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Bobin kurutma makinesinin modellenmesi, optimizasyonu ve otomasyonu
(2010) Kahveci, Kamil; Akyol, Uğur; Cihan, Ahmet
[Abstract Nıt Available]
Buoyancy Driven Heat Transfer of Nanofluids in a Tilted Enclosure
(Asme, 2010) Kahveci, Kamil
Buoyancy driven heat transfer of water-based nanofluids in a differentially heated, tilted enclosure is investigated in this study. The governing equations (obtained with the Boussinesq approximation) are solved using the polynomial differential quadrature method for an inclination angle ranging from 0 deg to 90 deg, two different ratios of the nanolayer thickness to the original particle radius (0.02 and 0.1), a solid volume fraction ranging from 0% to 20%, and a Rayleigh number varying from 10(4) to 10(6). Five types of nanoparticles, Cu, Ag, CuO, Al2O3, and TiO2 are taken into consideration. The results show that the average heat transfer rate from highest to lowest is for Ag, Cu, CuO, Al2O3, and TiO2. The results also show that for the particle radius generally used in practice (beta=0.1 or beta=0.02), the average heat transfer rate increases to 44% for Ra=10(4), to 53% for Ra=10(5), and to 54% for Ra=10(6) if the special case of theta=90 deg, which also produces the minimum heat transfer rates, is not taken into consideration. As for theta=90 deg, the heat transfer enhancement reaches 21% for Ra=10(4), 44% for Ra=10(5), and 138% for Ra=10(6). The average heat transfer rate shows an increasing trend with an increasing inclination angle, and a peak value is detected. Beyond the peak point, the foregoing trend reverses and the average heat transfer rate decreases with a further increase in the inclination angle. Maximum heat transfer takes place at theta=45 deg for Ra=10(4) and at theta=30 deg for Ra=10(5) and 10(6).
Çeltiğin yığın halinde kuruma davranışı
(Trakya Üniversitesi, 1998) Kahveci, Kamil; Cihan, Ahmet
ÖZET Çeltik insanların gıda ihtiyacını karşılayan önemli bir kültür bitkisi olup hasat sırasında yüksek nem oranlarına sahiptir ve hasat sonrası uygun bir kurutma işleminden geçirilmelidir. Kurutmanın amacı böceklenme ve küflenmeyi önleyici bir ortam yaratarak ürünü korumaktır. Çeltiğin kurutulması genellikle ısıtılmış havanın cebri konveksiyonu yardımıyla gerçekleştirilir. Bu çalışmada çeltiğin bir yığın halinde kuruma davranışı deneysel ve teorik olarak incelendi. Deneyler kuru baza göre nem oranı %24 olan rocco tipi çeltik kullanılarak gerçekleştirildi. Yükseklikleri 10 cm, 0 cm ve 30 cm olan dairesel kesitli çeltik sütunları 40°C, 50°C ve 60°C sıcaklıklarda kurutuldu. Deneylerde kurutma havası hızı olarak 1.5 m/s alındı. Karşılaştırma yapabilmek amacıyla aynı deney şartlarında tek tabaka çeltiğin de kuruma davranışı incelendi. Teorik model olarak Ece and Cihan (1993) tarafından tek tabaka çeltik için elde edilen ve Fick yasasına dayanan, daimi olmayan rejimde sıvı difüzyon denkleminin analitik çözümü kullanıldı. Kullanılan bu modelde, çeltiğin sonlu bir silindir geometrisine sahip homojen bir madde olduğu varsayılmıştır. Bu çözümün, çeltiğin yığın halinde kurumasını ifade edebilmek amacıyla kullanılabilmesi için difüzyon katsayısının kurutma havası sıcaklığına ve yığın yüksekliğine bağlı olarak değiştiği kabul edildi. Analitik çözüm sonuçlan ile deney dataları arasındaki farkların kareleri toplamı minimize edilerek efektif difüzyon katsayısı değerleri hesaplandı ve sıcaklık ve sütun yüksekliğine bağlı bir korelasyon geliştirildi. Teorik ve deneysel sonuçlar arasındaki uygunluk oldukça iyidir.
