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Numerical Analysis of Transient Convective Heat Transfer in a Dental Implant 牙科植入物中瞬态对流传热的数值分析
Pub Date : 2024-06-02 DOI: 10.37934/arnht.20.1.112
Muhammad Ikman Ishak, Ruslizam Daud, Siti Noor Fazliah Mohd Noor
Hot substance consumption can have adverse effects on the neighbouring bone tissue in proximity to a dental implant. Elevated temperatures at the interface between the bone and implant could potentially disrupt the local cellular processes crucial for osteointegration. The primary goal of this study was to analyse the temperature and heat flux distributions within the implant body, surrounding bone, and bone-implant interface when the implant system subjected to a thermal load of transient nature. Transient thermal finite element analysis was utilised to analyse a three-dimensional model of dental implant with three different lengths – 6, 10, and 13 mm – placed in a mandible section. In order to obtain realistic results, thermal load was applied through convection on the outer surface of the prosthesis, simulating exposure to a hot liquid with the temperature and convection heat transfer coefficient of 67°C and 0.005 W/mm2°C, respectively. The temperature of the other components in the model was maintained at a constant 37°C. The results showed that increasing the implant length generally led to lower temperature and heat flux levels in the implant body, bone, and bone-implant interface. The highest temperature and heat flux values were concentrated in the superior region, gradually decreasing toward the inferior region. Importantly, all maximum temperature values remained below the limits associated with cellular bone necrosis and remodelling, thereby reducing the risk of osteoporosis. It is noteworthy that, when considering transient thermal load, shorter implants pose a significantly higher risk of implant failure compared to longer ones.
食用高温物质会对牙科植入物附近的骨组织产生不利影响。骨与种植体界面温度升高可能会破坏对骨结合至关重要的局部细胞过程。本研究的主要目的是分析种植体、周围骨质以及骨-种植体界面在种植系统承受瞬态热负荷时的温度和热通量分布。瞬态热有限元分析法用于分析一个三维模型,该模型是将 6 毫米、10 毫米和 13 毫米三种不同长度的种植体植入下颌骨切面。为了获得逼真的结果,通过假体外表面的对流施加热负荷,模拟暴露在热液体中的情况,其温度和对流传热系数分别为 67°C 和 0.005 W/mm2°C。模型中其他组件的温度保持在恒定的 37°C。结果表明,增加种植体长度通常会降低种植体、骨和骨-种植体界面的温度和热通量水平。最高温度和热通量值集中在上部区域,并逐渐向下部区域降低。重要的是,所有最高温度值都低于与细胞骨坏死和重塑相关的极限值,从而降低了骨质疏松症的风险。值得注意的是,在考虑瞬时热负荷时,较短的种植体与较长的种植体相比,种植失败的风险要高得多。
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引用次数: 0
Newtonian Heating in Magnetohydrodynamic (MHD) Hybrid Nanofluid Flow Near the Stagnation Point over Nonlinear Stretching and Shrinking Sheet 非线性伸缩片上停滞点附近的磁流体混合纳米流体流中的牛顿加热现象
Pub Date : 2024-06-02 DOI: 10.37934/arnht.20.1.5367
Nurwardah Mohd Puzi, Mashitah Aziz, Nur Syazana Anuar, Norfifah Bachok, Iaon Pop
Hybrid nanofluids have demonstrated superior heat transfer performance in numerous applications. However, there remains a need for further research to broaden the scope of their potential applications. The unique behavior of hybrid nanofluids, driven by their potential for improved thermal efficiency, continues to be a focal point of investigation and exploration. This study focuses on the effects of Newtonian heating in MHD hybrid nanofluid near the stagnation point over a nonlinear stretching/shrinking sheet. The Tiwari and Das model, which is a single-phase model, was used to develop the mathematical model. The base fluid and the nanoparticles are assumed to be in thermal equilibrium; hence there is no thermal slip between them. The combination of metal (Cu) and metal oxide (Al2O3) nanoparticles with water (H2O) as the base fluid is used for the analysis. Furthermore, the governing equations are transformed using a similarity transformation technique into similarity equations, which are then solved numerically using a bvp4c function in MATLAB software. Numerical comparison with the published literature is conducted to validate the numerical results, and excellent agreement is found. The impact of physical parameters on the velocity, temperature, skin friction, and local Nusselt number is graphically deliberated. The outcomes suggest that non-unique solutions are found in a specific range of the shrinking parameter. It is also observed that increasing Cu (copper) nanoparticle volume fractions cause an increase in the skin friction coefficient and the local Nusselt number. The presence of magnetic and nonlinear parameters widens the range of solutions to exist while different observation is noticed with an increase in the volume fraction of Cu. Other than that, it has been shown that the Nusselt number increases as the magnetic parameter increases. Lastly, the rise of Newtonian heating contributes to an increase in the temperature profile. This investigation is crucial for understanding the thermal behavior of Cu-Al2O3/ H2O under the influence of physical factors like a magnetic field and Newtonian heating.
