summary: In this study, we investigated the supercritical heat transfer of CO2 in a horizontal tube with a diameter of 10.0 mm, covering a wide range of pressures, mass fluxes, and heat fluxes. The study revealed a non-monotonic increase in wall temperatures along the flow direction and observed both positive and negative wall temperature differences between the bottom and top tube. The findings were explained by the thermal conduction in the solid wall interacting with the stratified-wavy flow in the tube.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