Conjugate forced convective heat transfer in a sandwich panel with a Kagome truss core: The effects of strut length and diameter
(Pergamon-Elsevier Science Ltd, 2020) Kemerli, Ubade; Kahveci, Kamil
Heat exchangers with a cellular metal core have become an alternative to those with louvered fins due to their high heat transfer performance and mechanical strength. Because of the multi-functionality, they are mostly used in systems such as rockets and space vehicles or in others in need of both high heat transfer performance and mechanical strength. The geometrical parameters of the unit cell of cellular metals have important effects on both fluid and heat transfer characteristics and these effects need to be studied. Accordingly, conjugate forced convective heat transfer in a sandwich panel with a Kagome truss core both with a constant heat flux (CHF) and a constant temperature (CT) boundary condition was studied numerically in this study for various values of the Reynolds number, strut length, and strut diameter. The 3D turbulent flow and heat transfer was modeled by the RNG k-epsilon turbulence model. The near-wall behavior of the flow was modelled by enhanced wall treatment. The channel was extended before and after the Kagome core to avoid entrance and exit effects. The computational results were obtained for the Reynolds numbers in the range of about 6000-17000, for the strut lengths of 3, 5 and 7 mm, and for the strut diameters of 1.3 and 1.6 mm. A nonlinear regression analysis was also performed for the pressure loss coefficient and average Nusselt number. The numerical results show that complex flow structures develop in the flow field due to the presence of unit cells. The results also show that the pressure drop along the Kagome core increases considerably with decreasing strut length and increasing strut diameter. The average Nusselt number increases significantly when the strut length is decreased and shows a small increase with an increase in the strut diameter. The effect of strut diameter on average Nusselt number becomes marginal for strut length of 3 mm. The average heat transfer rate for a fixed pumping power shows a considerable increase with a decrease in the strut length and a small increase with the strut diameter for high values of strut length. On the other hand, for the strut length of 3 mm, it shows a small decrease with an increase in the strut diameter for the CT case and remains almost constant for the CHF case.
Determination of optimum operating conditions and simulation of drying in a textile drying process
(Taylor & Francis Ltd, 2013) Akyol, Ugur; Kahveci, Kamil; Cihan, Ahmet
In this study, drying behavior of viscose yarn bobbins was investigated experimentally to specify the optimum drying conditions and a drying model was proposed for simulation of drying. The experiments were conducted in a pressurized hot-air bobbin dryer, which was designed and manufactured based on the dryers used in the textile industry. Drying process was performed for various drying parameters: bobbin diameter, drying temperature, drying pressure, and volumetric flow rate of drying air. The results show that total drying time is strongly dependent on drying pressure, drying temperature, and volumetric flow rate and increase at these parameters shortens the drying time considerably. The results also show that the minimum energy consumption is for lower values of drying temperature and drying pressure and modest and higher values of volumetric flow rate. Simulation results show that the most appropriate model in describing the drying curves of viscose yarn bobbins is the stretched exponential model.
A differential quadrature solution of MHD natural convection in an inclined enclosure with a partition
(Asme, 2008) Kahveci, Kamil; Oeztuna, Semiha
Magnetohydrodynamics natural convection in an inclined enclosure with a partition is studied numerically using a differential quadrature method. Governing equations for the fluid flow and heat transfer are solved for the Rayleigh number varying from 10(4) to 10(6), the Prandtl numbers (0.1, 1, and 10), four different Hartmann numbers (0, 25, 50, and 100), the inclination angle ranging from 0 deg to 90 deg, and the magnetic field with the x and y directions. The results show that the convective flow weakens considerably with increasing magnetic field strength, and the x-directional magnetic field is more effective in reducing the convection intensity. As the inclination angle increases, multicellular flows begin to develop on both sides of the enclosure for higher values of the Hartmann number if the enclosure is under the x-directional magnetic field. The vorticity generation intensity increases with increase of Rayleigh number. On the other hand, increasing Hartmann number has a negative effect on vorticity generation. With an increase in the inclination angle, the intensity of vorticity generation is observed to shift to top left corners and bottom right corners. Vorticity generation loops in each region of enclosure form due to multicelluar flow for an x-directional magnetic field when the inclination angle is increased further. In addition, depending on the boundary layer developed, the vorticity value on the hot wall increases first sharply with increasing y and then begins to decrease gradually. For the high Rayleigh numbers, the average Nusselt number shows an increasing trend as the inclination angle increases and a peak value is detected. Beyond the peak point, the foregoing trend reverses to decrease with the further increase of the inclination angle. The results also show that the Prandtl number has only a marginal effect on the flow and heat transfer.
