Thermal Engineering最新文献

{"title":"Genesis, Morphology, and Composition of Corrosion Product Dissipative Forms in the Primary Coolant of a PWR Type Nuclear Reactor","authors":"B. A. Gusev,&nbsp;A. A. Efimov,&nbsp;L. N. Moskvin,&nbsp;A. N. Maksimova","doi":"10.1134/S0040601526700382","DOIUrl":"10.1134/S0040601526700382","url":null,"abstract":"<p>The article considers regularities relating to the behavior of dissipative corrosion product (CP) impurities (solid phase particles) existing in the primary circuit of a test bench serving as a prototype of a nuclear propulsion system as suspensions and deposits. For nuclear power plants (NPPs) equipped with PWR-type reactors, reducing water chemistries (WC) are adopted, including ammonia water chemistry and ammonia-boron-potassium water chemistry with boron control. The relevance of the study is stemming from rapid development of small modular nuclear power plants (SNPPs) in sparsely populated areas of Siberia and Far East. An explanation of the mechanism governing the formation of solid phase corrosion products is proposed. The article presents the results of experiments on studying the morphology, chemical, and radionuclide compositions of CPs formed in making purposeful changes of hydrodynamic, thermophysical, and physicochemical parameters of the primary circuit of a PWR-type reactor operating with an ammonia water chemistry, which may serve to a full extent as a reference one with respect to an SNPP. Owing to the revealed regularities, it became possible to determine the optimal process parameters of reagent-free decontamination. In the case of using the design water chemistry in the primary circuit, the CP composition, the corrosion rate of structural materials, and the content of radionuclides in activated corrosion products (ACPs) are kept at levels ensuring the minimal dose burden on the personnel during the NPP operation. Long-lived radionuclides in ACPs such as ⁶⁰Со and to a certain extent ⁵⁴Мn are the main sources causing exposure of the personnel serving the NPP during repair works. In the case of using the ammonia water chemistry, the phase composition of corrosion deposits and suspensions in the coolant is determined, irrespectively of the NPP design features, by nonstoichiometric magnetite spinel, the composition of which includes elements of alloying additions and their activation products. The chemical composition of solid phase corrosion products separated from coolant samples is essentially identical with the composition of Grade 0Kh18N10T steel, which is the coolant circuit main structural material.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"73 9","pages":"783 - 796"},"PeriodicalIF":1.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Condition Monitoring and Diagnosis of a Drum Boiler Using Algorithms of the Paraconsistent Annotated Logic: Condition Monitoring Model of Drum Steam","authors":"Ae Chun Ri,&nbsp;Sungjin Kim,&nbsp;Su Gil Kim,&nbsp;Yong Chol Ri,&nbsp;Chol Song Won,&nbsp;Kwang Myong Kim","doi":"10.1134/S0040601525600555","DOIUrl":"10.1134/S0040601525600555","url":null,"abstract":"<p>In this work, a condition monitoring model of drum steam using Paraconsistent Annotated Logic (PAL) was investigated to provide the mathematical and logical foundation for the application of PAL to monitor condition of steam in boiler drum. Three methods are proposed in order to calculate evidence degrees from steam pressure and temperature and evaluate steam state in the drum. The Paraconsistent Analysis Node (PAN) takes evidence diagrams as input to analyze and process the inconsistency and uncertainty of signals corresponding to pressure and temperature. The PAN outputs the resultant real evidence degree, the Contradiction Degree and the Normalized contradiction degree. A network of paraconsistent analysis (PANnet) which is combined with these methods is also proposed in order to analyze and treat the contradiction. And based on this, the application of PAL for condition monitoring of drum steam, one of the local systems of the Fault Detection and Diagnosis (FDD) for Thermal Power Plants (TPPs), is demonstrated. For two faults, the fault detection times are reduced by 60 and 64%, respectively, compared to the conventional ones. The condition monitoring and diagnosis of evaporators as well as boiler drum can be improved by using this steam condition monitoring model.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"73 9","pages":"772 - 782"},"PeriodicalIF":1.