International Journal of Heat and Fluid Flow最新文献

{"title":"Performance evaluation of dovetail fin variants derived from a rectangular fin for laptop heat sinks","authors":"Yogesh Chouksey,&nbsp;Nitin Shrivastava,&nbsp;Sunil Kumar","doi":"10.1016/j.ijheatfluidflow.2026.110256","DOIUrl":"10.1016/j.ijheatfluidflow.2026.110256","url":null,"abstract":"<div><div>Cooling compact electronics, such as laptops, is challenging due to strict size limitations and the low thermal capacity of air. While rectangular fins are commonly used, dovetail fins with tip clearance may offer improved thermal performance. This study investigates the thermal–hydraulic behaviour of rectangular and dovetail fin heat sinks under these constraints. Initially, a rectangular channel heat sink was designed and later modified to a channel heat sink incorporating a rectangular fin with tip clearance. This fin was further adapted into three dovetail fin variants by varying the root and tip thicknesses to evaluate the feasibility of replacing rectangular fins. CFD analyses were conducted in ANSYS Fluent for inlet air velocities ranging from 1 to 6 m/s (corresponding Reynolds number varies from 2054–12323), with the top surface of the heat sink maintained at a constant temperature of 360 K. Temperature distribution, heat transfer, pressure drop, and effectiveness were evaluated, considering weight in the performance comparison. Dovetail fins outperformed the rectangular fin, enhancing heat convection by up to 20.6% but with a 66.7% increase in weight and substantially higher pressure drops. The dovetail variant with weight equal to the rectangular fin achieved up to 2.2% higher performance with only a marginal increase in pressure drop, indicating its potential as a promising alternative.</div></div>","PeriodicalId":335,"journal":{"name":"International Journal of Heat and Fluid Flow","volume":"119 ","pages":"Article 110256"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The flow and heat transfer performance of a novel double-spiral heat sink for processing unit cooling","authors":"Feiyu Chen ,&nbsp;Chenghao Liu ,&nbsp;Xin Wu ,&nbsp;Shida Yao ,&nbsp;Wenguang Liu ,&nbsp;Wei Chang","doi":"10.1016/j.ijheatfluidflow.2026.110299","DOIUrl":"10.1016/j.ijheatfluidflow.2026.110299","url":null,"abstract":"<div><div>The escalating thermal power of processors demands advanced cooling solutions. This study proposes a novel double-spiral heat sink (DSHS) with dual inlets and outlets to address this challenge. First, experiments were conducted to test the performance of different inlet methods. When cooling water flows in from the end with a larger radius of curvature, the temperature difference of the CPU can be 49.3% lower than other methods. A decrease in the radius of curvature enhances the disturbance of the fluid, mitigating the negative impact of rising water temperature on the temperature difference. The simulation results show good consistency with the experimental data. The optimal spiral dimensions are determined to be <em>r</em> = 3 mm and <em>R</em> = 15 mm based on the geometric parameter analysis. Compared with single spiral heat sink (SSHS), DSHS can reduce the pressure drop by 48.3% and temperature difference by 64.1%. In addition, the DSHS is compared with the serpentine heat sink (SHS) to prove its advantages. The results show that the average temperature of the DSHS is slightly lower than that of the SHS, while the pressure drop, temperature difference, and performance evaluation criterion are all significantly better than those of the SHS. DSHS can dissipate a maximum heat of 438 W. The varying radius of curvature of DSHS can continuously disrupt the boundary layer and enhance heat transfer. Furthermore, by slotting the wall surface, the pressure drop is reduced by 10% without affecting the heat dissipation. The DSHS maintains its performance benefits across different working fluids such as ethylene glycol solution and transformer oil, showing its advantage of wide applicability. The proposed DSHS provides a promising alternative design of heat sinks for the processing unit cooling applications.