{"title":"Numerical investigation of thermal energy storage characteristics of dual phase change material in double elliptic pipe","authors":"Nessrine Sayoud , Ahmet Yüksel , Abdelghani Laouer , Mohamed Teggar , Müslüm Arıcı , Noureddine Brihi","doi":"10.1016/j.icheatmasstransfer.2025.108921","DOIUrl":"10.1016/j.icheatmasstransfer.2025.108921","url":null,"abstract":"<div><div>Latent heat storage offers high thermal energy density. However, the low storage rate is a challenge to address. This study aims to evaluate the effects of cascading dual-phase change material (dual-PCM) within a double elliptic pipe on thermal performance and storage rates. The melting process of dual-PCM in the enclosure is numerically analyzed. The numerical model is validated by comparison with experimental data of the literature. Nine design configurations are examined, focusing on the orientation (vertical and horizontal) and the inclination of the elliptic enclosure in order to find out the most effective storage unit. The thermal and flow fields are analyzed alongside the evolution of the melt fraction, charging times, and stored energy. Results indicate that the cascading dual-PCM inside an outer horizontal elliptic enclosure with an inner vertical heating elliptic pipe reduce thermal energy storage time by up to 49 %, demonstrating the most efficient melting process. Furthermore, the study indicates that vertical elliptical pipes reduce thermal energy storage time by 24.7 % compared to horizontal ones, and that lower inclination angles provided a faster and more uniform melting process. Dual-PCM configurations in horizontal orientations significantly enhance energy storage efficiency.</div></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":"164 ","pages":"Article 108921"},"PeriodicalIF":6.4,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shengnan Meng , Han Gong , Xiaoxin Zeng , Longyu Yang , Bingcheng Wang , Zheng Cui , Xiaoteng Ma
{"title":"Molecular dynamics of boiling heat transfer under passive liquid driven mechanism based on capillary flow in rough nanochannels","authors":"Shengnan Meng , Han Gong , Xiaoxin Zeng , Longyu Yang , Bingcheng Wang , Zheng Cui , Xiaoteng Ma","doi":"10.1016/j.icheatmasstransfer.2025.108912","DOIUrl":"10.1016/j.icheatmasstransfer.2025.108912","url":null,"abstract":"<div><div>The boiling under capillary flow greatly affects the heat transfer performance of the passive two-phase heat dissipation devices. In this study, sinusoidal structures with various amplitudes (3.615 Å, 7.23 Å and 10.845 Å) and periods (<span><math><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>×</mo><mn>624</mn><mspace></mspace><mi>Å</mi></math></span>, <span><math><mfrac><mn>2</mn><mn>15</mn></mfrac><mo>×</mo><mn>624</mn><mspace></mspace><mi>Å</mi></math></span> and <span><math><mfrac><mn>1</mn><mn>10</mn></mfrac><mo>×</mo><mn>624</mn><mspace></mspace><mi>Å</mi></math></span>) are constructed to characterize rough microchannels. The capillary flow and boiling under capillary flow in various nanochannels are investigated separately by molecular dynamics simulations. The results show that adding rough elements to wall surface reduces the maximum velocity of the liquid at least 22.9 % compared to the smooth surface. The rough elements can effectively enhance the local heat transfer efficiency and trigger the flow boiling. At the same time, the expansion of the bubble leads to the blockage and prevents the liquid supply, leading to deterioration of heat transfer. Increasing the roughness by increasing the amplitude of the sinusoidal structure will increase the heat transfer coefficient but decrease the total heat absorption. A better approach is to increase roughness by decreasing the period of sinusoidal structure, which has a favorable effect on both heat transfer coefficient and total heat absorption. The rough surface leads to an increase in the concentration of liquid atoms near the wall, enhancing the effectiveness of heat transfer.</div></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":"164 ","pages":"Article 108912"},"PeriodicalIF":6.4,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wei Li , Le Zhang , Tianwen Li , Jianghui Zhang , Yuan Dong , Lian-yun Wei , Jianfu Zhao , Zhixiao Zhang , David J. Kukulka