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Achieving More Efficient Energy Generation by Complexes on the Basis of Hydropower Resources with the Possibility of Energy Storage during Operation as Part of Autonomous Power Supply Systems","authors":"M. A. Biryulin,&nbsp;A. V. Volkov,&nbsp;A. M. Dobrenko,&nbsp;A. A. Druzhinin,&nbsp;M. O. Sheikin","doi":"10.1134/S0040601526700370","DOIUrl":"10.1134/S0040601526700370","url":null,"abstract":"<p>The possibility of achieving more efficient electricity generation by energy complexes on the basis of hydropower resources with predominantly using them in autonomous power supply systems is analyzed. The choice of daily amount of electricity production as a criterion for estimating the energy complex performance is substantiated. Methods for improving the generation efficiency are considered, such as daily load profile optimization, also when there is a buffer energy storage in the power system; combined generation of electricity; extremum seeking control of hydroelectric power units and maneuverable hydroelectric power units in the operation modes of micro pumped storage hydroelectric (microPSH) power plants, as well as electrochemical energy storage units, and their combinations. Special attention is paid to extremum seeking control implementation methods for various types of electric generators, which make it possible to increase the daily amount of electricity generated by both newly developed and existing complexes on the basis of hydropower resources without introducing significant changes in the design layout with taking into account stabilization of the autonomous electric network parameters. A new simpler and more accurate extremum seeking control method by monitoring mechanical rather than electrical parameters is proposed. To confirm the theoretical hypotheses on implementing extremum seeking control, field experiment data are given and analyzed, which testify that the proposed method is well grounded and highly efficient in nature. The costs of electricity in using different methods for storing it and for achieving better efficiency of its generation are compared, and versions of their combined use are considered. It has been confirmed that there is a significant potential for achieving more efficient electricity generation with the use of hydropower resources, and practical methods for achieving this aim are described.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"73 9","pages":"757 - 763"},"PeriodicalIF":1.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical Simulation of Compressor Flow Path Inlet Compartments Icing under Adverse Weather Conditions","authors":"P. A. Goryachev","doi":"10.1134/S0040601526700333","DOIUrl":"10.1134/S0040601526700333","url":null,"abstract":"<p>Ice accretion on the components of on-land power equipment and aircraft equipment under harsh weather conditions adversely affects their operation. Icing may emerge both near the ground surface and at significant altitudes. The article proposes an advanced 3D ice accretion model, which covers a wide range of outdoor conditions (supercooled droplets, dry ice crystals, and mixed phase), as well as various icing surface states (dry or moistened, heated or nonheated). Special attention is paid to simulating the processes in the compressor flow path, in particular, to ice accretion on dry heated surfaces when a flow of dry ice crystals deposits on them. The model describes conjugate unsteady heat transfer from an object’s heated surface to the accreting ice buildup, which has a complex multilayer inner structure. The ice layer may contain accumulated liquid water. This water can flow over the ice surface in the form of hillocks, rivulets, and films, and in the case of submelting, cavities filled with liquid water may occur on the heated surface. The predicted ice locations and mass and dimension characteristics are compared with experimental data obtained on the compressor flow path model. It has been confirmed that the interconnected and interrelated physical effects accompanying ice accretion, such as heat and mass transfer, the degree to which ice crystals are submelted in the carrier flow and captured by the ice buildup surface, as well as ice erosion, are described in a correct way. In carrying out predictions, a Pi-shaped curve representing the dependence of ice buildup rate on the crystals submelting degree has been obtained, which is in good agreement with the experimental data.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"73 9","pages":"730 - 744"},"PeriodicalIF":1.