</div></div>","PeriodicalId":335,"journal":{"name":"International Journal of Heat and Fluid Flow","volume":"119 ","pages":"Article 110299"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146170482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cavitation and associated entropy production characteristic of a pump turbine in pumping mode based on a modified Zwart-Gerber-Belamri model","authors":"Xiuli Mao ,&nbsp;Jiaren Hu ,&nbsp;Pengju Zhong ,&nbsp;Tong Mu ,&nbsp;Zhiping Zhang ,&nbsp;Shenggen Li","doi":"10.1016/j.ijheatfluidflow.2026.110288","DOIUrl":"10.1016/j.ijheatfluidflow.2026.110288","url":null,"abstract":"<div><div>This study develops a modified Zwart-Gerber-Belamri (MZGB) cavitation model in which the saturation vapor pressure is defined dynamically. The proposed model is then applied to investigate the cavitation evolution and entropy production characteristics of a pump turbine under multiple pumping conditions. Numerical predictions based on the MZGB model show closer agreement with experimental data than those from the ZGB model, with an accuracy of 96.17% for pressure variation. With decreasing flow rate and cavitation number, the cavitation region extends along the blade suction surface, and coupled cavitation-vortex structures form within the runner, increasing both cavitation and vortex volume. The precipitation of cavitation bubbles, accompanied by energy absorption, weakens the pressure pulsations within the cavitation region. By contrast, in the non-cavitation region at 0.8 times of the flow rate at the best efficiency point (0.8<em>Q</em>_BEP), the maximum amplitude is 12 times that at 1.0<em>Q</em>_BEP and 1.9 times that at 0.6<em>Q</em>_BEP. Due to vortex development and flow separation in the runner, the dominant frequency of pressure pulsations corresponds to the runner rotating frequency (<em>f</em>_n) at 1.0<em>Q</em>_BEP, while that at 0.8<em>Q</em>_BEP is dominated by 3<em>f</em>_n. In contrast, 0.6<em>Q</em>_BEP exhibits multiple pressure pulsation peaks within <em>f</em>/<em>f</em>_n ≤ 5. Furthermore, as <em>C_σ</em> and flow rate decrease, the primary entropy production region extends to both the runner and guide vane domains, while the dominant mechanism of entropy production transfers from the wall shear dissipation to the turbulent dissipation. These findings provide a theoretical guidance for the cavitation risk assessment and the energy loss mitigation in pump turbines.</div></div>","PeriodicalId":335,"journal":{"name":"International Journal of Heat and Fluid Flow","volume":"119 ","pages":"Article 110288"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mechanism of cycloidal trailing-edge blades in suppressing pressure pulsation and vibration in centrifugal pumps","authors":"Yahui Hu ,&nbsp;Qinyang Li ,&nbsp;Jian Chen ,&nbsp;Guanghua Gan ,&nbsp;Chengyi Yi","doi":"10.1016/j.ijheatfluidflow.2026.110305","DOIUrl":"10.1016/j.ijheatfluidflow.2026.110305","url":null,"abstract":"<div><div>To suppress pressure pulsation and flow-induced vibration in a fire-fighting centrifugal pump, cycloidal trailing-edge blades are designed according to the cycloidal principle, and three variants are assessed using transient CFD, combined with time–frequency analysis and coherent-structure identification based on the <em>Q</em>-criterion. The results show that cycloidal shaping reorganises the impeller-exit wake by weakening shear-layer roll-up and wake intermittency, thereby alleviating the tongue-adjacent impeller–volute interaction and reducing the broadband disturbance level. Consequently, pressure fluctuations are reduced in both the impeller passage and the volute, with a pronounced attenuation of low-frequency components below 50 Hz. Among the three designs, the B2 configuration achieves the best overall suppression, reducing impeller pressure-coefficient fluctuations by 42–55 percent and attenuating the oscillations of radial and axial loads, while producing smoother force waveforms. These findings link the effectiveness of the cycloidal trailing edge to wake reorganisation and reduced tongue-induced excitation, providing a practical geometric strategy to improve the stability and vibration–noise characteristics of fire-fighting centrifugal pumps.</div></div>","PeriodicalId":335,"journal":{"name":"International Journal of Heat and Fluid Flow","volume":"119 ","pages":"Article 110305"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146170020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A review of the immersion liquid cooling technology for high-performance data centers","authors":"Chunjie Yang,&nbsp;Xianfeng Zhu,&nbsp;Guangyi Zhang,&nbsp;Gui Pan,&nbsp;Xingchuan Wang","doi":"10.1016/j.ijheatfluidflow.2026.110282","DOIUrl":"10.1016/j.ijheatfluidflow.2026.110282","url":null,"abstract":"<div><div>In the context of global digital transformation, the rapid expansion of data centers has intensified the challenge of high-power cooling. Traditional air cooling, with its limited efficiency, is increasingly inadequate to meet current demands. Immersion liquid cooling (ILC) has thus emerged as a critical research focus in data center thermal management, owing to its superior heat dissipation capabilities, excellent temperature uniformity, and energy-saving advantages. This paper provides a comprehensive analysis of ILC technology, examining coolant classification and selection criteria, the operating