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Yazar "Kurt, Huseyin" seçeneğine göre listele

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  • Küçük Resim Yok
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    A comparative assessment of SPECO and MOPSA on costing of exergy destruction
    (Inderscience Enterprises Ltd, 2020) Uysal, Cuneyt; Ozen, Dilek Nur; Kurt, Huseyin; Kwak, Ho Young
    This paper presents the comparison of specific exergy costing (SPECO) and modified productive structure analysis (MOPSA) method to test their abilities on costing of exergy destruction. MOPSA method is applied to a combined supercritical CO(2)regenerative cycle and organic Rankine cycle using zeotropic mixtures for gas turbine waste heat recovery system. The results obtained with applying SPECO method to the system are taken from literature. The exergy destruction cost rate of overall system is obtained to be $86.08/h and $1,113.13/h for MOPSA and SPECO methods, respectively. The exergoeconomic factor of overall system is found to be 31.88% for SPECO method, while this value is found to be 85.82% for MOPSA method. The obtained results with applying MOPSA method for exergy destruction cost rate are significantly lower and more consistent compared to the results obtained by SPECO method.
  • Küçük Resim Yok
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    Comparison of Different Cooling Options for Photovoltaic Applications
    (Ieee, 2018) Ozkul, Feyzullah Behlul; Kayabasi, Erhan; Celik, Erdal; Kurt, Huseyin; Arcaklioglu, Erol
    A temperature increase plays a negative role on photovoltaic (PV) panel conversion efficiency by increasing recombination rates. In this study, air- and water-cooling options were simulated to investigate the efficiency behavior of a specific PV panel made of heterojunction Silicon (Si) whilst PV panel was cooling in operation by using ANSYS-FLUENT. For air cooling, two different options were suggested: air cooling with four different flow speeds and air cooling with a heat sink addition with three different flow speeds. As for water-cooling three flowrates were considered. Temperature distributions of PV panels for the all cooling options were demonstrated as a function of flow velocity of air and flowrate of water for different cooling conditions and compared with each other. The influence of temperature difference on panel conversion efficiency were also discussed. As a result, heat sink with a proper flow arrangement cooling option showed the best performance in terms of minimum material, minimum cost and minimum complexity with the 42 degrees C, 38.4 degrees C, 35.9 degrees C average surface temperatures and 20.9%, 21.3%, 21.5% panel efficiencies.
  • Küçük Resim Yok
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    Detailed comparison of the methods used in the heat transfer coefficient and pressure loss calculation of shell side of shell and tube heat exchangers with the experimental results
    (Taylor & Francis Inc, 2023) Alperen, Munip Alpaslan; Kayabasi, Erhan; Kurt, Huseyin
    In this study, results of HTRI Xchanger software used in the analysis of shell and tube heat exchangers (STHE), and Kern and Bell-Delaware methods, which are the conventional methods used for calculation of shell side heat transfer coefficient (SSHTC) and pressure loss (PL), were compared with experimental data. An experimental study was considered for Heat exchanger (HE) dimensions and fluid properties from literature. Then SSHTC and PL values were calculated using Kern and Bell-Delaware methods and HTRI Xchanger software for the measured shell side flowrates. SSHTC and PL values calculated for lower shell side mass flowrates by Kern method deviated from experimental results at low ratios. In addition, deviations in high flowrates values increasingly moved away from experimental results. In the Bell-Delaware method, although low deviations were observed in the high shell-side mass flowrates, the deviations increased at low flow rates and diverged from the experimental results. The deviation of SSHTC values calculated by the HTRI Xchanger program was found to be massively independent from the shell side flowrate. In addition, as in Bell-Delaware method, it has been observed that deviations in the shell side pressure loss (SSPL) calculations increased with increasing shell-side mass flowrate. As a result, SSHTC was calculated with average deviations of + 17, ?11, and + 18%, by Kern and Bell-Delaware methods and HTRI Xchanger software respectively. Similarly, shell side PL was found with + 64, ?25, and ?32% average deviation, respectively.