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neural Network Simulation of Burner Operation Parameters","authors":"M. A. Tarulin,&nbsp;E. P. Kop’ev,&nbsp;O. V. Sharypov","doi":"10.1134/S0040601526700230","DOIUrl":"10.1134/S0040601526700230","url":null,"abstract":"<p>The article presents the results of studying the applicability of deep learning methods for predicting the operation parameters of a liquid fuel fired burner with steam-assisted atomization and a gas generation chamber, which is intended for combusting low grade liquid hydrocarbon fuels and waste based on a flame visual analysis. The scientific novelty of the study is that with steam-assisted atomization it is possible to obtain visual flame patterns differing from those obtained using conventional methods, for interpreting of which a dedicated approach is required. A modified architecture of the dense convolutional neural network DenseNet-121 is proposed with weights pretrained on the ImageNet data set, which is adapted to solving the regression problem of predicting the device process operation parameters (fuel and superheated steam flowrates). The DenseNet-121 architectureс with dense interlayer connections is able to efficiently draw fine visual features from the flame images, which are critical for establishing the functional dependences. The regression subnetwork includes fully connected layers with the rectified linear unit (ReLU) activation and Dropout regularization. Validation on an independent test sample of experimental data has shown high accuracy of the model: for the fuel flowrate, the mean absolute error (MAE) is 3.8%; the root mean square error (RMSE) is 9%, and the determination coefficient <i>R</i>² = 0.957; for steam flowrate the MAE is 2.6%; RMSE is 4%, and <i>R</i>² = 0.994. The achieved results (<i>R</i>² &gt; 0.95 for both the parameters) confirm that the model is able to catch complex interrelations between the flame visual characteristics and burner operation parameters. The proposed solution is aimed at developing an intellectual tool for prompt contactless monitoring and optimization of liquid fuel combustion processes in burners with steam-assisted atomization and a gas generation chamber.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"73 9","pages":"764 - 771"},"PeriodicalIF":1.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Development of a Thermal Oil Pentane Evaporator Design for an ORC Unit","authors":"M. M. Vinogradov,&nbsp;V. I. Kuznetsov,&nbsp;D. N. Moisin,&nbsp;I. S. Antanenkova","doi":"10.1134/S0040601526700357","DOIUrl":"10.1134/S0040601526700357","url":null,"abstract":"<p>A vapor generator is among the most complex and thermally stressed component of the thermal cycle circuit of a power unit operating according to the organic Rankine cycle (ORC). As a rule, the ORC unit vapor generators intended for recovering the waste heat in industrial processes are “connected” to the source via an intermediate thermal oil loop. With such an arrangement, thermal oil, which has the maximum possible temperature, enters sequentially first the vapor generator’s evaporating and then heating part, in which it transfers heat to the power unit’s low-boiling working fluid (LBWF). The study addresses matters concerned with designing the evaporator, in the tubes of which the LBWF is heated to the saturation temperature at a specified pressure, boils, and is superheated prior to be supplied to a turbine (an expansion engine). Oil coolers of stationary power units operating on steam as working fluid are considered as prototypes for design implementation of the ORC unit evaporator: vertical shell and tube devices, including those with smooth tubes, with “disc–ring” type partitions with nonsealed and sealed process gaps, as well as with low knurled fins on tubes, with “disc–ring” type partitions, and sealed process gaps. The article presents the results of a review of experimental data and applicability analysis of existing models for calculating the heat transfer coefficient and critical heat flux for LBWF boiling in tubes, which can be recommended for including them into the device thermal-hydraulic design calculation. The procedure for calculating the pentane evaporator for a thermal capacity of 1440 kW for a 500 kWe ORC unit has been tested. A “field of solutions” has been obtained for the layout versions of the evaporator heat transfer surface composed of tubes made of carbon steel, stainless steel, brass, and copper, having an outer diameter of 10, 12, 14, 16, and 18 mm and wall thickness from 0.5 to 2.5 mm, as well as finned tubes the finning ratio of which was varied from 2.2 to 2.4. By applying correlation analysis methods, a data array on the optimal layout versions of the heat transfer surface for devices of all designs considered has been set up. Recommendations on selecting the design version of a pentane evaporator as part of an ORC unit have been compiled.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"73 9","pages":"703 - 717"},"PeriodicalIF":1.