{"title":"Correlations of condensation heat transfer in hydrophobic enhanced tubes with using R32","authors":"Wei Li , Le Zhang , Tianwen Li , Jianghui Zhang , Yuan Dong , Lian-yun Wei , Jianfu Zhao , Zhixiao Zhang , David J. Kukulka","doi":"10.1016/j.icheatmasstransfer.2025.108886","DOIUrl":"10.1016/j.icheatmasstransfer.2025.108886","url":null,"abstract":"<div><div>An experimental study of condensation heat transfer is performed in enhanced surface stainless steel tubes using refrigerant R32. An evaluation of the effect of hydrophobicity on condensation heat transfer is accomplished by comparing the performance of three enhanced tubes (hydrophobic (HYD), herringbone (HB), and hydrophobic/herringbone composite (HYD/HB)) to one smooth tube. Parameters include: saturation temperatures of 35 °C and 45 °C; mass flow rates of 100 kg/(m<sup>2</sup>·s) and 150 kg/(m<sup>2</sup>·s); and vapor qualities in the range from 0.2 to 0.9. A new condensation flow heat transfer correlation is established based on hydrophobicity and flow pattern analysis. The results indicate: (i) for varying mass flow rates, the HB tube exhibits superior heat transfer performance compared to the HYD and HYD/HB tube; (ii) as vapor quality increases, the HTC of the HYD tube gradually increases and becomes equal to that of the HB tube; (iii) for a vapor quality above 0.6, the HYD tube outperforms the HB tube. Five condensation flow HTC models are evaluated; experimental values were compared and analyzed with the calculated results in order to investigate the condensation flow heat transfer mechanism of enhanced tubes. Condensation flow heat transfer correlations in HYD, HB, and HYD/HB can predict data points within ±20 % including 80 % of the data points, and within ±25 % including 93 % of the data points.</div></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":"164 ","pages":"Article 108886"},"PeriodicalIF":6.4,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xiaowen Wang , Maolong Liu , Junsen Fu , Xu Yan , Hongkang Tian , Tenlong Cong , Yao Xiao , Hanyang Gu
{"title":"Pool boiling experimental study on the impact of deposition on the nucleate boiling and bubble behavior of horizontally-placed tubes","authors":"Xiaowen Wang , Maolong Liu , Junsen Fu , Xu Yan , Hongkang Tian , Tenlong Cong , Yao Xiao , Hanyang Gu","doi":"10.1016/j.icheatmasstransfer.2025.108890","DOIUrl":"10.1016/j.icheatmasstransfer.2025.108890","url":null,"abstract":"<div><div>During the operation of the nuclear reactor, the corrosion particles deposited on the fuel cladding will change surface characteristics and affect the boiling heat transfer. However, due to the intricate structure of the deposition layer, the mechanism of the impact of deposition on nucleate boiling is not clear at present. A pool boiling experiment was carried out to investigate the effect of particle deposition on the bubble behavior and nucleate boiling heat transfer characteristics. The effect of deposition time and heat fluxes on the nucleate boiling was investigated. The effect mechanism of particle deposition on the circumferential heat transfer was revealed. The results indicate that the tube surface becomes more hydrophilic after deposition, and the deposited tube presents a boiling heat transfer state with the down-side surface in the form of large bubbles and the up-side surface in the form of a continuous stream of small bubbles. Furthermore, during the deposition process, the heat transfer coefficient decreases rapidly at the initial period, then increases slightly and stabilizes. Meanwhile, the rod circumferential temperature distribution varied before and after deposition, and the deterioration of the heat transfer coefficient of the up-side surface is more serious due to the influence of gravity deposition. The current tests show that corrosion particle deposition has a great impact on heat transfer, the post-deposition heat transfer coefficient can be reduced to 25% of its original value.</div></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":"164 ","pages":"Article 108890"},"PeriodicalIF":6.4,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sen Huang, Guoyuan Zhang, Yunlong Li, Xun Luo, Ruyi Yuan