  • Küçük Resim Yok
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    Determination of cutting parameters for silicon wafer with a Diamond Wire Saw using an artificial neural network
    (Pergamon-Elsevier Science Ltd, 2017) Kayabasi, Erhan; Ozturk, Savas; Celik, Erdal; Kurt, Huseyin
    An Artificial Neural Network (ANN) simulation was utilized to predict surface roughness values (R-a) for a Silicon (Si) ingot cutting operation with a Diamond Wire Saw (DWS) cutting machine. Experiments were done on a DWS cutting machine to obtain data for training, testing and validation of the ANN. The DWS cutting operation had three parameters affecting surface quality: spool speed, z axis speed and oil ratio in a coolant slurry. Other parameters such as wire tension, wire thickness, and work piece diameter were assumed as constant. The DWS cutting machine performed 28 cutting operations with different values of the selected three parameters and new cutting parameters were derived for different cutting conditions to achieve the best surface quality by using the ANN. Wafers 400 mu m thick were cut from a n-type single crystalline Si ingot in a STX 1202 DWS cutting machine. R-a values were measured three times from different regions of the wafers. In ANN simulation 70% of R-a values were used as training, 15% of R-a values were used as validation and 15% of R-a values were used to test data in ANN. The ANN simulation results validated training output data with success above 99%. Consequently, the R-a values corresponding to the cutting parameters, and also proper cutting parameters for specific R-a values were determined for DWS cutting using the ANN. (C) 2017 Elsevier Ltd. All rights reserved.
  • Küçük Resim Yok
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    Determination of lapping parameters for silicon wafer using an artificial neural network
    (Springer, 2018) Ozturk, Savas; Kayabasi, Erhan; Celik, Erdal; Kurt, Huseyin
    An artificial neural network (ANN) simulation was utilized to determine the lapping parameters such as rotation speed, lapping duration and lapping pressure under a constant slurry supply for n-type crystalline Silicon (c-Si) wafers. Experiments were done with a Logitech PM5 lapping and polishing machine to obtain input data and target data for training, testing and validation of ANN. Lapping operation had five main parameters affecting surface quality: rotation speed, lapping duration, lapping pressure, flowrate of abrasive slurry and particle size in abrasive slurry. However, in this study slurry flowrate was assumed constant due the researches performed before. 218 lapping operations were performed with different values of the selected parameters and new lapping parameters were derived for different lapping conditions to achieve the best surface quality by using an ANN. In this study, wafers in 400 A mu m thickness cut under identical conditions from n-type single c-Si ingot in a STX 1202 DWS cutting machine were employed. Surface roughness (R (a) ) values were measured three times from different points of the wafers after lapping with a contact type surface roughness measurement tool using a microscopic scale stylus profiler (SP). In ANN simulation 70% of R (a) values were utilized for training, 15% of R (a) values were utilized for validation and 15% of R (a) values were utilized for test data. Results obtained from ANN simulation validated with a success above 99%.
  • Küçük Resim Yok
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    Determination of micro sized texturing and nano sized etching procedure to enhance optical properties of n-type single crystalline silicon wafer
    (Springer, 2017) Kayabasi, Erhan; Kurt, Huseyin; Celik, Erdal
    Crystalline silicon (c-Si) wafer was manufactured by applying micro texture and nano etching process without lapping and polishing for solar cell applications. Before micro texture and nano etching, wafers were exposed to chemical polishing process in high concentrated alkaline solution to remove saw damages and obtain a surface with low surface roughness (R-a). Uniform pyramidal structures were formed in alkaline solution. On pyramidal structures, nano sized porous shapes were formed by using Ag nano particles via wet chemical etching method. Micro textured and nano etched surface formed without any chemical mechanical (CM) lapping and polishing step, examined by Scanning Electron Microscope (SEM) for surface structure and UV-visible spectrometer for reflectance and absorbance measurements. Considerably good uniform porous surface with low reflectance was formed and compared with usual solar wafers produced with CM lapping and polishing. Furthermore, present process for preparing solar cell provides low cost, short time and less material consumption by removing lapping and polishing steps from overall process. Reflectance values were measured between 7 and 10% for best micro textured and nano etched c-Si wafers, respectively. Absorbance values were measured 0.4 and 1.2% for best micro textured and nano etched c-Si wafers, respectively. Curves of versus indicated the optical band gaps almost 1.12 e.V. for all wafers cut from same n-type single c-Si ingot.
