本文提出一種應用於電動馬達轉子冷卻之旋轉式圓柱環路脈衝熱管（rotating cylindrical pulsating heat pipe, RCPHP），並首次建立其汽–液塞振盪頻譜特徵與熱傳性能間之頻譜–熱傳對應關係。本文針對三種具有不同毛細通道幾何結構之 RCPHP（RCPHP-A、B、C），在涵蓋靜止與旋轉條件（Ca）、不同加熱功率（Bo）與冷凝段熱阻（Rth,con）之整體測試範圍內進行系統性實驗量測，深入分析其熱–流體動力耦合行為。量測與分析項目包括蒸發段與冷凝段之暫態壓力與溫度訊號、紐賽數、整體熱阻以及等效熱導率。
研究結果顯示，本文所提出之 RCPHP 具備獨特之分流交織結構，依據並聯熱阻定理與疊加原理，其 (Rth − Rth,con) 數值範圍可大幅降低至 0.046–0.38 K/W，顯著優於既有文獻中靜止式（0.17–3.99 K/W）與旋轉式（0.29–3.67 K/W）脈衝熱管，展現優異之相變熱傳性能。頻譜分析表明，旋轉狀態下之離心力會削弱原先由重力主導之通道差異，使壓力訊號頻譜由靜止條件下之多主導頻率寬頻分佈，收斂為以毛細通道模態（f1）與環狀歧管模態（f2）為主之雙主導頻率型態。其中，毛細通道之局部塞流動力頻率 f1 對操作參數具有明確響應，並主導蒸發段與冷凝段紐賽數、熱阻與等效熱導率之演化，進而成功建立旋轉式脈衝熱管之頻譜–熱傳對應關係。
基於上述物理機制，本文進一步建立各 RCPHP 之無因次振盪頻率 f1*、熱阻與等效熱導率經驗關係式，並導入經實驗驗證之三維數值模型中，以評估 RCPHP 應用於永磁同步馬達（permanent magnet synchronous motor, PMSM）之冷卻效能。模擬結果顯示，將 RCPHP 配置於轉子後，可提供強化之軸向熱傳能力，有效抑制轉子內部之軸向溫度梯度，進而顯著降低關鍵轉子磁鐵與鋼框之局部最高溫度（Tmax）。於 S1–S3 操作條件下，轉子磁鐵與鋼框之冷卻效能指標 η 分別可達 5.48–8.5% 與 5.5–8.63%。此外，RCPHP 不需額外輔助冷卻裝置與附加泵浦功耗，即可有效改善小型高速馬達旋轉組件之熱管理問題，顯示其具備應用於旋轉機械冷卻之潛力。

A case study that devises a novel tubular pulsating heat pipe (TPHP) with cooling applications to rotor in an electric motor unveils the first-time class spectrum-thermal synergy to signify the hydrothermal characteristics. The pressures and Nusselt numbers of evaporator and condenser, overall thermal resistance and effective thermal conductivity of three TPHPs with geometric variances in capillary channels are measured at the rotating speeds of 0, 300, 500, 700, and 900 rev/min across various heating and cooling conditions. Compared to the broad ranges of evaporator-to-condenser thermal resistance with the upper and lower bounds being 0.17 to 3.99 K/W (static) and 0.29 to 3.67 K/W (rotating) pulsating heat pipes in literature, the current range of 0.046 to 0.38 K/W highlights the enhanced thermal performance of the proposed rotating TPHPs. The correlation between primary thermal performance metrics of the rotating TPHPs and evaporator pressure signatures is interrogated to elucidate the spectrum-thermal synergy between the vapor/liquid slug dynamics and the heat transfer performances ascribed to variations in heat flux, rotational speed and condensation condition. Based on the dominant vapor/liquid oscillation frequencies, a set of heat transfer correlations for each rotating TPHP is developed. These correlations, integrated into an experimentally verified numerical model, enable a quantitative assessment of cooling efficacy of TPHP under various rotor speeds and electromagnetic losses. Integrating TPHPs into the rotor of a permanent magnet synchronous motor lowered peak temperatures in the magnet stripes and steel frame by 5.48–8.5% and 5.5–8.63%. This innovation offers an efficient, passive cooling attribute that functions without extra power or accessories. Such a self-driven mechanism endorses the cooling potential of TPHP for the thermal management of high-speed rotating components.

[1] A.T. de Almeida, F.J.T.E. Ferreira, J. Fong, Perspectives on electric motor market transformation for a net zero carbon economy, Energies (2023) 16(3):1248.
[2] R. Wrobel and P. H. Mellor, A general cuboidal element for three-dimensional thermal modelling, IEEE Transactions on Magnetics, 46 (2010), 3197-3200.
[3] M. Shi, T. Li, S. Yuan, L. Zhang, Y. Ma, Y. Gao, Iron loss and temperature rise analysis of a transformer core considering vector magnetic hysteresis characteristics under direct current bias, Materials (2024) 3767.
[4] Y. Zhang, Y. Song, S. Sun, S. Yu, Coupled magnetic-thermal fields analysis of permanent magnet synchronous motor for ship propulsion based on a 3D analytical model, Applied Thermal Engineering, 279 (2025) 127895.
[5] K.N. Gyftakis, J.L. af G.H. de Siqueira, and S.V. Zidani, Efficiency increase of an induction motor by improving cooling performance, IEEE Transactions on Energy Conversion, 17 (2002) 1-6.