混合纳米流体在许多应用中都表现出卓越的传热性能。然而,仍需进一步研究,以扩大其潜在应用范围。混合纳米流体在提高热效率方面的潜力使其独特的行为成为研究和探索的焦点。本研究的重点是 MHD 混合纳米流体在非线性拉伸/收缩片上停滞点附近的牛顿加热效应。数学模型采用了 Tiwari 和 Das 模型(单相模型)。假设基础流体和纳米粒子处于热平衡状态,因此它们之间不存在热滑移。分析中使用了金属(Cu)和金属氧化物(Al2O3)纳米颗粒与水(H2O)作为基础流体。此外,利用相似性转换技术将控制方程转换为相似性方程,然后利用 MATLAB 软件中的 bvp4c 函数对其进行数值求解。将数值结果与已发表的文献进行对比验证,发现两者非常吻合。以图形方式讨论了物理参数对速度、温度、表皮摩擦和局部努塞尔特数的影响。结果表明,在收缩参数的特定范围内可以找到非唯一解。同时还观察到,增加 Cu(铜)纳米粒子的体积分数会导致皮肤摩擦系数和局部努塞尔特数增加。磁性和非线性参数的存在扩大了解决方案的范围,而随着铜的体积分数增加,观察结果也有所不同。此外,研究还表明,随着磁性参数的增加,努塞尔特数也会增加。最后,牛顿加热的增加导致了温度曲线的上升。这项研究对于理解 Cu-Al2O3/ H2O 在磁场和牛顿加热等物理因素影响下的热行为至关重要。
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引用次数: 0
Numerical Solution of Heat Equation using Modified Cubic B-spline Collocation Method 使用修正的立方 B-样条配位法数值求解热方程
Pub Date : 2024-06-02 DOI: 10.37934/arnht.20.1.2335
Mudassar Iqbal, Nooraini Zainuddin, Hanita Daud, Ramani Kanan, Rahimah Jusoh, Atta Ullah, Ilyas Kareem Khan
In this paper, a collocation method is presented based on the Modified Cubic B-spline Method (MCBSM) for the numerical solution of the heat equation. The PDE is fully discretized by using the Modified Cubic B-spline basis collocation for spatial discretization and the finite difference method is used for the time discretization. A numerical example from PDE is used to evaluate the accuracy of the proposed method. The numerical results are evaluated in comparison to the exact solutions. The findings consistently indicate that the suggested technique provides good error estimates. We also discovered that our proposed method was unconditionally stable. Hence, based on the results and the efficiency of the method, the method is suitable for solving heat equation.
本文提出了一种基于修正三次 B-样条法(MCBSM)的配准法,用于热方程的数值求解。在空间离散化中使用修正三次 B-样条法对 PDE 进行完全离散化,在时间离散化中使用有限差分法。利用一个 PDE 数值实例来评估所提出方法的准确性。数值结果与精确解进行了比较评估。结果一致表明,建议的技术提供了良好的误差估计。我们还发现,我们提出的方法是无条件稳定的。因此,基于该方法的结果和效率,该方法适用于求解热方程。
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引用次数: 0
Activation energy, Rotational and Hall current Effects of Magnetohydrodynamic 3D flow of Non-Newtonian Hybrid Nanofluid over a Stretched Plate 拉伸板上非牛顿混合纳米流体的磁流体动力三维流动的活化能、旋转和霍尔电流效应
Pub Date : 2024-06-02 DOI: 10.37934/arnht.20.1.3652
Dr.V.Ramachandra Reddy Vaddemani, Yeddula Rameswara Reddy, Donti Ratnam Srinivasan
Nanofluids are of great importance to researchers as they have significant uses industrially due to their high heat transfer rates. Recently, a new class of nanofluid, ‘‘hybrid nanofluid” is being used to further enhance the heat transfer rate. This new model in 3D is employed to examine the impact of activation energy, Rotational and hall current on a Non-newtonian hybrid Fe3O4/Al2O3 nanofluid flow over-stretched plate. Using similarity transformations, the controlling partial differential equations are turned into a set of nonlinear ordinary differential equations. For that system of equations, the shooting method is used to generate numerical solutions. The impact of various entry parameters on transversal and longitudinal velocities, temperature, heat flow and surface shear stress are studied numerically and graphically. A good correlation between the earlier studies is obtained in specific cases showing the convergence criteria of the present procedure. Further, the physical significance of the contributive parameters is presented through graphs and tables. The observation shows that the particle concentration for the hybrid nanofluid augments the fluid velocity. Moreover, the inclusion of dissipative heat favors enhancing the fluid temperature for the involvement of the particle concentration.