  • Küçük Resim Yok
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    The effects of component dimensions on heat transfer and pressure loss in shell and tube heat exchangers
    (Taylor & Francis Inc, 2019) Kayabasi, Erhan; Alperen, Munip Alpaslan; Kurt, Huseyin
    In this study, the effects of geometric properties such as baffle spacing, baffle cut, sealing strips, gaps between heat exchanger components, number of tubes and tube passes have been investigated for shell and tube heat exchangers (STHE). For this purpose, geometrical dimensions and data of a specific heat exchanger (HE) used in an industrial application have been obtained. The HTRI Xchanger Suite Educational software was utilized to analyze the reference HE, to verify the results of the software and the output temperatures of the fluids, the shell side heat transfer coefficient (HTC) and the pressure loss (PL) values were compared with the experimental data. After confirming that the results of the software were within the acceptable deviation values, the geometric dimensions of the reference design were changed and new analyzes were carried out to examine the effects of several dimension options on the performance of STHE. Results were discussed in a detailed and comprehensive manner via curves.
  • Küçük Resim Yok
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    Effects of Electrical Properties on Determining Materials for Power Generation Enhancement in TEG Modules
    (Springer, 2019) Ozturk, Turgut; Kilinc, Enes; Uysal, Fatih; Celik, Erdal; Kurt, Huseyin
    This study aimed to increase the energy efficiency of thermoelectric generators designed by considering the electrical properties of p- and n-type semiconductor materials for reducing the costs associated with the experiments, errors, and long production processes. Accordingly, the estimation of the energy amount to be produced by the thermoelectric materials was achieved by different doping elements using three different parameters such as skin-depth, electrical conductivity and dielectric constant. Additionally, the findings were supported by experimental results. In contrast to the conventionally used black-box type approach and estimation methods, an inference was obtained on the actual values of the materials.
  • Küçük Resim Yok
    Öğe
    ENTROPY GENERATION OF ZIRCONIA-WATER NANOFLUID FLOW THROUGH RECTANGULAR MICRO-CHANNEL
    (Vinca Inst Nuclear Sci, 2018) Uysal, Cuneyt; Arslan, Kamil; Kurt, Huseyin
    The fluid flow and heat transfer characteristics and entropy generation of zirconia, ZrO2-water, nanofluid flow through a rectangular micro-channel are numerically investigated. The flow is considered under single-phase 3-D steady-state incompressible laminar flow conditions. The constant heat flux is applied to the bottom surface of micro-channel. The finite volume method is used to discretize the governing equations. As a result, the average Nusselt number decreases with increasing nanoparticle volume fraction, while the average Darcy friction factor is not affected. Moreover, the total entropy generation decreases with increase in nanoparticle volume fraction, while the Bejan number is almost not affected.
  • Küçük Resim Yok
    Öğe
    Estimating Seebeck Coefficient of a p-Type High Temperature Thermoelectric Material Using Bee Algorithm Multi-layer Perception
    (Springer, 2017) Uysal, Fatih; Kilinc, Enes; Kurt, Huseyin; Celik, Erdal; Dugenci, Muharrem; Sagiroglu, Selami
    Thermoelectric generators (TEGs) convert heat into electrical energy. These energy-conversion systems do not involve any moving parts and are made of thermoelectric (TE) elements connected electrically in a series and thermally in parallel; however, they are currently not suitable for use in regular operations due to their low efficiency levels. In order to produce high-efficiency TEGs, there is a need for highly heat-resistant thermoelectric materials (TEMs) with an improved figure of merit (ZT). Production and test methods used for TEMs today are highly expensive. This study attempts to estimate the Seebeck coefficient of TEMs by using the values of existing materials in the literature. The estimation is made within an artificial neural network (ANN) based on the amount of doping and production methods. Results of the estimations show that the Seebeck coefficient can approximate the real values with an average accuracy of 94.4%. In addition, ANN has detected that any change in production methods is followed by a change in the Seebeck coefficient.