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of Profiling the Curving of the Tip Part of a Unshrouded Blade on its Aerodynamic Efficiency","authors":"A. V. Granovskiy,&nbsp;I. V. Afanasiev,&nbsp;L. I. Bekreneva,&nbsp;B. I. Kurmanov","doi":"10.1134/S0040601526700345","DOIUrl":"10.1134/S0040601526700345","url":null,"abstract":"<p>The development of tip clearance control and monitoring systems in gas turbines has led to a trend toward eliminating shrouds on rotor blades in a number of high-power stationary gas turbines, such as the SGT5-4000F, SGT-8000H, and others. Eliminating shrouds opens the possibility of optimizing turbine parameters, increases the degree of freedom in selecting the number of blades in the rotor, allows the reduction of rotor blades weight and, consequently, reduces the contour load on clearance above the unshrouded rotor blade (RB), which is not always possible, especially in aircraft turbines. To reduce inductive tip losses, several patents propose forming the tip area portion of the rotor blade with a slight curvature of the blade toward the suction surface in the circumferential direction. This minimizes the pressure difference between the pressure and suction surfaces near the blade tip. However, no quantitative estimates of this effect are provided. To obtain quantitative estimates of the impact of blade curvature at the tip area a computational study of the flow structure and energy loss level in the considered region was conducted using state-of-the-art CFD approaches for solving the 3D Navier-Stokes equations in a steady-state RANS formulation. In the first stage of the study, calculations were performed using the proprietary (in-house code) 3D NS software package. However, in the absence of experimental data the validation, justification and visualization of proprietary the numerical results obtained using the 3D NS program, computational studies of the flow in a rotor blade row with an open tip clearance were also conducted with the commercial software packages ANSYS FLUENT and ANSYS CFX. The computational study of the flow structure demonstrated a positive effect of this measure, resulting from a significant reduction in vortex formation zones due to flow in the tip clearance and, consequently, a reduction in losses when the rotor blade tip is tilted toward the suction surface.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"73 9","pages":"718 - 729"},"PeriodicalIF":1.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Research on Thermal Conductivity of Graphene-Paraffin Composite Phase Change Materials","authors":"Qin Wang,&nbsp;Zihua Wu,&nbsp;Haiping Hong,&nbsp;Haoyan Sun,&nbsp;Xiaoxiao Yu,&nbsp;Huaqing Xie","doi":"10.1134/S0040601526700369","DOIUrl":"10.1134/S0040601526700369","url":null,"abstract":"<p>In this study, the thermal conductivity of paraffin matrix was improved by adding functional graphene. Composite phase change materials (PCMs) based on paraffin and acid-treated graphene were prepared and tested at various treatment temperatures (90, 120, and 150°C) with varying mass fractions of the filler. Preliminary acid treatment of graphene reduced the interfacial thermal resistance and improved the dispersion stability of the filler in the matrix due to the introduction of functional groups onto its surface. The following key characteristics were determined for the obtained samples: dispersion stability of graphene, micromorphological structure, and chemical compatibility of the components. Fourier-transform infrared spectroscopy results showed that graphene treated with acid at 120°C exhibited more pronounced absorption peaks, indicating a higher content of O–H, C=O, and C–O bonds compared to graphene treated at other temperatures. Thermal conductivity measurements of the composite PCM samples at various temperatures revealed that at 60°C, the maximum increase in thermal conductivity (23.2%) relative to pure paraffin was observed for the paraffin composite with 0.1 wt% acid-treated graphene (treated at 120°C). This confirms that the acid treatment temperature of 120°C is optimal. When the mass fraction of graphene in this composite was increased to 0.9%, the thermal conductivity reached 0.314 W/(m K), which is 49.55% higher than that of pure paraffin.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"73 9","pages":"745 - 756"},"PeriodicalIF":1.