Heat Transfer Theory Research Articles

Hydrothermal Coupling Analysis of Frozen Soil Temperature Field in Stage of Pipe Roof Freezing Method

Taking the Sanya River Mouth Channel project as a case study, this research explores the minimum brine temperature required for the pipe-jacking freezing method during staged freezing. Based on the heat transfer theory of porous media, a three-dimensional model of the actual working conditions was established using COMSOL 6.1 finite element software. By adjusting the brine cooling scheme, the development and distribution patterns of the freezing curtain under different brine temperatures were analyzed. The results indicate that as the staged freezing brine temperature increases, the thickness of the freezing curtain decreases linearly, and the closure of isotherms is inhibited. When the brine temperature is −8 °C, the thickness of the freezing curtain meets the minimum requirement and effectively achieves the freezing effect under both low and high seepage flow conditions. Additionally, seepage significantly affects the formation of the freezing curtain, causing it to shift towards the direction of seepage, with the degree of shift becoming more pronounced as the seepage velocity increases. When the seepage velocity is so high that the thickness of the freezing curtain on one side is less than 2 m, the impact of seepage on the freezing curtain can be reduced by decreasing the hydraulic head difference in the freezing area or by increasing the arrangement of freezing pipes, thereby enhancing the freezing effect.

Analytical Solutions for Thermo-Mechanical Coupling Bending of Cross-Laminated Timber Panels

This study presents analytical solutions grounded in three-dimensional (3D) thermo-elasticity theory to predict the bending behavior of cross-laminated timber (CLT) panels under thermo-mechanical conditions, incorporating the orthotropic and temperature-dependent properties of wood. The model initially utilizes Fourier series expansion based on heat transfer theory to address non-uniform temperature distributions. By restructuring the governing equations into eigenvalue equations, the general solutions for stresses and displacements in the CLT panel are derived, with coefficients determined through the transfer matrix method. A comparative analysis shows that the proposed solution aligns well with finite element results while offering superior computational efficiency. The solution based on the plane section assumption closely matches the proposed solution for thinner panels; however, discrepancies increase as panel thickness rises. Finally, this study explores the thermo-mechanical bending behavior of the CLT panel and proposes a modified superposition principle. The parameter study indicates that the normal stress is mainly affected by modulus and thermal expansion coefficients, while the deflection of the panel is largely dependent on thermal expansion coefficients but less affected by modulus.

EVALUATION OF THE EFFICIENCY OF THE WALNUT DRYING PROCESS IN A CONVECTIVE-VIBRATING DRYER

The drying operation is the most energy-intensive of all technological operations of post-harvest processing of plant agricultural products. Improving the energy efficiency of drying equipment is a top priority in planning and implementing technologies for post-harvest processing of agricultural products, including walnuts. There are a number of ways to increase the efficiency of the drying process, therefore, even at the stage of theoretical and laboratory research, it is important to evaluate the proposed measures and means. Analysis of recent studies and publications shows that the assessment of the efficiency of the drying process was carried out, in most cases, according to two criteria – the coefficient of efficiency and the specific consumption of thermal energy for moisture evaporation. In some cases, along with the energy analysis, the exergetic analysis was also performed. Exergetic analysis allows you to look for ways to increase the efficiency of the drying plant, analyzing the causes of the loss of exergy in the units and substantiating recommendations for improving the cycles of thermal power plants. Laboratory and production tests for drying walnuts were carried out on a convective-vibration dryer. At the same time, the following energy indicators were achieved: the efficiency of the unit was 0.4 with a specific energy consumption for moisture evaporation of 3.91 MJ/kg. In the calculation and design of heat exchangers, including dryers elements of similarity theory are used. In the general theory and practice of heat transfer, including the study of drying processes, about two dozen criteria are used. To assess the effectiveness of the walnut drying process, it is proposed, first of all, to use the criteria of Nusselt and Reynolds. Comparison of similar criteria of two (or more) processes or structural elements can give a decision on the feasibility of using a certain element of the system.