  • Küçük Resim Yok
    Öğe
    Exergetic and thermoeconomic analyses of a coal-fired power plant
    (Elsevier France-Editions Scientifiques Medicales Elsevier, 2017) Uysal, Cuneyt; Kurt, Huseyin; Kwak, Ho-Young
    Exergetic and thermoeconomic analyses of a coal-fired power plant with 160 MW capacity where located in Turkey were performed. Specific Exergy Costing (SPECO) and Modified Productive Structure Analysis (MOPSA) methods were separately applied to the system to determine the unit exergy cost of electricity generated by the coal-fired plant. The differences of these methods were discussed. As a result, the exergy efficiency of coal-fired power plant is found to be 39.89%. The equipment having the highest improvement potential is determined as boiler. The unit specific exergy cost of electricity generated by the system obtained for SPECO and MOPSA thermoeconomic analysis methods are 12.14 US$/GJ and 14.06 US$/GJ, respectively. The unit specific exergy cost of electricity obtained by using MOPSA thermoeconomic method is the same as the one obtained by the overall cost-balance equation for the coal-fired power plant. (C) 2017 Elsevier Masson SAS. All rights reserved.
  • Küçük Resim Yok
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    Exergy analysis of a spark ignition engine for different crankshaft speeds
    (Pamukkale Univ, 2019) Ozdalyan, Bulent; Uysal, Cuneyt; Kurt, Huseyin
    In this study, a spark ignition (SI) engine performance is exergetically investigated for different crankshaft speeds. The test engine is VSG413 SI type engine fueled with 95 octane gasoline. The test engine has 1.3 l volume, four stroke, four cylinder, 45 kW maximum power capacity and 98 Nm maximum torque capacity. The experiments are realized under fully loaded test conditions. The crankshaft speed is changed between 1200 rpm and 5000 rpm. In the calculations, actual operating data obtained by experiments are used. It is found that maximum energy and exergy efficiencies are obtained at crankshaft speed of 2500 rpm, which are 29.78% and 27.77%, respectively. Entropy generation rate increases with increase in crankshaft speed and ranged from 0.059 kW/K to 0.253 kW/K for all study.
  • Küçük Resim Yok
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    An experimental and artificial neural network investigation on the laminar flow of magnetorheological fluids through circular pipes
    (Elsevier, 2022) Gedik, Engin; Kurt, Huseyin; Pala, Murat; Alakour, Abdulla
    Fluids can change their physical properties when they are exposed to magnetic fields. Magnetorheological (MR) fluids are classified as smart materials because their viscoelastic properties can increase by the application of the magnetic field. Accordingly, they are used in different engineering applications such as flow control and vibration damping. In this study, three different types of MR fluids flow in circular pipes with diameters of 10 and 15 mm and length of 300 mm were experimentally investigated with and without applying the magnetic field. An electromagnetic device was designed and manufactured in order to create a magnetic field induction for experiments. Throughout the experiments, the range of magnetic field induction value was B = 0-0.15 T, increased to 0.01 T. Based on the results obtained by the experimental study, it can be asserted that applying the magnetic field prompted an increase in the viscosity of MR fluids, leading to decreasing flow velocity. At B = 0.15 T, which is the highest value of the magnetic field, the flow velocity values dropped by 95%. Subsequently, the artificial neural networks algorithms are used in accordance with the obtained results to develop a correlation that clarifies the effect of the magnetic field on the flow velocity. The results show that the experimental and ANN models perform very similarly, and the ANN algorithm yields better results as a tool to predict the MR fluid flow behavior.
  • Küçük Resim Yok
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    EXPERIMENTAL INVESTIGATION OF THE EFFECTS OF VESSEL DESIGN AND HYDROGEN CHARGE PRESSURE ON METAL HYDRIDE BASED HYDROGEN STORAGE PARAMETERS
    (Turkish Soc Thermal Sciences Technology, 2014) Kayfeci, Muhammet; Bedir, Fevzi; Kurt, Huseyin
    The hydrogen charge time in metal hydride vessel (MHV) is strongly influenced by the heat transfer from hydride vessel. In this study, the effect of parameters such as reactor geometry and alloy characteristics on hydrogen charge procedure is studied experimentally. In the experimental setup two different types of hydride vessel are designed and manufactured. Both vessels have the same interior volume; the un-finned type vessel cooled with natural convection and the second one was manufactured with fins around the vessel. The temperature variations of the vessel at four locations were measured charging with a range of pressure from 2 to 8 bar. The finned vessel show the lowest temperature increase with the fastest charging time under all charging pressures investigated. The stored hydrogen mass was measured as 0.82, 0.94, 1.15 wt% on un-finned vessel and 0.91, 1.01, 1.24 wt% on finned vessel at 2, 6 and 10 bar respectively. The experimental results show that the charge time of the vessel is considerably reduced, when the used fins manufacture on vessel. Furthermore, the addition of Al to the LaNi5 alloys has caused to reduce the hydrogen charge time and decreased of the stored hydrogen mass.