{"title":"Simulation and experiment of boiling two-phase flow and heat transfer in mini-channels with reticulated pore structure","authors":"Sen Huang, Guoyuan Zhang, Yunlong Li, Xun Luo, Ruyi Yuan","doi":"10.1016/j.icheatmasstransfer.2025.108899","DOIUrl":"10.1016/j.icheatmasstransfer.2025.108899","url":null,"abstract":"<div><div>In order to satisfy the operational requirements of electronic devices with small volumes, high heat flow densities, and uniform temperatures, a reticulated pore mini-channel heat sink unit (porosity>72 %) is designed. The mechanism of efficient heat transfer by boiling phase change is studied with deionized water as the cooling medium. A two-phase flow model based on VOF theory is developed, and an experimental platform for testing the boiling two-phase flow and its heat transfer performance in millimeter-scale pore channels is built. The single-phase convective thermal performance and boiling two-phase flow status and heat transfer properties of the heat sink are obtained. The findings indicate that as flow velocity increases, the maximum increase of Nusselt number in two-phase flow can reach 77.2 % in contrast to that in single-phase flow, and maximum reduction in temperature difference across the heated surface can reach 20.1 %. The Nusselt number for the reticulated pore structure is 56.2 % higher than that of a straight mini-channel heat sink, and the heated surface experiences a maximum temperature drop of 3.42 K. Multiple sets of experimental and theoretical results under two-phase flow in pore mini-channels show good consistency. The maximum relative difference in error of the heated surface temperature is only 3.1 %, and the average relative difference in error of the total thermal resistance is 6.68 %. The research will offer significant theoretical and practical contributions to the design of high-efficiency heat sinks with pore mini-channel structure by the boiling phase transition mechanism.</div></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":"164 ","pages":"Article 108899"},"PeriodicalIF":6.4,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Why people shape roofs the same way","authors":"A. Bejan , P. Mardanpour","doi":"10.1016/j.icheatmasstransfer.2025.108909","DOIUrl":"10.1016/j.icheatmasstransfer.2025.108909","url":null,"abstract":"<div><div>The roofs of houses look similar in profile, especially in villages and old settlements. Why? The question is about the common angle of inclination. The answer comes from heat transfer by natural convection. Inspired by the evolution of the <em>sapiens</em> toward more power from the adoption of artifacts, we show that the existence of common roof shapes can be reasoned from the needs of those who live under the roof. Is there a shape that, while reducing the heat loss to the ambient, reduces the human effort (gathering firewood, etc.)? We consider two classes of roof shapes, Λ and cone, and two roof sizes, small and large (respectively, two flow regimes, laminar and turbulent). In laminar natural convection, the common profile of the Λ and the cone looks shallow, with height/base ratios comparable with 1/4. In turbulent flow, the Λ and the cone look like an equilateral triangle. These findings reinforce the evolutionary record of human civilization toward economy of effort and longer life. They also present an opportunity for the future ‘energy design’ of buildings: the external shape has a significant effect on the heat loss from the building.</div></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":"164 ","pages":"Article 108909"},"PeriodicalIF":6.4,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143714794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chenglong Wang , Yachen Guo , Hanlong Liu , Abdelmalek Bouazza , Gangqiang Kong , Xuanming Ding
{"title":"Heat transfer of energy pipe piles with spiral heat exchanger","authors":"Chenglong Wang , Yachen Guo , Hanlong Liu , Abdelmalek Bouazza , Gangqiang Kong , Xuanming Ding","doi":"10.1016/j.icheatmasstransfer.2025.108913","DOIUrl":"10.1016/j.icheatmasstransfer.2025.108913","url":null,"abstract":"<div><div>This paper presents a study on heat transfer for energy pipe piles with a spiral heat exchanger (i.e., spiral-tube energy pipe pile). Physical model testing and a heat transfer analytical model were used to analyze the thermal performance of spiral-tube energy pipe piles filled with different backfill materials. The analytical model was developed using the law of energy conservation and Laplace transforms, and its reliability was validated against both experimental data and numerical simulation results. Furthermore, the model was utilized to conduct full-scale pile simulations and analyze the factors influencing heat transfer. Compared to the classical models for heat transfer, the proposed model was found to be more suitable. This study shows that the choice of backfill materials influences the heat exchange efficiency of spiral-tube energy pipe piles due to variations in their thermal properties. Furthermore, lowering the pile's thermal conductivity increases the amount of heat transferred into the surrounding soil. Additionally, variations in the soil's thermal properties significantly affect the heat transfer in energy pipe piles.