Study on cooling efficiency and mechanism of lithium-ion battery thermal runaway inhibition by additives enhanced water mist based on boiling heat transfer theory

In recent years, fire and explosion accidents caused by thermal runaway (TR) of lithium-ion batteries (LIB) have occurred frequently, which has become one of the main obstacles restricting its development. Therefore, it is urgent to develop fire extinguishing agents with high cooling efficiency to inhibit the growth of TR. The water mist is an effective choice, but it shows poor performance with the rise in cell temperature under TR. In this study, two additives, KCl and the nonionic fluorocarbon surfactant FC-4430, were added to the water mist to improve the cooling efficiency. In addition, the inhibition effect exerted by the modified water mist during the whole process of lithium-ion battery TR was experimentally investigated. Furthermore, the influence of water mist with additives on the Leidenfrost effect in the high temperature range was deduced, and the reinforcement cooling mechanism was analyzed by heat transfer theory. The results show that KCl and FC-4430 can increase the initial cooling rate in the high temperature range by 48.6%–120%. The reinforcement mechanism is attributed to changing the medium's physical parameters with additives. On the one hand, the Leidenfrost point of the droplets on the cell surface is increased, which in turn extends the temperature range of the nucleate boiling stage, and on the other hand, the heat flux density and heat transfer of the water mist in the film boiling state are increased.

Analysis on Fluid-Solid Coupled Heat Transfer of the High Speed Rocket Sled Slipper

Abstract In order to determine the heat transfer situation in the gap between the slipper and the rail in high speed rocket sled test, based on heat transfer theory and the calculation results of the steady-state flow field in the narrow gap between the slipper and the rail, coupled calculations were conducted on the flow field around the slipper and the slipper structure field. With a heating time of 0.1s, aerodynamic heat transfer results of the slipper structure with different gaps and different Mach numbers were obtained. The results showed that the temperature of the slipper increased with the increase of Mach number, and the thermal environment of the slipper was the most severe when the gap was 5mm and Mach number was 6, the internal temperature of the slipper gap was about 200K higher than the outer surface part, and only the outer layer material of the slipper, which is about 1mm thick, is significantly heated.

Research on the Correlation between the Barrel Temperature and the Parameters of Interior Ballistic and Charge

Abstract Aiming at the problem that the barrel life of a large calibre artillery is obviously lower than the international advanced level, and the thermal erosion inside the barrel is serious, based on modern interior ballistic theory and heat transfer theory, a simulation of one-dimensional two-phase flow interior ballistic, heat exchange process between gas-solid two-phase flow and the barrel is carried out. The influence of maximum pressure in bore, charge, propellant explosion temperature, barrel structure and other parameters on the barrel temperature is obtained, and the correlation between the barrel temperature and parameters of interior ballistic and charge is analyzed, providing direction for the design of low-ablation interior ballistic and charge.

CONTROL OF GASOLINE VAPOR CONTENT IN ORGANIZED EMISSIONS OF GAS STATIONS

Goal. To theoretically justify a method for controlling the content of gasoline vapors in the organized emissions of gas stations across the full range of possible concentrations, in order to determine the volume of petroleum product emissions into the atmosphere. Methods. The work uses analytical methods of researching the processes occurring in thermocatalytic sensors, based on the main provisions of the theory of heat and mass transfer and molecular diffusion in gases, evaluation and generalization of research results. The results. It was established that the heat release on the working thermocouple depends on the mass of the fuel components and the product of the lower heat of combustion of the component and its diffusion coefficient. The highest sensitivity of the sensor is characteristic of the most volatile components of gasoline (pentane, benzene, toluene, etc.). For heavier hydrocarbons, the sensitivity of the sensor decreases. The output signal of the thermocatalytic sensor is proportional to the concentration of gasoline vapors in the fuel-air mixture only under the condition that the limiting agent in the mixture that determines the reaction rate is gasoline vapors. Therefore, in order to measure emissions of gasoline vapors in the entire possible range of concentrations, the mixture must be pre-prepared for control by metered feeding into a measuring chamber with both an emissions and atmospheric air sensor. It was determined that the main requirement in this case is to maintain the linearity of the sensor’s output signal across the full range of concentrations, which is achieved under the condition that the diffusion flow of fuel at the maximum possible content of fuel vapors in the emissions does not exceed 80% of the stoichiometric diffusion flow of fuel and oxidizer to the catalytic surface-active element. Scientific novelty. A condition has been established that minimizes the error in measuring the content of petrol vapors in the organized emissions of petrol stations due to composition changes. Specifically, gas analyzers should be calibrated using a petrol vapor mixture, with the heat release during oxidation on the catalytically active element being close to the average heat release from all components. Practical value. The conducted studies allow recommending thermocatalytic sensors for use in monitoring systems of organized emissions of oil and fuel facilities, which allow forming and substantiating requirements for standards of losses and maximum permissible levels of emissions, and speeding up the process of development and implementation of effective measures to reduce them. Key words: emissions, vapors of petroleum products, environment, control, methods, fuel-air mixtures, thermocatalytic sensors.