A differential quadrature solution of natural convection in an enclosure with a finite-thickness partition
(Taylor & Francis Inc, 2007) Kahveci, Kamil
Natural convection in a rectangular enclosure divided by a partition with a finite thickness and conductivity is studied numerically. A temperature difference is imposed between the two isothermal vertical walls, and the other two walls are assumed adiabatic. Governing equations with the Boussinesq approximation are solved using the polynomial differential quadrature (PDQ) method. The results show that flow on either side of the enclosure is unicellular for low values of the aspect ratio. A multicellular flow forms the flow field in the bigger zone of the enclosure for higher aspect ratios. With increasing aspect ratio, heat transfer shows an increasing trend and reaches a maximum value. Beyond the maximum point, the foregoing trend reverses to decrease with further increase of the aspect ratio. The average Nusselt number decreases toward a constant value as the partition is distanced from the hot wall toward the middle of the enclosure. Decreasing the thermal conductivity ratio produces higher average Nusselt numbers. However, for higher aspect ratios, the increasing trend of the average Nusselt number with decreasing thermal conductivity ratio reverses to decrease as the thermal conductivity ratio is decreased further below a certain value.
A diffusion based model for intermittent drying of rough rice
(Springer, 2008) Cihan, Ahmet; Kahveci, Kamil; Hacihafizoglu, Oktay; de Lima, Antonio G. B.
In this study, intermittent drying behavior of single layer rough rice with a moisture content of between 22 and 24% on the dry basis was simulated by means of a liquid diffusion model based on a prolate spheroid geometry. For this purpose, solution of the liquid diffusion equation was fitted to the experimental data for the drying air temperature 40 degrees C, drying velocity 1.5 ms(-1) and tempering periods ranging from 0 to 1 h. In order to make a comparison, solution of the liquid diffusion equation for a finite cylindrical geometry was also fitted to the experimental data. The results show that the liquid diffusion model based on a prolate spheroid geometry explains the drying behavior of rough rice more accurately. The results also show that greater variations occur in diffusion coefficient with increasing tempering time for prolate spheroid geometry which is more realistic geometry for a rough rice grain.
DRYING BEHAVIOR OF CULTURED MUSHROOMS
(Wiley, 2010) Celen, Soner; Kahveci, Kamil; Akyol, Ugur; Haksever, Aysen
In this study, the drying behavior of cultured mushrooms with an initial moisture content of 93% (drying basis [d.b.]) was investigated experimentally for different slice thicknesses and drying air temperatures, and the suitability of various drying models in defining the drying behavior of mushrooms was determined by statistical analysis. Drying operation was carried out at temperatures of 40, 45, 50 and 60C and at a fixed air velocity of 2 m/s. The slice thicknesses of mushrooms were taken as 2, 4 and 6 mm. The experimental results show that the drying temperature has a significant effect on the moisture removal from mushrooms. However, it is also observed that increasing the temperature above a certain value for large values of slice thickness does not have a considerable effect on the drying rate. It may also be concluded from the experimental results that the increase in the slice thickness slows down the drying rate significantly. Furthermore, the results of statistical analysis show that the most suitable model in defining the drying behavior of mushrooms is the diffusion approach model.
Drying Behavior of Polyester Based Yarn Bobbins in a Hot-Air Bobbin Dryer
(Trans Tech Publications Ltd, 2011) Cihan, Ahmet; Kahveci, Kamil; Akyol, Ugur; Akal, Dincer
Drying behavior of polyester based yarn bobbins (67% polyester, 33% viscose) was simulated for different drying air temperatures by a simultaneous heat and mass transfer model. In the model, it was assumed that mass transfer is occurred by the diffusion mechanism. In the study, firstly drying behavior of polyester bobbins for different drying air temperatures has been determined experimentally. The experiments were conducted on an experimental hot-air bobbin dryer designed and manufactured based on hot-air bobbin dryers used in textile industry. In the experimental setup, temperatures of different points of the bobbins were measured by thermocouples placed inside the bobbins and weight of the bobbins during the drying period were determined by a load cell. Then moisture ratio and temperature values of the model have been fitted to the experimental ones. The fit was performed by selecting the values for the diffusion coefficient and the thermal diffusivity in the model in such a way that these values make the sum of the squared differences between the experimental and the model results for moisture ratio and temperature minimum. The results show that there is a good agreement between the model results and the experimental ones. The results also show that temperature has a significant effect on mass transfer and temperature dependence of the diffusion coefficient may be explained by an Arrhenius type relation.