纳米流体具有很高的热传导率,在工业上有重要用途,因此对研究人员来说非常重要。最近,一种新型纳米流体 "混合纳米流体 "被用于进一步提高传热速率。这种新的三维模型用于研究活化能、旋转和霍尔电流对拉伸板上非牛顿混合 Fe3O4/Al2O3 纳米流体流动的影响。通过相似变换,控制偏微分方程被转化为一组非线性常微分方程。对于该方程组,采用射击法生成数值解。通过数值和图形研究了各种入口参数对横向和纵向速度、温度、热流和表面剪应力的影响。在特定情况下,与之前的研究结果有很好的相关性,显示了本程序的收敛标准。此外,还通过图形和表格展示了相关参数的物理意义。观察结果表明,混合纳米流体的颗粒浓度会提高流体速度。此外,由于颗粒浓度的影响,散热的加入有利于提高流体温度。
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引用次数: 0
A Transient Heat Transfer Analysis of Thermal Necrosis-Aided Dental Implant Removal 热坏死辅助拔除牙种植体的瞬态传热分析
Pub Date : 2024-06-02 DOI: 10.37934/arnht.20.1.1322
Muhammad Ikman Ishak, Ruslizam Daud, Siti Noor Fazliah Mohd Noor
A prevalent and widely favoured solution for replacing lost teeth is the use of dental implants. The removal of dental implants, even when they are osseointegrated but unsuccessful, can be traumatic, resulting in the loss of healthy bone and adding complexity to the treatment procedure. Reducing the trauma associated with implant removal can be achieved by intentionally weakening the bone-implant attachment. To achieve this objective, a suggested approach involves utilising thermal necrosis to aid in the minimally invasive removal of implants. The objective of this study was to use finite element analysis to explore the optimal power output for intentionally inducing thermal necrosis in a dental implant. SolidWorks software was utilised to create a three-dimensional model of a dental implant assembly, which includes an abutment, screw, and implant body integrated into a segment of mandibular bone. The model was subsequently analysed using ANSYS software, applying device powers ranging from 5 to 40 W in 5 W increments on the top surface of the abutment. The results of the study showed that there was a considerable elevation in the temperatures of the bone and implant, even when employing the low power settings commonly used in electrosurgical procedures. Elevating the power level has led to a decrease in the time required for the bone and implant to reach 47°C, the initial temperature at which bone necrosis occurs. However, it is crucial to take into account the significant temperature rise in the implant body at higher power levels. The implementation of lower power settings could present a viable approach to achieving controlled osteonecrosis.