Analysis of Factors Influencing the Reaction Intensity of Composite Propellants with Different Casing Materials under Slow Cook-off

Abstract By conducting slow cook-off tests on solid composite propellants, the combustion response characteristics of propellants under different casing materials were investigated. Propellant slow cook-off combustion experiments were designed and carried out. Combining the morphological changes of propellant thermal decomposition weight loss with theories of material mechanics and heat transfer, the heat transfer process and physical state of the propellant before ignition were examined to explore their effects on after ignition reaction intensity. The results indicated that the reaction intensity varied with different casing materials. When the casing material is 45# steel, spontaneous ignition occurred at 214.88, with a slider speed of 14.83 m/s, classifying the reaction as deflagration. For 2A12 aluminum casing material, spontaneous ignition occurred at 199.13, with a slider speed of 0.71 m/s, classifying the reaction as combustion. When the casing material is carbon fiber composite, the reaction was classified as combustion. Different casing materials influence the reaction intensity through their thermal physical parameters and casing constraint strength, providing guidance for the selection and design of casing materials and constraints in slow cook-off combustion of motors.

Optimization of bobbin tool friction stir welding parameters of AZ31 magnesium alloy based on FEM and its influence mechanism on mechanical properties

Based on the 3D transient heat transfer theory, the finite element model of bobbin tool friction stir welding (BT-FSW) of AZ31 magnesium alloy sheet is established. The effects of different process parameters on the quality of BT-FSW joint of magnesium alloy were discussed using temperature distribution, mechanical properties, fracture morphology analysis, and EDS element distribution analysis. The results show that in the process of BT-FSW, the cross-section temperature of the plate is symmetrically distributed in an hourglass shape, the AS is slightly lower than that of RS, and the transverse temperature is distributed in an ‘M’ shape. When the rotating speed is 700 rpm and the welding speed is 180 mm/min, the weld surface is smooth, and its ultimate tensile strength can reach 81.82% of the base metal strength. The tensile specimen is quasi-cleavage fracture. When the heat input is insufficient, there are a lot of Al8Mn5 Precipitated phases in the TMAZ fracture zone, which increases the fracture brittleness of the joint. When the heat input is enough, the precipitated phase dissolves evenly, the river-like fracture surface of the joint retains the dimple characteristics, and the mechanical properties are improved.

Study on heat transfer behavior of CFS-PSB composite walls

The cold-formed thin-walled steel (CFS)-paper straw board (PSB) composite walls takes as the research object. The thermal performance of the wall was analyzed by the building heat transfer theory and the finite element analysis software ANSYS, explored the influence of relevant parameters on heat transfer coefficient of composite wall and proposed supplementary correction coefficient for applying the type of composite walls. The heat flux density field, temperature distribution field, node temperature, and heat transfer coefficient of the walls were also obtained. The specific parameters analyzed using this model mainly included the insulation material, web height, thickness of the section steel, width of the flange, length of the hole, number of hole rows, and horizontal and longitudinal spacing of the holes. The findings show that an increase in the web height reduces the heat transfer coefficient of the composite wall, which is conducive to improving the thermal insulation performance of the walls. The CFS-PSB composite wall with a web opening can significantly improve the heat transfer performance of the wall, reduce heat loss, and control the local thermal bridging phenomenon. The hole length, specific gravity of the openings, and number of openings were the main parameters affecting the thermal insulation performance of the walls.