principles and performance of various liquid-cooling structures, and their practical applications. Two primary coolant types—oil-based and fluorocarbon-based—are evaluated, along with three main ILC system configurations: buoyancy-driven single-phase, pump-driven single-phase, and two-phase systems, each suited to different heat load scenarios. Performance improvement strategies, including passive and active enhancement techniques, are also explored. The research concludes that ILC has entered the stage of large-scale demonstration, significantly improving energy efficiency and exhibiting clear trends toward higher density and modularization. However, challenges such as high costs, operational complexity, and the lack of unified standards persist. Future efforts should prioritize technological innovation, cost reduction, and standardization to facilitate wider adoption and support the development of green, efficient data centers.</div></div>","PeriodicalId":335,"journal":{"name":"International Journal of Heat and Fluid Flow","volume":"119 ","pages":"Article 110282"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146170022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical study of flow and heat transfer performance in a novel microchannel under pulsating flow conditions","authors":"Chunquan Li,&nbsp;Jirong Huang,&nbsp;Yilong Hu,&nbsp;Cailin Li,&nbsp;Hongyan Huang","doi":"10.1016/j.ijheatfluidflow.2025.110228","DOIUrl":"10.1016/j.ijheatfluidflow.2025.110228","url":null,"abstract":"<div><div>This paper presents a numerical study of the flow and heat transfer performance of a trapezoidal cavity rib-double rectangular circular fin microchannel heat sink (TR-DRRF) combined with a pulsating fluid. The SIMPLEC algorithm is adopted for the pressure–velocity coupling using second order upwind discretization equations. The TR-DRRF microchannel is analyzed in comparison with straight rectangular microchannel (SR), trapezoidal cavity fin microchannel (TR) and trapezoidal cavity fin-single rectangular circular fin microchannel (TR-SRRF). Results indicate that the dual rectangular circular fins of the TR-DRRF significantly increase the fluid–solid interface area, disrupt thermal boundary layer development, and alter flow field distribution. At Reynolds number (Re) = 400, its maximum temperature (<span><math><msub><mrow><mi>T</mi></mrow><mrow><msub><mrow></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></msub></math></span>) is reduced by 48 K, 15.8 K, and 5.96 K compared to SR, TR, and TR-SRRF, respectively. while the Nusselt number (Nu) increased by 88.72%, 41.76%, and 13.03%, respectively. The performance evaluation criterion (PEC) improved by over 7% compared to the other three designs. The introduction of pulsating flow significantly enhances the overall thermal performance of TR-DRRF compared to steady flow at the same Re number. The core mechanism involves the sustained development of the flow boundary layer and the generation of secondary flow/counterflow. Among these, square-wave pulsed flow exhibits the most effective heat transfer enhancement. Pulsation parameters exert distinct effects: frequencies in the range of 0.2–5 Hz impair heat transfer, whereas those in the range of 5–70 Hz enhance it. Increasing frequency enhances overall heat dissipation performance (PEC outperforms steady flow at f <span><math><mo>&gt;</mo></math></span> 10 Hz). Increasing amplitude (0.2–1.2 m/s) enhances heat transfer (reducing <span><math><msub><mrow><mi>T</mi></mrow><mrow><msub><mrow></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></msub></math></span> by up to 2.1 K) but increases pressure loss. Only when amplitude <span><math><mo>&lt;</mo></math></span> 0.7 m/s does the overall performance surpass steady flow.</div></div>","PeriodicalId":335,"journal":{"name":"International Journal of Heat and Fluid Flow","volume":"119 ","pages":"Article 110228"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-scale analysis of solute dispersion in free and forced convection flow between two parallel plates filled with a porous medium","authors":"Aruna A,&nbsp;Swarup Barik","doi":"10.1016/j.ijheatfluidflow.2025.110234","DOIUrl":"10.1016/j.ijheatfluidflow.2025.110234","url":null,"abstract":"<div><div>This study investigates the transverse concentration distribution of contaminant transport in free and forced convective flow within a parallel plate filled with a porous medium. The solute undergoes irreversible boundary reactions at the plates. Most previous studies explored similar configurations in free and forced convective flows by incorporating magnetic effects. However, our study introduces a porous medium, which more accurately reflects real-world scenarios, such as pores in particles within flowing