Search results for: heat equation

Authors: Safwan Kanan, Jonathan Dewsbury, Gregory Lane-Serff

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A salinity gradient solar pond is a free energy source system for collecting, converting and storing solar energy as heat. In this paper, the principles of solar pond are explained. A mathematical model is developed to describe and simulate heat and mass transfer behavior of salinity gradient solar pond. Matlab codes are programmed to solve the one dimensional finite difference method for heat and mass transfer equations. Temperature profiles and concentration distributions are calculated. The numerical results are validated with experimental data and the results are found to be in good agreement.

Keywords: finite difference method, salt-gradient solar-pond, solar energy, transient heat and mass transfer

Procedia PDF Downloads 369

Authors: Sakkarin Chingulpitak, Somchai Wongwises

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Over the past several decades, the development of electronic devices has led to higher performance. Therefore, an electronic cooling system is important for the electronic device. A heat sink which is a part of the electronic cooling system is continuously studied in the research field to enhance the heat transfer. To author’s best knowledge, there have been only a few articles which reported the thermal performance of plate-fin heat sink with perforation. This research aims to study on the flow and heat transfer characteristics of the solid-fin heat sink (SFHS) and laterally perforated plate-fin heat sink (LAP-PFHS). The SFHS and LAP-PFHSs are investigated on the same fin dimensions. The LAP-PFHSs are performed with a 27 perforation number and two different diameters of circular perforation (3 mm and 5 mm). The experimental study is conducted under various Reynolds numbers from 900 to 2,000 and the heat input of 50W. The experimental results show that the LAP-PFHS with perforation diameter of 5 mm gives the minimum thermal resistance about 25% lower than SFHS. The thermal performance factor which takes into account the ratio of the Nusselt number and ratio of friction factor is used to find the suitable design parameters. The experimental results show that the LAP-PFHS with the perforation diameter of 3 mm provides the thermal performance of 15% greater than SFHS. In addition, the simulation study is presented to investigate the effect of the air flow behavior inside the perforation on the thermal performance of LAP-PFHS.

Keywords: heat sink, parallel flow, circular perforation, non-bypass flow

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Authors: N. K. Chougule, G. V. Parishwad

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The pin fin heat sink is a novel heat transfer device to transfer large amount of heat through with very small temperature differences and it also possesses large uniform cooling characteristics. Pin fins are widely used as elements that provide increased cooling for electronic devices. Increasing demands regarding the performance of such devices can be observed due to the increasing heat production density of electronic components. For this reason, extensive work is being carried out to select and optimize pin fin elements for increased heat transfer. In this paper, the effects of design parameters and the optimum design parameters for a Pin-Fin heat sink (PFHS) under multi-jet impingement case with thermal performance characteristics have been investigated by using Taguchi methodology based on the L9 orthogonal arrays. Various design parameters, such as pin-fin array size, gap between nozzle exit to impingement target surface (Z/d) and air velocity are explored by numerical experiment. The average convective heat transfer coefficient is considered as the thermal performance characteristics. The analysis of variance (ANOVA) is applied to find the effect of each design parameter on the thermal performance characteristics. Then the results of confirmation test with the optimal level constitution of design parameters have obviously shown that this logic approach can effective in optimizing the PFHS with the thermal performance characteristics. The analysis of the Taguchi method reveals that, all the parameters mentioned above have equal contributions in the performance of heat sink efficiency. Experimental results are provided to validate the suitability of the proposed approach.