Numerical simulation of thermal deformation of oil distribution sleeve based on heat transfer theory

Numerical simulation of thermal deformation of oil distribution sleeve based on heat transfer theory

Prediction of the Temperature Field in a Tunnel during Construction Based on Airflow–Surrounding Rock Heat Transfer

It is important to determine the ventilation required in the construction of deep and long tunnels and the variation law of tunnel temperature fields to reduce the numbers of high-temperature disasters and serious accidents. Based on a tunnel project with a high ground temperature, with the help of convection heat transfer theory and the theoretical analysis and calculation method, this paper clarifies the contribution of various heat sources to the air demand during tunnel construction, and reveals the important environmental parameters that determine the ventilation value by changing the construction conditions. The results show that increasing the fresh air temperature greatly increases the required air volume, and the closer the supply air temperature is to 28 °C, the more the air volume needs to be increased. The air temperature away from the palm face is not significantly affected by changes in the supply air temperature. Adjusting the wall temperature greatly accelerates the rate of temperature growth. The supply air temperature rose from 15 to 25 °C, while the tunnel temperature at 800 m only increased by 1.5 °C. Over a 50 m range, the wall temperature rose from 35 to 60 degrees Celsius at a rate of 0.0842 to 0.219 degrees Celsius per meter. The total air volume rises and the surface heat transfer coefficient decreases as the tunnel’s cross-section increases. For every 10 m increase in the tunnel diameter, the temperature at 800 m from the tunnel face drops by about 0.5 °C. Changing the distance between the air duct and the tunnel face has little influence on the temperature distribution law. The general trend is that the farther the air duct outlet is from the tunnel face, the higher the temperature is, and the maximum difference is within the range of 50 m~250 m from the tunnel face. The maximum difference between the air temperatures at 12 m and 27 m is 0.79 °C. The geological structure and geothermal background have the greatest influence on the temperature prediction of high geothermal tunnels. The prediction results are of great significance for guiding tunnel construction, formulating cooling measures, and ensuring construction safety.

Temperature field analysis in tunnel construction ventilation with emphasis on duct leakage and thermal conductivity

Mechanical ventilation is the primary measure for cooling during construction of high geo-temperature tunnel. Based on heat transfer theory and characteristics of press-in ventilation, a comprehensive calculation model considering the influence of construction process is proposed, and the reliability of the model is verified by on-site test. The effects of duct leakage rate and thermal conductivity of different excavation length on temperature field distribution during construction ventilation were analyzed based on the prediction model. The following conclusions are drawn: As the excavation length increases, the duct outlet temperature first increases and then decreases. The duct outlet temperature is mainly affected by geo-temperature and boundary control temperature of working face, the air leakage rate and excavation length are not the main factors. The highest temperature in the duct is about 40 °C. The distance between the position of highest temperature and working face increases with the increase of excavation length and decreases with the increase of air leakage rate. With the increase of excavation length, the impact of thermal conductivity on outlet temperature of duct is first enhanced and then stabilized under the same excavation length. The heat-insulated duct can effectively reduce the outlet air temperature and prolong the service life of the duct, while minimizing the air leakage of the duct.

Analysis of Peri-Implantitis Photothermal Therapy Effect According to Laser Irradiation Location and Angle: A Numerical Approach.

In recent years, dental implants have become increasingly popular around the world. However, if the implant is not properly managed, inflammation may occur, and the implant itself may need to be removed. Peri-implantitis is a common inflammation that occurs in dental implants, and various laser treatments have recently been studied to eliminate it. In this study, the situation of removing peri-implantitis using photothermal therapy, one of the various laser treatments, was analyzed theoretically and numerically. The temperature distribution in the tissue for various laser irradiation locations, angles, and power was calculated based on heat transfer theory, and the degree of thermal damage to tissue was analyzed using the Arrhenius damage integral. In addition, the thermally damaged region ratio of inflamed and normal tissue was analyzed using the Arrhenius thermal damage ratio and normal tissue Arrhenius thermal damage ratio to confirm the trend of treatment results for each treatment condition. The results of the study showed that if only the thermal damage to the inflamed tissue is considered, the laser should be angled vertically, and the laser should be applied to the center of the inflamed tissue rather than close to the implant. However, if the thermal damage to the surrounding normal tissue is also considered, it was found that the laser should be applied at 1.0 mm from the right end of the inflamed tissue for maximum effect. This will allow for more accurate clinical treatment of peri-implantitis in the future.

Study on internal heat transfer characteristics of a wind turbine blade

Abstract Based on the theory of computational fluid dynamics and computational heat transfer, ANSYS FLUENT software is used to simulate the internal space flow field and temperature field of a wind turbine blade. The temperature field distribution of the blade was studied under different conditions, and the heating law inside the blade was analyzed. The results show that the temperature of the blade tip, the end face on both sides of the web and the area near the outlet of the wind turbine are obviously lower, and the low temperature phenomenon can be alleviated simply by increasing the inlet speed and temperature of the blade. Compared with increasing the inlet air temperature, increasing the inlet air speed of the blade can more effectively enhance the convective heat transfer of the air, so as to increase the temperature of the blade surface rapidly. When the inlet wind speed of the wind turbine blade is 30m/s and the inlet temperature is 100°C, the average temperature of the outer wall of the blade is about 50°C, which can meet working requirements of the blade. It takes about 20 seconds from the beginning of heating to the internal temperature of the blade reaching a stable state.