</div></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":"164 ","pages":"Article 108913"},"PeriodicalIF":6.4,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143714793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wenqiang Zhang , Zhi Wen , Dan Wang , Lei Guo , Fuyun Su , Xinbin Wang , Qihao Yu
{"title":"Numerical modelling and mechanism of water-heat-deformation of subgrade under heating effect in cold regions","authors":"Wenqiang Zhang , Zhi Wen , Dan Wang , Lei Guo , Fuyun Su , Xinbin Wang , Qihao Yu","doi":"10.1016/j.icheatmasstransfer.2025.108911","DOIUrl":"10.1016/j.icheatmasstransfer.2025.108911","url":null,"abstract":"<div><div>Heating method shows considerable potential for mitigating frost heave of subgrade in cold regions. However, the water-heat-deformation characteristics of subgrade under the coupling effect of freezing-thawing and heating effect remain unclear, which hampers the optimization and widespread application of heating method. Therefore, this paper proposes a numerical model of subgrade water-heat-deformation considering heating effect. The influence and mechanism of heating effect on water-heat-deformation of subgrade is systematically analyzed. The results show that the heating effect changes the water-heat-deformation state of subgrade. Furthermore, the combined influence of shady-sunny slope effect and ballast layer ensures that ground temperature near the subgrade center remains above 0 °C, thereby preventing the formation of ice lenses and frost heave. However, the shoulders on both sides enter a freezing state, and freezing rate, freezing depth and frost heave are reduced by more than 45 %, 60 % and 60 % respectively compared with the comparison subgrade. The freezing depth, driving force and rate of water migration are significantly affected by heating effect, which increases the pathways of water upward migration and greatly weakens the segregated frost heave of subgrade. This is the primary mechanism through which the heating method effectively mitigates frost heave in subgrades.</div></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":"164 ","pages":"Article 108911"},"PeriodicalIF":6.4,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143714792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
T. Salahuddin , Madiha Nazir , Mair Khan , Shah Muhammad , Muhammad Idrees
{"title":"Blood flow study in stenotic arteries through porous medium with heat generation","authors":"T. Salahuddin , Madiha Nazir , Mair Khan , Shah Muhammad , Muhammad Idrees","doi":"10.1016/j.icheatmasstransfer.2025.108894","DOIUrl":"10.1016/j.icheatmasstransfer.2025.108894","url":null,"abstract":"<div><div>Due to its significance in biological medicine, the passage of blood through stenotic arteries is one of the primary fields of study in mathematical fluid dynamics. The purpose of this research is to determine how human circulation influences a stenosed blood vessel. In the current study, micropolar fluid is assumed to represent human blood. Our goal in the present research is to analyze heat generation and chemical reaction in micropolar fluid flowing via a stenosed artery inserted in a porous material. To simulate the temperature and concentration distributions caused by blood flow with artery stenosis computationally with the assistance of MATLAB, the constitutive equations and boundaries are simplified to non-dimensional notation by utilizing similarity transformations. For reducing the complexity of partial differential equations (PDEs), the long wavelength (LWL) and low-Reynolds numeral (LRN) approaches are employed. The Crank-Nicolson approach has been employed for evaluating the boundary conditions and governing equations for fluid flow. An appropriate geometry has been considered in order to figure