rivers or other environments. We develop an analytical solution of the dispersion coefficient, mean and transverse concentration using a multi-scale technique. The present study examines the effects of Grashof number (<span><math><mi>G</mi></math></span>), porous parameter and relative viscosity in the presence of boundary absorptions on the solute dispersion. Higher porous parameter values reduce permeability, limit solute spreading, and maintain a peak in the mean concentration distribution. In porous media, a negative <span><math><mi>G</mi></math></span> enhances solute dispersion near the upper boundary, whereas a positive <span><math><mi>G</mi></math></span> influences dispersion when the lower boundary absorbs. The buoyancy forces dominate for <span><math><mrow><mi>G</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> or <span><math><mrow><mi>G</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span>, driving the flow toward the heating or cooling plates and intensifying non-uniformity in the transverse concentration distribution. This effect becomes more significant with higher porosity and viscosity, as the porous medium reduces permeability and increases resistance to fluid motion. When boundary reactions are considered in the presence of a porous medium under free and forced convection, they cause uneven solute distribution as the walls absorb solute. A higher porous parameter increases resistance to fluid flow, which amplifies concentration gradients and enhances non-uniformity.</div></div>","PeriodicalId":335,"journal":{"name":"International Journal of Heat and Fluid Flow","volume":"119 ","pages":"Article 110234"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hybrid photovoltaic–thermal and solar thermal collectors with integrated phase change materials: toward sustainable greenhouse energy systems","authors":"Soroush Entezari ,&nbsp;Meysam Khatibi ,&nbsp;Mikhail Sorin","doi":"10.1016/j.ijheatfluidflow.2026.110268","DOIUrl":"10.1016/j.ijheatfluidflow.2026.110268","url":null,"abstract":"<div><div>Greenhouses require substantial energy for heating, cooling, and electricity, yet current renewable solutions rarely provide all three simultaneously. Most existing systems supply either thermal or electrical output and lack integrated storage, creating mismatches between solar availability and greenhouse demand and reinforcing dependence on fossil fuels. This study addresses this problem by developing and analyzing a hybrid photovoltaic–thermal (PVT) and solar thermal (ST) collector system integrated with phase change materials (PCMs) for combined power generation and heat storage in greenhouse applications. A three-dimensional numerical model examines the effects of PCM type (RT21, RT31, RT35) and heat transfer fluid flow rate under typical summer conditions in Sherbrooke, Québec, Canada. Results indicate that low-melting PCMs (RT21) achieve rapid phase change before solar noon, offering early-day cooling but limited afternoon buffering. Conversely, higher-melting PCMs (RT31, RT35) extend heat absorption throughout peak irradiance, optimizing PV thermal regulation. Parametric analysis reveals that reduced HTF flow rates maximize PCM utilization and outlet temperatures, whereas higher flow rates prioritize electrical stability. Exergy results indicate a fundamental trade-off: RT21 maximizes daily-average thermal exergy through superior temperature gradients, while RT35 optimizes electrical exergy by maintaining lower cell temperatures. Increasing HTF flow rate enhances electrical exergy but reduces thermal exergy by lowering the temperature level of the delivered heat. A 100 m² installation yields approximately 455 kWh/day of thermal energy and 35.5 kWh/day of electricity (July/August), satisfying nearly all thermal loads and 30–34% of electrical demand. This configuration achieves a significant mitigation of 77–78 kg CO₂e/day, primarily through the displacement of carbon-intensive natural gas heating.</div></div>","PeriodicalId":335,"journal":{"name":"International Journal of Heat and Fluid Flow","volume":"119 ","pages":"Article 110268"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146073601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The effect of composite cement-based materials on the heat loss of geothermal wellbores","authors":"Kai Wei ,&nbsp;Ao Wang ,&nbsp;Desheng Wu ,&nbsp;Hao Chen ,&nbsp;Yulong Liu","doi":"10.1016/j.ijheatfluidflow.2026.110257","DOIUrl":"10.1016/j.ijheatfluidflow.2026.110257","url":null,"abstract":"<div><div>Geothermal energy is a widely distributed, high-potential, stable, and reliable non-carbon clean renewable energy source, playing a critical role in energy transition and low-carbon development. Geothermal wells are the primary technical