Bridging micro nature with macro behaviors for granular thermal mechanics

The connection between micro-level characteristics and macroscopic properties in granular heat transfer and mechanics is fundamental and crucial. This study proposes a novel discrete element approach incorporating granular heat transfer, contact bonding, and granular stress tensor models to investigate the mechanical and thermal responses of continuum media composed of constituent spheres. Eight benchmark tests were devised to bridge the long-standing gap between micro and macro properties in granular materials. Through these tests, the numerical solutions obtained from discrete element modeling match well with existing analytical or finite element solutions derived from continuum-based theory. This validation underscores the rationality and reliability of the granular heat transfer model, contact bonding model, and granular stress tensor model. Moreover, the study highlights the consistency between continuum-based theory and discontinuum-based theory. A minor distinction between continuum-based models and discrete element models emerges near the boundaries due to variations in the specification of boundary conditions. This discrepancy can be clarified by Saint-Venant's Principle, thus validating the accuracy of the microscale heat transfer and mechanics theory for granular materials. Five mono-disperse packing structures, including simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), hexagonal close packing (HCP), and random packing (Random), were further analyzed to examine their influence on heat transfer performance. Numerical results reveal that higher coordination numbers and solid volume fractions correspond to higher apparent thermal conductivity of granular assemblies, thus elucidating the connection between micro packing configurations and macroscopic heat transfer properties. The apparent thermal conductivity for different crystal configurations follows the sequence: HCP ≒ FCC > BCC ≒ Random > SC. To improve the accuracy and physical relevance of the proposed model, the effect of particle contact area needs to be further incorporated into the granular heat transfer model.

Effective ignition energy for capacitor short-circuit discharge in explosive environments

Capacitors short-circuit discharge in an explosive environment can ignite and detonate the surrounding explosive media, causing dangerous accidents. At low voltages, this kind of discharge constitutes a micro-nano discharge; because the discharge gaps here are of the order of only microns to nanometers, the discharge process, electrode energy consumption, explosive media ignition energy, and other energy relationships are unclear. To study the relationships between the capacitor storage energy and various kinds of dissipation energies under short-circuit discharge, a model comprising conical and spherical cylinder microbumps is proposed based on the cathode surface morphology obtained by three-dimensional profiling and scanning electron microscopy, respectively. Then, the second-order non-chi-squared differential equations were established based on the principle of energy conservation and heat balance to deduce the relationships between the cathode surface temperature and height of the microbump, conical angle, and spherical radius; further, the energy consumed by the anode surface is calculated based on the theory of heat transfer. Using heat conduction theory, the energy consumed by the microbumps on the cathode surface is calculated, and the energy consumed on the anode surface is deduced using the surface heat source as the loading heat source. The residual energy of the capacitor is calculated from the discharge time and voltages before and after discharge, and the effective energy of the gas is calculated using the law of conservation of energy. Finally, the discharge channel energy, electrode energy consumption, and end residual energy of the discharge capacitor are used to derive the effective ignition energy of the explosive gas. This research is of great significance for the design of intrinsically safe circuits with high power.

Flameless venting characteristics and design model of micro-nano PMMA dust explosion

The effects of Fe–Ni foam thickness and dust size on flame propagation, reduced overpressure, and venting efficiency in 30 μm and 150 nm polymethyl methacrylate (PMMA) dust explosions were investigated. The flame quenching mechanism was revealed by coupling the heat transfer and flow of the dust flame within the Fe–Ni foam. It is found that micron dust is more prone to quenching than nano dust, and the differences in the quenching process of micro-nano dust are explained by combining the dust combustion kinetics and the theory of inter-particle heat transfer. The pressure venting mechanism of micro-nano dust was analysed under different thicknesses of Fe–Ni foam, and the thermal expansion effect of the flame passing through the Fe–Ni foam and its flow resistance significantly increased the reduced explosion overpressure. The flow continuity of the micro-nano dust was classified by means of the Knudsen number (Kn), which elucidates the effect of dust size differences on the pressure evolution. A prediction model for the maximum reduced explosion overpressure is proposed based on the explosion pressure venting of micro-nano dust. Changes in vented pressure have a direct impact on the efficiency of flameless venting. Nano-dust has an efficiency of more than 20 % lower than that of micron dust.