Keywords: Pin Fin Heat Sink (PFHS), Taguchi method, CFD, thermal performance

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Authors: Maxim Glushenkov, Alexander Kronberg

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Isobaric expansion (IE) process is an alternative to conventional gas/vapor expansion accompanied by a pressure decrease typical of all state-of-the-art heat engines. The elimination of the expansion stage accompanied by useful work means that the most critical and expensive parts of ORC systems (turbine, screw expander, etc.) are also eliminated. In many cases, IE heat engines can be more efficient than conventional expansion machines. In addition, IE machines have a very simple, reliable, and inexpensive design. They can also perform all the known operations of existing heat engines and provide usable energy in a very convenient hydraulic or pneumatic form. This paper reports measurement made with the engine operating as a heat-to-shaft-power or electricity converter and a comparison of the experimental results to a thermodynamic model. Experiments were carried out at heat source temperature in the range 30–85 °C and heat sink temperature around 20 °C; refrigerant R134a was used as the engine working fluid. The pressure difference generated by the engine varied from 2.5 bar at the heat source temperature 40 °C to 23 bar at the heat source temperature 85 °C. Using a differential piston, the generated pressure was quadrupled to pump hydraulic oil through a hydraulic motor that generates shaft power and is connected to an alternator. At the frequency of about 0.5 Hz, the engine operates with useful powers up to 1 kW and an oil pumping flowrate of 7 L/min. Depending on the temperature of the heat source, the obtained efficiency was 3.5 – 6 %. This efficiency looks very high, considering such a low temperature difference (10 – 65 °C) and low power (< 1 kW). The engine’s observed performance is in good agreement with the predictions of the model. The results are very promising, showing that the engine is a simple and low-cost alternative to ORC plants and other known energy conversion systems, especially at low temperatures (< 100 °C) and low power range (< 500 kW) where other known technologies are not economic. Thus low-grade solar, geothermal energy, biomass combustion, and waste heat with a temperature above 30 °C can be involved into various energy conversion processes.

Keywords: isobaric expansion, low-grade heat, heat engine, renewable energy, waste heat recovery

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Authors: Can Yao, Chang Dong Sheng

Abstract:

The heat released by wood pellets during storage will cause self-heating and even self-ignition. In this work, the heat release rates of pine, fir wood and mahogany pellets at 30–70℃ were measured by TAM air isothermal calorimeter, and the kinetic analysis was performed by iso-conversion ratio and non-steady-state methods to evaluate its self-heating potential. The results show that the reaction temperature can significantly affect the heat release rate. The higher the temperature, the greater the heat release rate. The heat release rates of different kinds of wood pellets are obviously different, and the order of the heat release rates for the three pellets at 70℃ is pine > fir wood > mahogany. The kinetic analysis of the iso-conversion ratio method indicates that the distribution of activation energy for pine, fir wood and mahogany pellets under the release of 0.1–1.0 J/g specific heat are 58–102 kJ/mol, 59–108 kJ/mol and 59–112 kJ/mol, respectively. Their activation energies obtained from the non-steady-state kinetic analysis are 13.43 kJ/mol, 19.19 kJ/mol and 21.09 kJ/mol, respectively. Both kinetic analyses show that the magnitude of self-heating risk for the three pellet fuels is pine pellets > fir wood pellets > mahogany pellets.

Keywords: isothermal calorimeter, kinetics, self-heating, wood pellets

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Authors: Muhammad Azmain Abdullah, Ar Rashedul, Mohammad Ali

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This paper scrutinizes the influences of turbulence on heat transport rate, Nusselt number. The subject matter of this investigation also deals with the improvement of heat transfer efficiency of the swirl flow obtained by rotating a twisted tape in a circular pipe. The conditions to be fulfilled to observe the impact of Reynolds number and rotational speed of twisted tape are: a uniform temperature on the outer surface of the pipe, the magnitude of velocity of water varying from 0.1 m/s to 0.7 m/s in order to alter Reynolds number and a rotational speed of 200 rpm to 600 rpm. The gyration of twisted tape increase by 17%. It is also observed that heat transfer is exactly proportional to inlet gauge pressure and reciprocally proportional to increase of twist ratio.