means for geothermal energy extraction. As the core component of geothermal exploitation, a geothermal well consists of a multilayer composite system comprising the casing, cement sheath, and surrounding formation, within which heat transfer processes are highly complex. In this study, a heat transfer model for the casing–cement sheath–formation coupled system is established, together with a thermal conductivity evaluation model for cement-based composites. Numerical simulations are performed to investigate the effects of key influencing factors—including fluid flow conditions, thermophysical properties of the casing and cement sheath, and thermal properties of cementitious composites—on the heat extraction performance of geothermal wells. The results demonstrate that the thermal conductivity of the cement sheath has a significant impact on heat extraction capacity. Reducing the cement sheath thermal conductivity effectively increases the wellhead production temperature, decreases wellbore heat loss, and mitigates the influence of formation parameter uncertainty under different formation conditions. Furthermore, incorporating thermal insulation materials such as glass beads, slag microspheres, and aerogel particles into the cement sheath markedly lowers its thermal conductivity, with aerogel particles exhibiting the most pronounced effect, achieving a reduction of approximately 30%. The proposed models and findings provide theoretical support and technical guidance for optimizing geothermal well design and enhancing the efficiency of geothermal energy exploitation.</div></div>","PeriodicalId":335,"journal":{"name":"International Journal of Heat and Fluid Flow","volume":"119 ","pages":"Article 110257"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometric confinement and fluid properties effects on stability and heat transfer of thermal convection in lateral heated cavities","authors":"Hua Hu ,&nbsp;Juan-Juan Qin ,&nbsp;Lai-Yun Zheng ,&nbsp;Xu-Long Li ,&nbsp;Bing-Xin Zhao","doi":"10.1016/j.ijheatfluidflow.2026.110312","DOIUrl":"10.1016/j.ijheatfluidflow.2026.110312","url":null,"abstract":"&lt;div&gt;&lt;div&gt;A numerical study is performed to investigate two-dimensional natural convection in a laterally heated cavity, with particular emphasis on the coupled effects of the aspect ratio (&lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;), Rayleigh number (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;), and Prandtl number (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;). The simulations cover mainly the ranges &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;01&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;01&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. A fourth-order compact finite-difference scheme combined with a third-order TVD Runge–Kutta time integration is employed to ensure numerical stability and adequate resolution of unsteady flow features. The results reveal that heat transfer is strongly influenced by the Prandtl number. As &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; increases, the flow transitions from unsteady to steady behavior and the overall heat transfer is enhanced. For low-Prandtl-number fluids (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;), such as gases and liquid metals, nonlinear solution bifurcations emerge, becoming increasingly pronounced at larger aspect ratios and higher Rayleigh numbers. The onset of unsteadiness is associated with a critical Rayleigh number &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, marking the transition from steady to unsteady convection. Scaling analyses show that &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∼&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for air and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∼&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for water, indicating a reduced sensitivity to geometric confinement for high-&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; fluids. The aspect ratio is found to exert a non-monotonic influence on heat transfer. The average Nusselt number (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;av&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;) attains its maximum at an optimal aspect ratio &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; that shifts toward smaller values as &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; increases. Additionally, the heat transfer follows a power-law dependence on the Rayleig","PeriodicalId":335,"journal":{"name":"International Journal of Heat and Fluid Flow","volume":"119 ","pages":"Article 110312"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146170021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}