使用牙科植入物来替换失去的牙齿是一种普遍且广受欢迎的解决方案。拔除牙科种植体,即使是在骨结合但不成功的情况下,也会造成创伤,导致健康骨质流失,增加治疗过程的复杂性。可以通过有意削弱骨与种植体的附着力来减少与种植体移除相关的创伤。为了实现这一目标,一种建议的方法是利用热坏死来帮助微创拔除种植体。本研究的目的是利用有限元分析来探索有意诱导牙科植入物热坏死的最佳功率输出。研究人员利用 SolidWorks 软件创建了牙科种植体组件的三维模型,该组件包括基台、螺钉和植入下颌骨的种植体。随后使用 ANSYS 软件对模型进行分析,在基台顶面施加 5 到 40 W 的设备功率,以 5 W 为增量。研究结果表明,即使采用电外科手术中常用的低功率设置,骨和种植体的温度也会显著升高。功率水平的提高导致骨和种植体达到 47°C 所需的时间缩短,而 47°C 是发生骨坏死的初始温度。但是,必须考虑到在较高功率下植入体的温度会显著升高。采用较低的功率设置是实现骨坏死可控的可行方法。
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引用次数: 0
A Numerical Study to Improve the Efficiency of Solar Collector used for water heating using Phase Change Material 利用相变材料提高太阳能集热器热水效率的数值研究
Pub Date : 2024-03-03 DOI: 10.37934/arnht.17.1.113
Hazim A. Al-Zurfi, Muna Ali Talib, Qasim H. Hassan, Ghaith J. Aljabri
Solar water heaters are an effective technology for harnessing renewable solar energy to provide hot water for households and businesses. However, their efficiency can be impacted by factors like intermittent sunshine, heat losses, and low radiation intensity. The aim of this study is to increase the efficiency of solar water heaters through the use of phase change materials (PCMs). PCMs have the ability to store latent heat during phase change, releasing it later when needed. This study uses numerical simulations to analyze the effect of integrating different PCMs into a flat plate solar collector design. The findings could then be validated experimentally and applied to improve the real-world performance of solar water heating systems. The PCMs are placed inside the collector to absorb heat during the day and release it after sunset to continue heating the water. The research seeks to determine the optimal PCM properties, structure, and placement within the collector to maximize heat storage and transfer. The efficiency and performance of the solar collector system with different PCM configurations have been compared to those of a conventional collector without PCM. The outcomes uncover that the use of suitable PCMs can significantly improve the efficiency and heat output of the solar collector, especially during periods of low radiation and after sunset. The optimal PCM configuration maintains higher water temperatures for longer, allowing solar water heating to continue into the evening. The results may provide valuable insights for using PCMs to boost the efficiency of solar thermal technologies
太阳能热水器是利用可再生太阳能为家庭和企业提供热水的有效技术。然而,间歇性日照、热损失和低辐射强度等因素会影响其效率。本研究的目的是通过使用相变材料(PCMs)来提高太阳能热水器的效率。相变材料能够在相变过程中储存潜热,并在需要时释放出来。本研究利用数值模拟来分析将不同的 PCM 集成到平板太阳能集热器设计中的效果。研究结果可以通过实验进行验证,并应用于改善太阳能热水系统的实际性能。PCM 被放置在集热器内,白天吸收热量,日落后释放热量,继续加热水。这项研究旨在确定集热器内最佳的 PCM 特性、结构和位置,以最大限度地储存和传递热量。采用不同 PCM 配置的太阳能集热器系统的效率和性能与不含 PCM 的传统集热器进行了比较。研究结果表明,使用合适的 PCM 可以显著提高太阳能集热器的效率和热量输出,尤其是在低辐射时段和日落后。最佳的 PCM 配置可以在较长时间内保持较高的水温,使太阳能热水器可以持续到傍晚。这些结果为利用 PCMs 提高太阳能热技术的效率提供了宝贵的启示。
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引用次数: 0
Impact of Biomass Fuel Feeding Ratio in Co-firing Circulating Fluidized Bed Boiler: A Computational Fluid Dynamics Study 生物质燃料进料比在共燃循环流化床锅炉中的影响:计算流体动力学研究
Pub Date : 2024-03-03 DOI: 10.37934/arnht.17.1.4454
Sorathan Tanprasert, Nuttima Rangton, Warunee Nukkhong, Pitakchon Wises, P. Piumsomboon, B. Chalermsinsuwan
Nowadays, our global population is on a notable rise, coupled with an annual surge in energy consumption. The prevailing reliance on fossil fuels, especially in electricity generation, has significantly contributed to environmental pollution and exacerbated global warming. The circulating fluidized bed, distinguished for its continuous operation and effective heat transfer in the combustion chamber, emerges as a prominent boiler type. Furthermore, the use of biomass fuel, recognized for its renewable and environmentally friendly characteristics, presents an attractive option. Hence, exploring a co-firing system incorporating both coal and biomass as fuel feeds for the boiler holds promise, necessitating optimization for efficient energy production and reduced gas emissions. This study employs computational fluid dynamics to simulate the intricate interactions of solid fuel and flue gas reactions within the boiler, utilizing the two-fluid method for multiphase flow simulation. The circulating fluidized bed boiler in focus employs subbituminous coal, woodchips as biomass sources, and sand as the bed material. Model validation against operational data, including bed temperature, flue gas velocity outlet, and carbon dioxide mass fraction, indicates minimal deviation. Examination of the biomass ratio's impact on fuel feed reveals a reduction in sulfur dioxide emissions with an increasing biomass ratio, attributed to the lower sulfur content in woodchips compared to coal. However, a heightened woodchip blending ratio results in diminished boiler efficiency due to the altered heating value of the mixed solid fuel. The optimized biomass-to-coal ratio in fuel feeding is determined as 59.15%, achieving a maximized boiler efficiency of 82.84% and minimized pollution gas emissions of sulfur oxide and nitrogen oxide in accordance with industrial standards.