out the consequence of the stenosis pattern. There includes a visual discussion of the impact of several physical parameters on the axial velocity graph, heat and mass field, including coupling number <span><math><mfenced><mi>N</mi></mfenced></math></span>, chemical reaction <span><math><mfenced><mi>ξ</mi></mfenced></math></span>, micropolar <span><math><mfenced><mi>m</mi></mfenced></math></span>, Schmidt <span><math><mfenced><mi>Sc</mi></mfenced></math></span>, Prandtl <span><math><mfenced><mo>Pr</mo></mfenced></math></span> and heat generation parameter <span><math><mfenced><mi>Q</mi></mfenced></math></span>. The present study validates the choice of machine learning approach as a promising solution to model micropolar fluid flow and future work in this area.</div></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":"164 ","pages":"Article 108894"},"PeriodicalIF":6.4,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143725809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal designs of hybrid jet impingement microchannel heat sink across various pumping powers: A deep-learning approach","authors":"M. Tajik , M.R. Hajmohammadi , K. Vafai","doi":"10.1016/j.icheatmasstransfer.2025.108902","DOIUrl":"10.1016/j.icheatmasstransfer.2025.108902","url":null,"abstract":"<div><div>Hybrid jet impingement/microchannel heat sinks (HJIMCHS) are an effective cooling technique for high heat flux electronics, providing efficient heat dissipation and enhanced temperature uniformity. To expand the applicability of HJIMCHS to a broader range of cooling challenges, it is crucial to optimize their heat transfer performance across a wide range of pumping powers (<span><math><mi>Π</mi></math></span>), rather than focusing on a single operating point. This study numerically solves the fluid flow and heat transfer characteristics of a silicon-based HJIMCHS with water as the coolant, and then the geometric variables of the HJIMCHS, including jet slot length (<span><math><msub><mi>L</mi><mi>jet</mi></msub></math></span>), jet slot and channel width (<span><math><msub><mi>W</mi><mi>jet</mi></msub></math></span>), jet slot height (<span><math><msub><mi>H</mi><mi>jet</mi></msub></math></span>), and the number of microchannels (<em>N</em>), are simultaneously optimized over a broad range of <span><math><mi>Π</mi></math></span> (<span><math><mn>0.01</mn><mspace></mspace><mi>W</mi><mo>≤</mo><mi>Π</mi><mo>≤</mo><mn>0.15</mn><mspace></mspace><mi>W</mi></math></span>). The optimization process employs the non-dominated sorting genetic algorithm II (NSGA-II), powered by a surrogate artificial neural network model, and objective functions are total thermal resistance (<span><math><msub><mi>R</mi><mi>T</mi></msub></math></span>), maximum temperature difference on the bottom wall (<span><math><mi>TD</mi></math></span>), and entropy generation rate (<span><math><msub><mover><mi>S</mi><mo>̇</mo></mover><mi>gen</mi></msub></math></span>). Optimal trade-offs between pumping power and the objective functions are explored by optimizing the HJIMCHS design at each pumping power. Results indicate that using <span><math><msub><mover><mi>S</mi><mo>̇</mo></mover><mi>gen</mi></msub></math></span> as an objective function across all <span><math><mi>Π</mi></math></span> values may lead to inferior heat transfer performance, necessitating careful consideration. Additionally, with a heat flux of <span><math><mn>200</mn><mspace></mspace><mi>W</mi><mo>/</mo><msup><mi>cm</mi><mn>2</mn></msup></math></span>, for <span><math><mi>Π</mi><mo>=</mo><mn>0.057</mn><mspace></mspace><mi>W</mi></math></span>, the optimal compromise solution results in <span><math><msub><mi>R</mi><mi>T</mi></msub><mo>=</mo><mn>0.0963</mn><mspace></mspace><mi>K</mi><mo>/</mo><mi>W</mi></math></span> and <span><math><mi>TD</mi><mo>=</mo><msup><mn>2.9</mn><mo>°</mo></msup><mi>C</mi></math></span>, similarly for <span><math><mi>Π</mi><mo>=</mo><mn>0.15</mn><mspace></mspace><mi>W</mi></math></span> the results are <span><math><msub><mi>R</mi><mi>T</mi></msub><mo>=</mo><mn>0.079</mn><mspace></mspace><mi>K</mi><mo>/</mo><mi>W</mi></math></span> and <span><math><mi>TD</mi><mo>=</mo><msup><mn>2.3</mn><mo>°</mo></msup><mi>C</mi></math></span>.</div></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":"164 ","pages":"Article 108902"},"PeriodicalIF":6.4,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}