Keywords: swirl flow, twisted tape, twist ratio, heat transfer

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Authors: Jayesh Mahitkar, V. K. Singh, Surendra Singh Kachhwaha

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Wire Mesh Heat Pipe (WMHP) as an effective component of thermal control system in the payload of spacecraft, utilizing ammonia to transfer efficient amount of heat. One dimensional generic and robust mathematical model with partial-analytical hydraulic approach (PAHA) is developed to study inside behaviour of WMHP. In this model, inside performance during operation is investigated like mass flow rate, and velocity along the wire mesh as well as vapour core is modeled respectively. This numerical model investigate heat flow along length, pressure drop along wire mesh as well as vapour line in axial direction. Furthermore, WMHP is modeled into equivalent resistance network such that total thermal resistance of heat pipe, temperature drop across evaporator end and condenser end is evaluated. This numerical investigation should be carried out for single layer and double layer wire mesh each with heat input at evaporator section is 10W, 20 W and 30 W at condenser temperature maintained at 20˚C.

Keywords: ammonia, heat transfer, modeling, wire mesh

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Authors: Jana Pichova, Lubos Hes, Vladimir Bajzik

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Protective clothing is designed to keep a wearer save in hazardous conditions or enable perform short time working operation without being injured or feeling discomfort. Firefighters or other related workers are exposed to abnormal heat which can be conductive, convective or radiant type. Their garment is proposed to resist this conditions and prevent burn injuries or dead of human. However thermal comfort of firefighter exposed to high heat source have not been studied yet. Thermal resistance is the best representative parameter of thermal comfort. In this study a new method of testing of thermal resistance of special clothing exposed to high radiation heat source was designed. This method simulates human body wearing single or multi-layered garment which is exposed to radiative heat. Setup of this method enables measuring of radiative heat flow in time without effect of convection. The new testing method is verified on chosen group of textiles for firefighters.

Keywords: protective clothing, radiative heat, thermal comfort of firefighters, thermal resistance of special garments

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Authors: Tugba Yilmaz Aydin, Ergun Guntekin, Murat Aydin

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Effects of heat treatment on the elastic constants of cedar wood (Cedrus libani) were investigated. Specimens were exposed to heat under atmospheric pressure at four different temperatures (120, 150, 180, 210 °C) and three different time levels (2, 5, 8 hours). Three Young’s modulus (EL, ER, ET) and six Poisson ratios (μLR, μLT, μRL, μRT, μTL, μTR) were determined from compression test using bi-axial extensometer at constant moisture content (12 %). Three shear modulus were determined using ultrasound. Six shear wave velocities propagating along the principal axes of anisotropy were measured using EPOCH 650 ultrasonic flaw detector with 1 MHz transverse transducers. The properties of the samples tested were significantly affected by heat treatment by different degree. As a result, softer treatments yielded some amount of increase in Young modulus and shear modulus values, but increase of time and temperature resulted in significant decrease for both values. Poisson ratios seemed insensitive to heat treatment.

Keywords: cedar wood, elastic constants, heat treatment, ultrasound

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Authors: Toufic Abd El-Latif Sadek

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The Asphalt object represents the asphalted areas, like roads. The best original data of thermal images occurred at a specific time during the days of the year, by preventing the gaps in times which give the close and same brightness from different objects, using seven sample objects, asphalt, concrete, metal, rock, dry soil, vegetation, and water. It has been found in this study a general timing equation for capturing satellite thermal images at different locations, depends on a fixed time the sunrise and sunset; Capture Time= Tcap =(TM*TSR) ±TS.

Keywords: asphalt, satellite, thermal images, timing equation

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Authors: Ranajay Bhowmick

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Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion

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Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Khaoula Hidouri, Ali Benhmidene, Bechir Chouachi

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The purification of brackish seawater becomes a necessity and not a choice against demographic and industrial growth especially in third world countries. Two models can be used in this work: simple solar still and simple solar still coupled with a heat pump. In this research, the productivity of water by Simple Solar Distiller (SSD) and Simple Solar Distiller Hybrid Heat Pump (SSDHP) was determined by the orientation, the use of heat pump, the simple or double glass cover. The productivity can exceed 1.2 L/m²h for the SSDHP and 0.5 L/m²h for SSD model. The result of the global efficiency is determined for two models SSD and SSDHP give respectively 30%, 50%. The internal efficiency attained 35% for SSD and 60% of the SSDHP models. Convective heat coefficient can be determined by attained 2.5 W/m²°C and 0.5 W/m²°C respectively for SSDHP and SSD models.