Drying kinetics of cotton based yarn bobbins in a pressurized hot-air convective dryer
(Sage Publications Ltd, 2017) Akal, Dincer; Kahveci, Kamil; Akyol, Ugur; Cihan, Ahmet
In this study, the drying kinetics of cotton bobbin drying process in a pressurized hot-air convective bobbin dryer was investigated, and a drying model was introduced for the simulation of drying. Tests were conducted for drying temperatures of 70?, 80?, and 90?; effective drying air pressures of 1, 2, and 3 bars; three volumetric flow rates of 42.5, 55, and 67.5 m(3)/h; and for three different bobbin diameters of 10, 14, and 18cm. Optimum drying conditions were specified in terms of drying time and energy consumption. Results indicate that the total drying time depends significantly on the drying temperature, pressure, and volumetric flow rate. Results show that the minimum energy consumption is obtained for low values of drying air temperatures and pressures, and for moderate and high values of drying air volumetric flow rates. It was also found that the Page model is suitable for simulating the drying behavior of cotton yarn bobbins. Finally, results show that effective diffusion coefficient values are between 1.132x10(-7) m(2)/s and 3.453x10(-7) m(2)/s depending on the values of drying parameters.
Experimental and numerical investigation of heat transfer in a channel with multiple phase change materials (PCMs)
(Elsevier, 2022) Akyol, Erhan; Hacihafizoglu, Oktay; Susantez, Cigdem; Kahveci, Kamil; Akyol, Ugur
In this study, the thermal performance of an air-phase change material (PCM) unit used in free cooling applications was examined experimentally and numerically by Comsol finite element simulation software. Effects of the air inlet temperature, velocity and also PCM configuration on the efficiency of the air-PCM unit were investigated. Experiments were performed on PCM unit, which is a channel including PCM plates inside and exposed to medium air entrance from one side. The air in contact with the plates inside this unit is cooled and contributes the room temperature to decrease. The experimental work was carried out at two different ambient temperatures in a well-insulated room. Three different configurations of paraffin-based pure RT22HC and RT25HC were studied. Effects of air inlet temperature and velocity on the heat transfer, channel outlet temperature, performance of the air-PCM heat exchanger, cooling power of the system and also total amount of heat absorbed by the PCM were investigated. The initial temperature of the PCMs is 16 degrees C and experiments were carried out for two different average inlet temperature values (27 and 29 degrees C) and two different average velocities (1.3 and 1.8 m/s) of the air at the channel entrance. According to the results, it was concluded that the air inlet temperature and air inlet velocity have a substantial effect on the thermal performance of the air-PCM unit. It was observed that the melting time decreased and the channel outlet temperature increased with the increase of air inlet temperature and velocity. 2 degrees C increase of in the inlet temperature increased the total amount of heat absorbed by PCMs by 31%, while an increase of the inlet velocity by 0.5 m/s increased it by 16%. The results revealed that the increase of the inlet velocity and with the inlet temperature increased the thermal energy absorbed by 44%. In addition, it was observed that the average efficiency increased by 37% with 2 degrees C increase of inlet temperature and 0.5 m/s decrease in the inlet velocity.
Faz Değiştiren Malzeme İçeren Silindirik Bir Isıl Enerji Deposunda Kanatçık Sayısı, Kalınlığı ve Üniform Olmayan Kanatçık Dağılımının Isıl Enerji Depolama Karakteristiği Üzerindeki Etkileri
(2018) Kahveci, Kamil; Akyol, Erhan; Susantez, Çiğdem
Faz değiştiren malzemeler yüksek ısı depolama özellikleri nedeniyle ısıl enerji depolamada sıklıkla kullanılır. Fakat bunların ısıl iletkenliklerinin düşük olması söz konusu uygulamalarda dezavantajdır ve birim zamanda depolanan ısıl enerji miktarını arttırabilmek için ısıl iletkenliği yüksek kanatçıklar kullanılır. Bu çalışmada faz değiştiren malzeme içeren silindirik bir ısıl enerji deposunda üniform olmayan kanatçık dağılımının, kanatçık sayısı ve kalınlığının ısıl enerji depolama karakteristiği üzerindeki etkileri Comsol sonlu elemanlar modelleme ve simülasyon programı vasıtasıyla incelenmiştir. Sistemin on iki saatlik yükleme süresi sonunda, üniform kanatçık dağılımında olduğu gibi üniform olmayan kanatçık dağılımında da sistemde depolanan enerjinin kanatçık sayısı ile önemli miktarda arttığı görülmüştür.