如今,全球人口显著增加,能源消耗也逐年激增。对化石燃料的普遍依赖,尤其是在发电方面,严重加剧了环境污染和全球变暖。循环流化床因其在燃烧室中的连续运行和有效传热而成为一种突出的锅炉类型。此外,生物质燃料具有可再生和环保的特点,使用生物质燃料是一种有吸引力的选择。因此,探索将煤炭和生物质作为锅炉燃料进料的联合燃烧系统前景广阔,需要对其进行优化,以实现高效的能源生产和减少气体排放。本研究采用计算流体动力学模拟锅炉内固体燃料和烟气反应的复杂相互作用,利用双流体法进行多相流模拟。重点研究的循环流化床锅炉采用次烟煤、木屑作为生物质源,沙子作为床层材料。根据运行数据(包括床层温度、烟气出口速度和二氧化碳质量分数)进行的模型验证表明,偏差极小。在研究生物质比率对燃料进料的影响时发现,随着生物质比率的增加,二氧化硫排放量会减少,这是因为与煤炭相比,木屑中的硫含量较低。然而,由于混合固体燃料的热值发生变化,木屑混合比的提高会降低锅炉效率。优化后的生物质与煤的给料比确定为 59.15%,锅炉效率达到最大值 82.84%,硫氧化物和氮氧化物的污染气体排放量降到最低,符合工业标准。
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引用次数: 0
Falkner-Skan Flow of Nanofluid with Convective Boundary Condition 带对流边界条件的纳米流体的 Falkner-Skan 流动
Pub Date : 2024-01-21 DOI: 10.37934/arnht.15.1.4352
Nurul Diana Mohammad, Nur Ilyana Kamis, Mohamad Hidayad Ahmad Kamal, Sharidan Shafie, Noraihan Afiqah Rawi
This study focuses on the investigation of nanofluid flow with convective boundary conditions past a static wedge by considering copper as the chosen nanoparticles and water as the conventional base fluid. The governing partial differential equations (PDE) are transformed into a set of nonlinear ordinary differential equations (ODE) by using an appropriate similarity transformation. The transformed governing equations are then solved numerically by using the Keller-box method. The significant impact of parameters included wedge angle parameter, mixed convection parameter, volume fraction of nanoparticle and Biot number are presented. The graphical analysis on velocity and temperature profiles revealed that the increasing values of all considered parameters causes the increment of velocity of the flow. Meanwhile, significant changes on the temperature profiles are clearly depicted on the increment of nanoparticle volume fraction as well as the Biot number.
本研究以铜为纳米粒子,水为传统基础流体,重点研究了纳米流体在对流边界条件下流过静态楔体的情况。通过适当的相似性变换,将控制偏微分方程(PDE)转换为一组非线性常微分方程(ODE)。然后使用 Keller-box 方法对转换后的控制方程进行数值求解。文中介绍了楔角参数、混合对流参数、纳米粒子体积分数和 Biot 数等参数的重要影响。对速度和温度曲线的图形分析表明,所有参数值的增加都会导致流速的增加。同时,纳米粒子体积分数和比奥特数的增加对温度曲线也有明显影响。
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引用次数: 0
Numerical Analysis of Fluid Flow and Heat Transfer Characteristics of Novel Microchannel Heat Sink 新型微通道散热器的流体流动和传热特性的数值分析
Pub Date : 2024-01-21 DOI: 10.37934/arnht.15.1.123
Yew Wai Loon, Nor azwadi Che Sidik, Yutaka Asako
Microchannel heat sinks have gained prominence in the field of thermal management, offering compact and efficient solutions for dissipating heat flux from high performance electronic devices. Escalating heat flux in modern electronic devices, such as those found in telecommunication equipment, industrial automation equipment, solar devices, and data centre servers has driven the continuous development of microchannel heat sink to achieve efficient thermal management. The critical challenge in thermal management for these devices is to develop a microchannel that enhances heat transfer performance and minimises pressure drop. Heat transfer and pressure drop are two competing factors that determine the practicability of the design for real world application. Improvement in heat transfer performance usually results in an increase in pressure drop and pumping power. This study addresses the challenges of designing microchannel through comprehensive numerical analysis of fluid flow and heat transfer characteristics of a novel design that combines ribs, secondary channels, and tertiary channels. The numerical results showed that the novel microchannel design achieves a favourable balance between heat transfer and pressure drop, demonstrating its potential to be used in application where high heat transfer and efficiency are paramount. To assess the performance of the microchannels, thermal resistance, a measure of system’s resistance to heat transfer is used. At the same pumping power, thermal resistance in the new design is consistently lower compared to other designs.