Keywords: productivity, efficiency, convective heat coefficient, SSD model, SSDHPmodel

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Authors: Hua Li, Hongwu Deng

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The turbine blade's leading edge is usually cooled by jet impingement cooling technology due to the heaviest heat load. For a rotating turbine blade, however, the channel orientation (β, the angle between the jet direction and the rotating plane) could play an important role in influencing the flow field and heat transfer. Therefore, in this work, the effects of channel orientation (from 90° to 180°) on heat transfer in a jet impingement cooling channel are experimentally investigated. Furthermore, the investigations are conducted under an isothermal boundary condition. Both the jet-to-target surface distance and jet-to-jet spacing are three times the jet hole diameter. The jet Reynolds number is 5,000, and the maximum jet rotation number reaches 0.24. The results show that the rotation-induced variations of heat transfer are different in each channel orientation. In the cases of 90°≤β≤135°, a vortex generated in the low-radius region of the supply channel changes the mass-flowrate distribution in each jet hole. Therefore, the heat transfer in the low-radius region decreases with the rotation number, whereas the heat transfer in the high-radius region increases, indicating that a larger temperature gradient in the radial direction could appear in the turbine blade's leading edge. When 135°<β≤180°; however, the heat transfer of the entire stagnant zone decreases with the rotation number. The rotation-induced jet deflection is the primary factor that weakens the heat transfer, and jets cannot reach the target surface at high rotation numbers. For the downstream regions, however, the heat transfer is enhanced by 50%-80% in every channel orientation because the dead zone is broken by the rotation-induced secondary flow in the impingement channel.

Keywords: heat transfer, jet impingement cooling, channel orientation, high rotation number, isothermal boundary

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Authors: Eleni Stefania Kalapoda

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Recurring heat waves due to the global climate change emergency pose continuous risks to human health and urban resources. Local and state decision-makers incorporate Heat Vulnerability Indices (HVIs) to quantify and map the relative impact on human health in emergencies. These maps enable government officials to identify the highest-risk districts and to concentrate emergency planning efforts and available resources accordingly (e.g., to reevaluate the location and the number of heat-relief centers). Even though the framework of conducting an HVI is unique per municipality, its accuracy in assessing the heat risk is limited. To resolve this issue, varied housing-related metrics should be included. This paper quantifies and classifies NYC’s single detached housing typology within high-vulnerable NYC districts using detailed energy simulations and post-processing calculations. The results show that the variation in indoor heat risk depends significantly on the dwelling’s design/operation characteristics, concluding that low-ventilated dwellings are the most vulnerable ones. Also, it confirmed that when building-level determinants of exposure are excluded from the assessment, HVI fails to capture important components of heat vulnerability. Lastly, the overall vulnerability ratio of the housing units was calculated between 0.11 to 1.6 indoor heat degrees in terms of ventilation and shading capacity, insulation degree, and other building attributes.

Keywords: heat vulnerability index, energy efficiency, urban heat, resiliency to heat, climate adaptation, climate mitigation, building energy

Procedia PDF Downloads 80

Authors: Fatih Kantas

Abstract:

Exhaust systems are key contributors to ground vehicles as a heat source. Understanding heat transfer in exhaust systems is related to defining effective parameter on heat transfer in exhaust system. In this journal, over 20 Nusselt numbers are investigated. This study shows advantages and disadvantages of various Nusselt numbers in different range Re, Pr and pulsating flow amplitude and frequency. Also (CAF) Convective Augmentation Factors are defined to correct standard Nusselt number for geometry and location of exhaust system. Finally, optimum Nusselt number and Convective Augmentation Factors are recommended according to Re, Pr and pulsating flow amplitude and frequency, geometry and location effect of exhaust system.