Non-Fourier computations of heat and mass transport in nanoscale solid-fluid interactions using the Galerkin finite element method

PurposeTo improve the thermal performance of base fluid, nanoparticles of three types are dispersed in the base fluid. A novel theory of non-Fourier heat transfer is used for design and development of models. The thermal performance of sample fluids is compared to determine which types of combination of nanoparticles are the best for an optimized enhancement in thermal performance of fluids. This article aims to: (i) investigate the impact of nanoparticles on thermal performance; and (ii) implement the Galerkin finite element method (GFEM) to thermal problems.Design/methodology/approachThe mathematical models are developed using novel non-Fourier heat flux theory, conservation laws of computational fluid dynamics (CFD) and no-slip thermal boundary conditions. The models are approximated using thermal boundary layer approximations, and transformed models are solved numerically using GFEM. A grid-sensitivity test is performed. The accuracy, correction and stability of solutions is ensured. The numerical method adopted for the calculations is validated with published data. Quantities of engineering interest, i.e. wall shear stress, wall mass flow rate and wall heat flux, are calculated and examined versus emerging rheological parameters and thermal relaxation time.FindingsThe thermal relaxation time measures the ability of a fluid to restore its original thermal state, called thermal equilibrium and therefore, simulations have shown that the thermal relaxation time associated with a mono nanofluid has the most substantial effect on the temperature of fluid, whereas a ternary nanofluid has the smallest thermal relaxation time. A ternary nanofluid has a wider thermal boundary thickness in comparison with base and di- and mono nanofluids. The wall heat flux (in the case of the ternary nanofluids) has the most significant value compared with the wall shear stresses for the mono and hybrid nanofluids. The wall heat and mass fluxes have the highest values for the case of non-Fourier heat and mass diffusion compared to the case of Fourier heat and mass transfer.Originality/valueAn extensive literature review reveals that no study has considered thermal and concentration memory effects on transport mechanisms in fluids of cross-rheological liquid using novel theory of heat and mass [presented by Cattaneo (Cattaneo, 1958) and Christov (Christov, 2009)] so far. Moreover, the finite element method for coupled and nonlinear CFD problems has not been implemented so far. To the best of the authors’ knowledge for the first time, the dynamics of wall heat flow rate and mass flow rate under simultaneous effects of thermal and solute relaxation times, Ohmic dissipation and first-order chemical reactions are studied.

Analysis and Experiment of Thermal Field Distribution and Thermal Deformation of Nut Rotary Ball Screw Transmission Mechanism

This study designs a differential dual-drive micro-feed mechanism, superposing the two “macro feed motions” (“motor drive screw” and “motor drive nut”) using the same transmission of “the nut rotary ball screw pair” structure. These two motions are almost equal in terms of speed and turning direction, thus the “micro feed” can be obtained. (1) Background: Thermal deformation is the primary factor that can restrict the high-precision micro-feed mechanism and the distribution of heat sources differs from that of the conventional screw single-drive system owing to the structure and motion features of the transmission components. (2) Discussion: This study explores the thermal field distribution and thermal deformation of the differentially driven micro-feed mechanism when two driving motors are combined at different speeds. (3) Methods: Based on the theory of heat transfer, the differential dual-drive system can be used as the research object. The thermal equilibrium equations of the micro-feed transmission system are established using the thermal resistance network method, and a thermal field distribution model is obtained. (4) Results: Combined with the mechanism of thermal deformation theory, the established thermal field model is used to predict the axial thermal deformation of the differential dual-drive ball screw. (5) Conclusions: Under the dual-drive condition, the steady-state thermal error of the nut-rotating ball screw transmission mechanism increases with the increase in nut speed and composite speed and is greater than the steady-state thermal error under the single screw drive condition. After reaching the thermal steady state, the measured thermal elongation at the end of the screw in the experiment is approximately 10.5 μm and the simulation result is 11.98 μm. The experimental measurement result demonstrates the accuracy of the theoretical analysis model for thermal error at the end of the screw.