微通道散热器为高性能电子设备提供了紧凑高效的散热解决方案,在热管理领域大放异彩。现代电子设备(如电信设备、工业自动化设备、太阳能设备和数据中心服务器中的设备)的热通量不断增加,推动了微通道散热器的不断发展,以实现高效的热管理。这些设备在热管理方面面临的关键挑战是开发一种既能提高传热性能又能最大限度减少压降的微通道。传热和压降是两个相互竞争的因素,决定了设计在实际应用中的实用性。传热性能的提高通常会导致压降和泵功率的增加。本研究通过对结合了肋片、二级通道和三级通道的新型设计的流体流动和传热特性进行全面的数值分析,解决了微通道设计所面临的挑战。数值结果表明,这种新型微通道设计在传热和压降之间实现了良好的平衡,证明了其在对传热和效率要求较高的应用中的应用潜力。为了评估微通道的性能,采用了热阻这一衡量系统传热阻力的指标。在相同的泵功率下,新设计的热阻始终低于其他设计。
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引用次数: 0
Mathematical Solution for Free Convection Flow of Brinkman Type Fluid in the Channel with the Effect of Accelerated Plate 具有加速板效应的布林克曼型流体在通道中自由对流的数学解法
Pub Date : 2024-01-21 DOI: 10.37934/arnht.15.1.5368
Mohamad Riduan Hashim, Zulkhibri Ismail, Ahmad Qushairi Mohamad, Muhammad Atif Akashah, Wan Nura'in Nabilah Noranuar, Lim Yeou Jiann, Sharidan Shafie
The main purpose of this research is to formulate the mathematical models and solution for the effect of accelerated plate on free convection flow in Brinkman type fluid through two vertical channels. Using the appropriate dimensionless variables, the dimensional governing energy and momentum equations are reduced to dimensionless equations subjected to the associated initial boundary conditions. The analytical solutions are obtained by using Laplace transform method. Dimensionless parameters are obtained through dimensionless processes such as Grashof number Gr, Acceleration plate parameter, R, Prandtl number Pr, Brinkman type fluid parameter and time, t. The mathematical findings for velocity and temperature are graphically plotted to investigate the influence of dimensionless variables on profiles. It is observed that fluid velocity increases with increasing of Gr and t whereas it decreases with increasing of , R and Pr. Besides that, it is found that temperature profiles decrease with a high value of Prandtl number, Pr while increase with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and also with numerical Gaver-Stehfest algorithm. Both comparisons show that the solution is to be in a mutual agreement.
本研究的主要目的是建立加速板对布林克曼型流体通过两个垂直通道的自由对流影响的数学模型并求解。通过使用适当的无量纲变量,在相关初始边界条件的作用下,将有量纲的能量和动量方程简化为无量纲方程。通过拉普拉斯变换法获得解析解。无量纲参数是通过无量纲过程获得的,如格拉肖夫数 Gr、加速度板参数 R、普朗特数 Pr、布林克曼型流体参数和时间 t。观察发现,流体速度随着 Gr 和 t 的增加而增加,而随着 R 和 Pr 的增加而减小。此外,还发现温度曲线随 Prandtl 数(Pr)的高值而减小,同时随时间(t)的高值而增大。为了验证结果,将极限情况下获得的结果与已公布的结果以及 Gaver-Stehfest 数值算法进行了比较。比较结果表明,两者的解法是一致的。
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引用次数: 0
期刊
Journal of Advanced Research in Numerical Heat Transfer
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