Keywords: exhaust gas flow, heat transfer correlation, Nusselt, Prandtl, pulsating flow

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Authors: Zhu Xinxin, Wang Hui, Yang Kai

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Heat flux is one of the most important test parameters in the ground thermal protection test. Slug calorimeter is selected as the main sensor measuring heat flux in arc wind tunnel test due to the convenience and low cost. However, because of excessive lateral heat transfer and the disadvantage of the calculation method, the heat flux measurement error of the slug calorimeter is large. In order to enhance measurement accuracy, the heat insulation structure and heat flux calculation method of slug calorimeter were improved. The heat transfer model of the slug calorimeter was built according to the energy conservation principle. Based on the heat transfer model, the insulating sleeve of the hollow structure was designed, which helped to greatly decrease lateral heat transfer. And the slug with insulating sleeve of hollow structure was encapsulated using a package shell. The improved insulation structure reduced heat loss and ensured that the heat transfer characteristics were almost the same when calibrated and tested. The heat flux calibration test was carried out in arc lamp system for heat flux sensor calibration, and the results show that test accuracy and precision of slug calorimeter are improved greatly. In the meantime, the simulation model of the slug calorimeter was built. The heat flux values in different temperature rise time periods were calculated by the simulation model. The results show that extracting the data of the temperature rise rate as soon as possible can result in a smaller heat flux calculation error. Then the different thermal contact resistance affecting calculation error was analyzed by the simulation model. The contact resistance between the slug and the insulating sleeve was identified as the main influencing factor. The direct comparison calibration correction method was proposed based on only heat flux calibration. The numerical calculation correction method was proposed based on the heat flux calibration and simulation model of slug calorimeter after the simulation model was solved by solving the contact resistance between the slug and the insulating sleeve. The simulation and test results show that two methods can greatly reduce the heat flux measurement error. Finally, the improved slug calorimeter was tested in the arc wind tunnel. And test results show that the repeatability accuracy of improved slug calorimeter is less than 3%. The deviation of measurement value from different slug calorimeters is less than 3% in the same fluid field. The deviation of measurement value between slug calorimeter and Gordon Gage is less than 4% in the same fluid field.

Keywords: correction method, heat flux calculation, heat insulation structure, heat transfer model, slug calorimeter

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Authors: M. Mosaad, J. H. Almutairi, A. S. Almutairi

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In this paper, saturated-vapour film condensation on a vertical wall with the backside cooled by forced convection is analyzed as a conjugate problem. In the analysis, the temperature and heat flux at the wall sides are assumed unknown and determined from the solution. The model is presented in a dimensionless form to take a broad view of the solution. The dimensionless variables controlling this coupled heat transfer process are discovered from the analysis. These variables explain the relative impact of the interactive heat transfer mechanisms of forced convection and film condensation. The study shows that the conjugate treatment of film condensation process yields results different from that predicted by a non-conjugate Nusselt-type solution, wherein the effect of the cooling fluid is neglected.

Keywords: film condensation, forced convection, coupled heat transfer, analytical modelling

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

Procedia PDF Downloads 278

Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

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Authors: Bi Yan-Qiang, Shang Yonghong, Lin Boying, Ji Xinyan, Li Xiyuan

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The heat-resistant material has important application in the aerospace field. The reliability of the connection between the heat-resisting material and the body determines the success or failure of the project. In this paper, lock-in infrared thermography non-destructive testing technology is used to detect the stability of the thermal-resistant structure. The phase relationship between the temperature and the heat flow is calculated by the numerical method, and the influence of the heating frequency and power is obtained. The correctness of the analysis is verified by the experimental method. Through the research, it can provide the basis for the parameter setting of heat flux including frequency and power, improve the efficiency of detection and the reliability of connection between the heat-resisting material and the body.