  • Küçük Resim Yok
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    Experimental investigation on the thermal performance of heat recovery system with gravity assisted heat pipe charged with R134a and R410A
    (Pergamon-Elsevier Science Ltd, 2016) Gedik, Engin; Yilmaz, Mustafa; Kurt, Huseyin
    The purpose of this study is to investigate the thermal performance of heat recovery system with gravity assisted heat pipe charged R134a and R410A working fluids and also determine the usefulness of heat pipe bundle system in heat recovery applications. For this purpose an experimental test rig was designed and built. Series of experimental tests were carried out by varying the flue gas temperature (75, 100, 125, 150 and 175 degrees C), flue gas velocity (1, 1.5, 2 and 2.5 m/s) and cooling water flow rates (1, 2, 3 and 4 l/min). Values of the overall effectiveness of the heat pipe heat recovery system are shown to vary with the flue gas velocity, as expected, but the results also allow the prediction of effectiveness variation with the variation of the flue gas temperature. Effectiveness of the heat pipe for both working fluids R134a and R410A has been varied averagely between 35.6% and 57.7% with a good agreement with the published results. Quantitatively, it is found that R134a working fluid is 14% more effective than R410A in heat pipe bundle system. (C) 2016 Elsevier Ltd. All rights reserved.
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    High performance Ca3-xAg0.3LaxCo4O9 materials for aerospace applications of thermoelectric devices
    (Springer, 2024) Sari, Mucahit Abdullah; Kilinc, Enes; Uysal, Fatih; Kurt, Huseyin; Celik, Erdal
    In the domain of aviation applications, the utilization of thermoelectric materials holds significant importance, particularly in regions characterized by notable thermal gradients, aimed at harnessing these gradients for electricity generation. This study advocates for the adoption of thermoelectric modules, specifically within the operational contexts of fixed-wing aircraft and satellites. These settings require resilient thermoelectric systems capable of effectively exploiting temperature differentials to enable electrical power generation, thus emphasizing the necessity of integrating such modules into their operational frameworks. Accordingly, this paper systematically elucidates the production and characterization of Ca3-xAg0.3LaxCo4O9 for thermoelectric applications in the aerospace sector. Ca3-xAg0.3LaxCo4O9 ceramics are synthesized via the sol-gel method employing Ca, Ag, La, and Co precursor materials. Distilled water serves as the solvent to dissolve the precursors, yielding homogeneous solutions. These solutions undergo magnetic stirring at 100 degrees C to achieve final homogeneity, with citric acid monohydrate introduced as a chelating agent to expedite xerogel formation. pH and turbidity measurements are conducted on the prepared solutions using a pH meter and turbidimeter, respectively. Following the gelation process, the resulting xerogel is dried at 200 degrees C for 2 h to eliminate moisture and undesirable gases. Subsequently, the dried powders are calcined at 800 degrees C for 2 h, yielding the final Ca3-xAg0.3LaxCo4O9 materials. The thermal, structural, microstructural, and thermoelectric properties of the materials are comprehensively characterized utilizing DTA-TG, FTIR, XRD, XPS, SEM, and thermoelectric measurement machines. It is ascertained that the produced semiconducting ceramic materials exhibit efficient suitability for thermoelectric generator production.
  • Küçük Resim Yok
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    High temperature thermopower of sol-gel processed Zn1-x-y Al x Me y O (Me: Ga, In)
    (Springer, 2017) Kilinc, Enes; Demirci, Selim; Uysal, Fatih; Celik, Erdal; Kurt, Huseyin
    In this study, dually doped samples of Zn1-x-y Al (x) Me (y) O (Me: Ga, In) were prepared by sol-gel process followed by hot isostatic pressing for high temperature thermoelectric applications. Material characterizations were performed with differential thermal analysis-thermogravimetry, Fourier transform infrared spectroscopy and X-ray diffraction on the target phases. Successful doping of the samples was confirmed by X-ray photoelectron spectroscopy and energy dispersive X-ray analysis. Thermopower values of the samples are found to be relatively high in analogy to semiconducting behavior in which negative values indicate electrons are the dominant charge carriers (n-type). Substitution of Zn2+ by Ga3+ and In3+ for Zn1-x-y Al (x) Me (y) O (Me: Ga, In) increases electron concentration in the samples and thereby decreases the thermopower values compared to Zn0.98Al0.02O. Considering the absolute values, In doped samples have higher thermopower (alpha (max) = -162 A mu V/K at 585 A degrees C for Zn0.96Al0.02In0.02O) compared to the Ga doped sample. Al and In dually doped Zn0.96Al0.02In0.02O could be considered as a promising n-type thermoelectric material for high temperature applications.