Finite Element Simulation of Drying of Rough Rice
(Trans Tech Publications Ltd, 2011) Hacihafizoglu, Oktay; Cihan, Ahmet; Kahveci, Kamil
Rough rice has high moisture content at harvest, and if their moisture content is not reduced to about 12% on the dry basis they decay due to infestation and mold growth. Drying process is generally performed by heating ambient air and then sending it by forced convection over the rough rice to be dried. The aim in heating air to a certain temperature is to reduce the relative humidity of the air, which has a positive effect on the drying potential. In this study, drying behavior of single layer rough rice for different drying air temperature was simulated by means of a liquid diffusion model numerically by finite element modeling and simulation software. The results show that temperature is an effective factor on the drying rate. The results also show that as drying proceeds, a moisture gradient develops within the grain. This slows down the drying rate considerably. Therefore, it can be concluded that performing drying with an intermittent period instead of continuous drying will cause a considerable energy-saving.
Forced convection in finned metal foams: The effects of porosity and effective thermal conductivity
(Elsevier France-Editions Scientifiques Medicales Elsevier, 2021) Kemerli, Ubade; Kahveci, Kamil
Metal foams are promising candidates for enhancing the thermal performance of heat exchangers due to their unique features such as high surface-area-to-volume ratio and stochastic orientation. However, limited heat dissipation in high porosity metal foams is found to be a significant constraint on the heat transfer enhancement. To overcome this issue, metal foam structures with fins were proposed. On the other hand, the enhancement of heat transfer obtained by the addition of fins is connected to the porosity and effective thermal conductivity of metal foams. This relationship needs to be considered in the design of the structures with finned metal foams properly. This study, accordingly, investigates the effects of porosity and effective thermal conductivity on flow and heat transfer in a channel with finned metal foams. First, a numerical model was established and validated with the experimental data in the literature. Next, the flow and heat transfer characteristics of metal foams with different porosities and effective thermal conductivities were investigated under different fin configurations. The numerical results show that the addition of fins does not yield a considerable increase in the friction factor, and heat transfer shows a considerable increase up to the addition of a certain number of fins. When the fin number is further increased, the enhancement in heat transfer becomes relatively limited for all metal foams considered in this study. The effective fin number depends on the porosity and effective thermal conductivity. The results also show that the contribution of fins to the heat transfer in the parameter range considered in the study varies between 40-115% and 70-150% at the lowest and highest velocities, respectively.
Investigation of models of the yarn-bobbin drying process by determination of their parameters using genetic algorithm
(Sage Publications Ltd, 2017) Susantez, Cigdem; Hacihafizoglu, Oktay; Kahveci, Kamil
In the first part of this study, the drying behavior of wool-acrylic yarn bobbins was investigated by a theoretical model and genetic algorithm method. Each candidate solution for D-o, D-1 and D-2 was presented on a single chromosome. The values of D-o, D-1 and D-2 yielding the best fit between the experimental and predicted moisture contents were obtained using the genetic algorithm. In the second part of this study, the suitability of various empirical and semiempirical models in the modeling of the drying process was investigated by the genetic algorithm. The population number was taken as 30 and the tournament selection method was used. The calculations were performed until the 20th generation for the theoretical model and 100th generation for the empirical and semiempirical models. The results show that the genetic algorithm can be successfully used in the modeling of the drying process of yarn bobbins. The results also show that the Verma etal. and Diffusion Approach models yield the best fit with experimental data.
A liquid diffusion model for thin-layer drying of rough rice
(Springer, 2008) Hacihafizoglu, Oktay; Cihan, Ahmet; Kahveci, Kamil; de Lima, Antonio G. B.