Keywords: infrared non-destructive, thermal insulation material, reliability, connection

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Authors: F. Hekmatipour, M. A. Akhavan-Behabadi, B. Sajadi

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In this paper, the combined free and forced convection heat transfer of the Copper Oxide-Heat Transfer Oil (CuO-HTO) nanofluid flow in horizontal and inclined microfin tubes is studied experimentally. The flow regime is laminar, and pipe surface temperature is constant. The effect of nanoparticle and microfin tube on the heat transfer rate is investigated with the Richardson number which is between 0.1 and 0.7. The results show an increasing nanoparticle concentration between 0% and 1.5% leads to enhance the combined free and forced convection heat transfer rate. According to the results, five correlations are proposed to provide estimating the free and forced heat transfer rate as the increasing Richardson number from 0.1 to 0.7. The maximum deviation of both correlations is less than 16%. Moreover, four correlations are suggested to assess the Nusselt number based on the Rayleigh number in inclined tubes from 1800000 to 7000000. The maximum deviation of the correlation is almost 16%. The Darcy friction factor of the nanofluid flow has been investigated. Furthermore, CuO-HTO nanofluid flows in inclined microfin tubes.

Keywords: nanofluid, heat transfer oil, mixed convection, inclined tube, laminar flow

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Authors: S. K. Deb, B. C. Sarma

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The concentrating solar thermal devices using low cost thin metallic reflector sheet of moderate reflectance can generate heat both at higher temperature for the receiver at it’s focus and at moderate temperature through direct solar irradiative heat absorption by the reflector sheet itself. Investigation on well insulated rear surface of the concentrator with glass covers at it’s aperture plane for waste heat recovery against the conventional radiative, convective & conductive heat losses for a bench model with a thermal analysis is the prime motivation of this study along with an effort to popularize a compact solar thermal polygeneration system.

Keywords: concentrator, polygeneration, aperture, renewable energy, exergy, solar energy

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Authors: Alireza Ghadiri, Soheila Memarzadeh, Arash Ghadiri

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Heat pipes are efficient heat transfer devices for solar hot water heating systems. However, the effective downward transfer of solar energy in an integrated heat pipe system provides increased design and implementation options. There is a lack of literature about flat plate wicked assisted heat pipe solar collector, especially with the presence of finned water-cooled condenser wicked heat pipes for solar energy applications. In this paper, the consequence of incorporating fins arrays into the condenser region of screen mesh heat pipe solar collector is investigated. An experimental model and a transient theoretical model are conducted to compare the performances of the solar heating system at a different period of the year. A good agreement is shown between the model and the experiment. Two working fluids are investigated (water and methanol) and results reveal that water slightly outperforms methanol with a collector instantaneous efficiency of nearly 60%. That modest improvement is achieved by adding fins to the condenser region of the heat pipes. Results show that the collector efficiency increase as the number of fins increases (upon certain number) and reveal that the mesh number is an important factor which affect the overall collector efficiency. An optimal heat pipe mesh number of 100 meshes/in. With two layers appears to be favorable in such collectors for their design and operating conditions.

Keywords: heat pipe, solar collector, capillary limit, mesh number

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: M. V. Bartashevich

Abstract:

The problem of heat transfer at thin laminar liquid film is solved numerically. A thin film of liquid flows down an inclined surface under conditions of variable heat flux on the wall. The use of thin films of liquid allows to create the effective technologies for cooling surfaces. However, it is important to investigate the most suitable cooling regimes from a safety point of view, in order, for example, to avoid overheating caused by the ruptures of the liquid film, and also to study the most effective cooling regimes depending on the character of the distribution of the heat flux on the wall, as well as the character of the blowing of the film surface, i.e., the external shear stress on its surface. In the statement of the problem on the film surface, the heat transfer coefficient between the liquid and gas is set, as well as a variable external shear stress - the intensity of blowing. It is shown that the combination of these factors - the degree of uniformity of the distribution of heat flux on the wall and the intensity of blowing, affects the efficiency of heat transfer. In this case, with an increase in the intensity of blowing, the cooling efficiency increases, reaching a maximum, and then decreases. It is also shown that the more uniform the heating of the wall, the more efficient the heat sink. A separate study was made for the flow regime along the horizontal surface when the liquid film moves solely due to external stress influence. For this mode, the analytical solution is used for the temperature at the entrance region for further numerical calculations downstream. Also the influence of the degree of uniformity of the heat flux distribution on the wall and the intensity of blowing of the film surface on the heat transfer efficiency was also studied. This work was carried out at the Kutateladze Institute of Thermophysics SB RAS (Russia) and supported by FASO Russia.