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New Technology for Oil-Free Startup and Flame Stabilization in the Boiler Furnace of TPP","authors":"Son-Guk Rim,&nbsp;Yong-Jun Kim,&nbsp;Tae-Son Yom,&nbsp;Jong-Chol Ri,&nbsp;Kuk-Chol Son","doi":"10.1134/S004060152560035X","DOIUrl":"10.1134/S004060152560035X","url":null,"abstract":"<p>The work puts forth a gliding arc discharge plasma-based technology for solid fuel ignition and flame stabilization. This technology helps burn effectively, eco-friendly the low-rank fuel from the Democratic People’s Republic of Korea. A gliding arc discharge-nonequilibrium plasma fuel system (GAD-NEPFS) has been developed for low-rank coal-fired thermal power plants (TPPs). The GAD-NEPFS is a pulverized fuel (PF) burner equipped with a gliding arc plasmatron, whose power consumption is 5–10 kW per burner. The GAD-NEPFS was introduced to the BKZ-210 boiler at TPP for start-up and flame stabilization tests. The PF is provided into the GAD-NEPFS through three inlets: source fuel inlet through a plasmatron and two others for auxiliary and primary fuel inlets, respectively. The source fuel produces heat while passing through plasmatron and this heat in turn ignites the auxiliary and primary fuel. The tests for ignition and flame stabilization were carried out using the GAD-NEPFS and the results were discussed. Numerical simulations and measurements were performed for both of traditional combustion and GAD-NEPFS combustion. The results show the growth of the combustion efficiency, the decrease of the nitrogen oxide concentration and the temperature at the exit of furnace.</p>","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"73 8","pages":"672 - 681"},"PeriodicalIF":1.3,"publicationDate":"2026-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Wall Temperature Measurement in Studying Refrigerant Vapor Condensation inside a Tube","authors":"O. O. Milman,&nbsp;A. Yu. Kartuesova,&nbsp;M. Sh. Mintsaev,&nbsp;A. V. Ptakhin","doi":"10.1134/S0040601526700291","DOIUrl":"10.1134/S0040601526700291","url":null,"abstract":"&lt;p&gt;The article presents a procedure for estimating the error &lt;span&gt;({{delta }}{{bar {t}}_{{max }}})&lt;/span&gt; in finding the tube wall average temperature &lt;span&gt;({{bar {t}}_{{text{w}}}})&lt;/span&gt;. This is necessary to perform reliable calculation of the heat transfer coefficient for refrigerant vapor condensation in the tube. A tube section mockup was developed, which was used in carrying out an experiment. Computer simulation was also carried out, by means of which the variation of &lt;span&gt;({{bar {t}}_{{text{w}}}})&lt;/span&gt; during the refrigerant accumulation was calculated, and the value by which the temperature at an individual point may differ from the temperature averaged over the tube’s entire inner surface was estimated. The measurement error has thus been determined. The influence of various parameters on the possible error in determining &lt;span&gt;({{bar {t}}_{{text{w}}}})&lt;/span&gt; was studied depending on the thermal sensor location: the coefficient of heat transfer from the tube external wall to water α&lt;sub&gt;1&lt;/sub&gt; [1000‒5000 W/(m&lt;sup&gt;2&lt;/sup&gt; K)], the average coefficient of heat transfer from refrigerant to the wall inner surface &lt;span&gt;({{{{alpha }}}_{{{text{av}}}}})&lt;/span&gt; [500‒2500 W/(m&lt;sup&gt;2&lt;/sup&gt; K)], wall thickness (δ&lt;sub&gt;w&lt;/sub&gt; = 1‒4 mm), and tube material (copper, brass, and steel). The maximum error of determining the “refrigerant–wall” heat transfer coefficient at different degrees of filling the tube cross section with condensate (the flooded sector angle φ was from 30° to 120°) was also estimated. In analyzing the &lt;span&gt;(delta {{bar {t}}_{{{text{max}}}}})&lt;/span&gt; calculation results, the ratio &lt;span&gt;({{{{alpha }_{1}}} mathord{left/ {vphantom {{{{alpha }_{1}}} {{{alpha }_{{{text{av}}}}}}}} right. kern-0em} {{{alpha }_{{{text{av}}}}}}})&lt;/span&gt; was taken as the key parameter. The largest error &lt;span&gt;({{delta }}{{bar {t}}_{{{text{max}}}}})&lt;/span&gt; was recorded in calculating &lt;span&gt;({{bar {t}}_{{text{w}}}})&lt;/span&gt; for tubes made of steel (from 12.3 to 43.5%); the smallest error was recorded for copper tubes (from 2.3 to18%), and intermediate error values were obtained for brass tubes (from 4.4 to 20.1%). The error &lt;span&gt;({{delta }}{{bar {t}}_{{{text{max}}}}})&lt;/span&gt; decreases with increasing the wall thickness δ&lt;sub&gt;w&lt;/sub&gt; of copper tubes and the cooling liquid (water) heat transfer coefficient α&lt;sub&gt;1&lt;/sub&gt;, whereas the wall thickness of steel tubes has almost no influence on the &lt;span&gt;({{delta }}{{bar {t}}_{{{text{max}}}}})&lt;/span&gt; calculation error. It has been determined that the wall temperature &lt;span&gt;({{t}_{{text{w}}}})&lt;/span&gt; at the cross section upper point is always higher than its average value, in view of which an adjusting correction &lt;span&gt;({{delta }}bar {t}_{{max }}^{{{'}}})&lt;/span&gt; was introduced, which helps decrease the error. It has been determined that &lt;span&gt;(delta {{bar {t}}_{{{text{max}}}}})&lt;/span&gt; decreases with increasing the wall thickness. Thus, for a copper wall thickness δ&lt;sub&gt;w&lt;/sub&gt; more than 4 mm, the error does not e","PeriodicalId":799,"journal":{"name":"Thermal Engineering","volume":"73 8","pages":"664 - 671"},"PeriodicalIF":1.3,"publicationDate":"2026-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}