In this study, the drying behavior of single-layer rough rice with a moisture content of between 22 and 24% on the dry basis was simulated by means of a liquid diffusion model, based on a prolate spheroid geometry. For this purpose, the solution of liquid diffusion equation was fitted to the experimental moisture ratios for drying air temperatures between 40 and 60 degrees C and velocity 1.5 m s(-1). In order to make a comparison, the predictions of liquid diffusion equations for a spherical and finite cylindrical geometry were also fitted to the experimental results. Modeling was performed by selecting the diffusion coefficients in diffusion equations in such a manner as to minimize the sum of the squared differences between the experimental results and the theoretical predictions. It was found that the liquid diffusion model, based on a prolate spheroid geometry, explains single-layer drying behavior of rough rice well. It was also found that the model, based on a prolate spheroid geometry, has better agreement with the experimental results than the other geometries.
A mathematical model for through-air drying process of yarn bobbins
(Taylor & Francis Ltd, 2022) Akyol, Ugur; Karakoca, Alper; Shaliyev, Rafayel; Kahveci, Kamil; Cihan, Ahmet
In this study, a mathematical model has been developed to simulate the through-air drying process of yarn bobbins. For this purpose, experimental data was obtained in a prototype experimental set up by passing pressurized hot air through the wool yarn bobbins. First of all, the physical phenomenon expressing the drying process has been reduced to the heat transfer problem and then a mathematical model has been written for the drying process which also includes the convective term. Using the experimental data, the coefficient included in the mathematical model was found by the extremal method. So, an inverse problem was solved. The accuracy of the model was checked by comparing with the experimentally obtained temperature values after solving a direct heat transfer problem in the given conditions. Good correlation between the obtained model results and the experimental results shows the accuracy of the mathematical model.
Mathematical modelling of drying of thin layer rough rice
(Elsevier, 2008) Hacihafizoglu, Okay; Cihan, Ahmet; Kahveci, Kamil
In this study, suitability of several drying models available in literature in defining thin layer drying behaviour of long-grain rough rice has been examined by using statistical analysis. For this purpose, drying models have been fitted to experimental data by means of the coefficients in the models for the drying air temperatures 40 degrees C, 45 degrees C, 50 degrees C, 55 degrees C, and 60 degrees C and at an airflow rate of 1.5 ms(-1) and 3.0 ms(-1). The results show that the Midilli et al. is the most appropriate model for drying behaviour of thin layer rough rice. Furthermore, among the two parameter models, the Page models and, among the three parameter models, the Verma et al. and the diffusion approach models give better fit. The coefficients a and b, the drying coefficient k and the exponent n in the Midilli et al. model can be expressed as a function of temperature and velocity of the drying air. (C) 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
MERKEZ DIŞI KATI İLETKEN BİR CİSİM İÇEREN DİKDÖRTGEN KAPALI BİR ORTAMDA SU BAZLI CuO NANOAKIŞKANLAR İÇİN KALDIRMA KUVVETİ ETKİLİ ISI TRANSFERİNİN NÜMERİK İNCELENMESİ
(2017) Susantez, Çiğdem; Kahveci, Kamil
Bu çalışmada, katı bir silindir içeren dikdörtgensel kapalı bir ortamda su bazlı CuO nanoakışkanlar için kaldırma kuvveti etkili ısı transferi farklı yükseklik genişlik oranı, katı silindirin yeri ve çapı, nanoparçacık hacim oranı ve Rayleigh sayısı değerleri için nümerik olarak incelenmiştir. Kapalı ortamın alt ve üst duvarları adyabatik iken, yan duvarları izotermaldir. Silindirin ısı iletim katsayısının baz akışkanınkine eşit olduğu varsayılmıştır. Yönetici denklemler Comsol Multiphysics sonlu eleman modelleme ve simülasyon yazılımı kullanılarak nümerik olarak çözülmüştür. Sonuçlar, ısı transferinin Rayleigh sayısı ve nanoparçacık hacim oranının artışı ve katı silindir çapının düşüşü ile önemli ölçüde arttığını göstermiştir. Sonuçlar aynı zamanda Rayleigh sayısının düşük değerleri için ısı transferinin yükseklik genişlik oranının artışı ile arttığını göstermiştir. Sonuçlar ayrıca ısı transferinin en yüksek değerlerini Rayleigh sayısının yüksek değerleri ve karesel kapalı ortam durumu için aldığını göstermiştir

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