Keywords: Heat Flux, Heat Transfer Enhancement, External Blowing, Thin Liquid Film

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Authors: Yanpei Zhen

Abstract:

The nonlinear Schrödinger (NLS) equation models wave dynamics in many physical problems related to fluids, plasmas, and optics. The standing periodic waves are known to be modulationally unstable, and rogue waves (localized perturbations in space and time) have been observed on their backgrounds in numerical experiments. The exact solutions for rogue waves arising on the periodic standing waves have been obtained analytically. It is natural to ask if the rogue waves persist on the standing periodic waves in the integrable discretizations of the integrable NLS equation. We study the standing periodic waves in the semidiscrete integrable system modeled by the high-order Ablowitz-Ladik (AL) equation. The standing periodic wave of the high-order AL equation is expressed by the Jacobi cnoidal elliptic function. The exact solutions are obtained by using the separation of variables and one-fold Darboux transformation. Since the cnoidal wave is modulationally unstable, the rogue waves are generated on the periodic background.

Keywords: Darboux transformation, periodic wave, Rogue wave, separating the variables

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

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Authors: L. Q. Yuan, J. Yang, A. Siddiqui

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A new regression uncertainty analysis methodology was applied to determine the uncertainties of the critical heat flux (CHF) power correlation for an advanced 43-element bundle design, which was developed by Canadian Nuclear Laboratories (CNL) to achieve improved economics, resource utilization and energy sustainability. The new methodology is considered more appropriate than the traditional methodology in the assessment of the experimental uncertainty associated with regressions. The methodology was first assessed using both the Monte Carlo Method (MCM) and the Taylor Series Method (TSM) for a simple linear regression model, and then extended successfully to a non-linear CHF power regression model (CHF power as a function of inlet temperature, outlet pressure and mass flow rate). The regression uncertainty assessed by MCM agrees well with that by TSM. An equation to evaluate the CHF power regression uncertainty was developed and expressed as a function of independent variables that determine the CHF power.

Keywords: CHF experiment, CHF correlation, regression uncertainty, Monte Carlo Method, Taylor Series Method

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Authors: Vipul M. Patel, H. B. Mehta

Abstract:

Closed Loop Pulsating Heat Pipe (CLPHP) is a passive two-phase heat transfer device having potential to achieve high heat transfer rates over conventional cooling techniques. It is found in electronics cooling due to its outstanding characteristics such as excellent heat transfer performance, simple, reliable, cost effective, compact structure and no external mechanical power requirement etc. Comprehensive understanding of the thermo-hydrodynamic mechanism of CLPHP is still lacking due to its contradictory results available in the literature. The present paper discusses the experimental study on 9 turn CLPHP. Inner and outer diameters of the copper tube are 2 mm and 4 mm respectively. The lengths of the evaporator, adiabatic and condenser sections are 40 mm, 100 mm and 50 mm respectively. Water is used as working fluid. The Filling Ratio (FR) is kept as 50% throughout the investigations. The gravitational effect is studied by placing the evaporator heater at different orientations such as horizontal (90 degree), vertical top (180 degree) and bottom (0 degree) as well as inclined top (135 degree) and bottom (45 degree). Heat input is supplied in the range of 10-50 Watt. Heat transfer mechanism is natural convection in the condenser section. Vacuum pump is used to evacuate the system up to 10^-5 bar. The results demonstrate the influence of input heat flux and gravity on the thermal performance of the CLPHP.

Keywords: CLPHP, gravity effect, start up, two-phase flow

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