  • Küçük Resim Yok
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    High-Temperature Thermoelectric Properties of Sol-Gel Processed Ca2.5Ag0.3RE0.2Co4O9 (RE: Y and Rare-Earths) Materials
    (Wiley-V C H Verlag Gmbh, 2020) Kilinc, Enes; Uysal, Fatih; Celik, Erdal; Kurt, Huseyin
    Herein, dually doped Ca2.5Ag0.3RE0.2Co4O9 (RE: La, Pr, Nd, Sm, Gd, Dy, Er, Yb, Eu, Tb, Ho, Lu, Ce, and Y) samples are synthesized by sol-gel technique and consolidated by cold pressing under high pressure to systematically scrutinize the influences of Y and rare-earth dually doping with Ag on transport properties of Ca3Co4O9 for high-temperature thermoelectric (TE) applications. Characterization results reveal that targeted phase is successfully produced, and doping of the compositions is provided. Doping of Y and rare-earth elements together with Ag into the Ca2+ site is effective in increasing the Seebeck coefficient and decreasing the electrical resistivity of the samples, thanks to the reduction in carrier concentration. Thermal conductivity of the samples is reduced related to the lower relative densities and alloy scattering originated from dually doping. Among the samples, Ca2.5Ag0.3Ho0.2Co4O9 and Ca2.5Ag0.3Eu0.2Co4O9 exhibit the highest power factor (PF) values of 0.65 and 0.62 mW m(-1) K-2 at 800 degrees C, respectively. These results are quite high for bulk oxide TE materials which can be assessed as potential oxide TE materials for high-temperature TE power generation.
  • Küçük Resim Yok
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    Investigating the Effects of Cooling Options on Photovoltaic Panel Efficiency: State of the Art and Future Plan
    (Ieee, 2018) Ozkul, Feyzullah Behlul; Kayabasi, Erhan; Celik, Erdal; Kurt, Huseyin; Arcaklioglu, Erol
    Currently, cooling of photovoltaic (PV) panels, a significant issue due the negative effect on panel efficiency, is subjected to intensive researches. For this purpose, numerous researches on cooling methods are performed to keep the panel efficiencies around the design values. In this study, a comprehensive literature review was presented to give the status of the technological improvement in cooling options. In addition, strong and weak aspects of the studies were discussed, and advantageous methods were emphasized for the further application of PV panels. Finally, future perspective of PV panel cooling studies was explored with proper cooling options in lower operating temperatures for higher operation efficiencies.
  • Küçük Resim Yok
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    An Investigation into the Effects of Box Geometries on the Thermal Performance of Solar Cookers
    (Taylor & Francis Inc, 2008) Kurt, Huseyin; Deniz, Emrah; Recebli, Ziyaddin
    The effect of box geometry, such as cylindrical and rectangular, on the performance of solar cookers has not been investigated. In this study, two different model box type solar cookers, which are in rectangular and cylindrical geometries, were constructed using the same material and were tested to investigate the effects of box geometries on the cooker performance. The experimental studies were conducted under the same operating conditions. The obtained results from the experiments were used to calculate the thermal efficiency and specific and characteristic boiling times. These parameters of the cookers were determined for 0.5, 1, and 1.5 kg of fresh water. It is observed that the cylindrical model has higher temperatures than the rectangular model under the same operating conditions. The thermal efficiency increased from 12.7 to 36.98% for cylindrical and 9.85 to 28.25% for rectangular model, when the quantity of water was increased from 0.5 to 1.5 kg; similarly, the characteristic boiling time was decreased from 39.56 to 14.35 for the cylindrical and 43.74 to 15.77 (min m-2 kg-1) for the rectangular model, respectively. The cylindrical model provided high thermal performance, which is indicated by high thermal efficiency and low characteristic boiling time, in comparison with the rectangular model.
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