[6] Shewalkar, A.G., Dhoble, A.S. & Thawkar, V.P. Review on cooling techniques and analysis methods of an electric vehicle motor. Journal of Thermal Analysis and Calorimetry, 149 (2024) 5919–5947.
[7] X. Li, X. Zhao, Z. Zhang, A. Avelin, S. Liu, H. Li, Selecting cooling methods for electric motors, Applied Thermal Engineering, 274 (2025) 126554.
[8] M. Asli, P. König, D. Sharma, E. Pontika, J. Huete, K.R. Konda, A. Mathiazhagan, T. Xie, K. Höschler, P. Laskaridis, Thermal management challenges in hybrid-electric propulsion aircraft, Progress in Aerospace Sciences, 144 (2024) 100967.
[9] S. Hyeon, C. Kim, K.-S. Lee, Thermal enhancement of an air-cooled motor with a flow guide, Int. J. Heat Mass Transfer, 183 (2022) 122228.
[10] T. Gammaidoni, J. Zembi, M. Battistoni, G. Biscontini, A. Mariani, CFD Analysis of an electric motor's cooling system: model validation and solutions for optimization, Case Studies in Thermal Engineering, 49 (2023) 103349.
[11] C. Tang, Z. Yu, J. Fu, J. Yang, H. Jiang, Temperature field analysis of an air-water composite cooling high-speed generator, Case Studies in Thermal Engineering, 65 (2025) 105646.
[12] Y. Jiang, Y. Lu, L. Chen, E. Zheng, C. Wang, Z. Luo, Y. Shi, X. Wang, L. Hu, S. Zhao, Modeling, analysis, and optimization of the asymmetric cooling system for a hybrid oil-cooled motor, Applied Thermal Engineering, 270 (2025) 126215.
[13] Z. Zhang, Q. Song, B. Ahmed, Y. Han, Fluid and thermal effect on temperature-dependent power increase of electric vehicle’s permanent magnet synchronous motor using compound water cooling method, Case Studies in Thermal Engineering, 65 (2025) 105543.
[14] Y. Kim, T.Y. Beom, T.W. Ha, S.W. Lee, I.G. Hwang, D.K. Kim, Study on oil cooling method for the powertrain of electric vehicles, Int. J. Heat Mass Transfer, 246 (2025) 127073.
[15] J. Hu, Z. Yao, Y. Xin, Z. Sun, Design and optimization of the jet cooling structure for permanent magnet synchronous motor, Applied Thermal Engineering, 250 (2025) 125051.
[16] J.-X. Wang, Y.-Z. Li, S.-N. Wang, H.-S. Zhang, X. Ning, W. Guo, Experimental investigation of the thermal control effects of phase change material based packaging strategy for on-board permanent magnet synchronous motors, Energy Conversion and Management, 123 (2016) 232-242.
[17] E.M.C. Contreras, G.A. Oliveira, E.P.B. Filho, Experimental analysis of the thermohydraulic performance of graphene and silver nanofluids in automotive cooling system, Int. J. Heat Mass Transfer, 132 (2019) 375-387.
[18] A. Tikadar, D. Johnston, N. Kumar, Y. Joshi, S. Kumar, Comparison of electro-thermal performance of advanced cooling techniques for electric vehicle motors, Applied Thermal Engineering, 183 (2021) 116182.
[19] C. Guo, L. Long, Y. Wu, K. Xu, H. Ye, Electromagnetic-thermal coupling analysis of a permanent-magnet in-wheel motor with cooling channels in the deepened stator slots, Case Studies in Thermal Engineering, 35 (2022) 102158.
[20] J.L. Anibal, C.A. Mader, J.R.R.A. Martins, Aerodynamic shape optimization of an electric aircraft motor surface heat exchanger with conjugate heat transfer constraint, Int. J. Heat Mass Transfer, 189 (2022) 122689.
[21] B. Li, Y. Yuan, P. Gao, Z. Zhang, G. Li, Cooling structure design for an outer-rotor permanent magnet motor based on phase change material, Thermal Science and Engineering Progress, 34 (2022) 101406.
[22] S. Kim, S. Lee, D.G. Kang, M.S. Kim, Motor cooling method using flow boiling of two-phase refrigerant and its analysis with lumped parameter thermal model, Int. J. Thermal Sciences, 192 (2023) 108458.
[23] Z. Li, W. Zhu, B. Wang, Q. Wang, J. Du, B. Sun, Optimization of cooling water jacket structure of high-speed electric spindle based on response surface method, Case Studies in Thermal Engineering, 48 (2023) 103158.
[24] W. Chen, Z. Mao, W. Tian, Water cooling structure design and temperature field analysis of permanent magnet synchronous motor for underwater unmanned vehicle, Applied Thermal Engineering, 240 (2024) 122243.
[25] Z. Chen, Z. Yu, J. Fu, J. Yang, Analysis and design of air-heat pipe composite cooling of high power density motor, Applied Thermal Engineering, 236 (2024) 121496.
[26] T. Zhang, J. Yao, S. Liao, X. Liu, Y. Xu, S. Yang, Cooling enhancement of permanent magnet synchronous motor coupled with heat pipes for electric vehicle, Applied Thermal Engineering, 279 (2025) 127572.
[27] R. Regan, K. Saviers, W. Zhao, A. Kuczek, J. Tangudu, J.A. Weibel, Embedded two-phase cooling in an additively manufactured stator prototype for a novel high-power-density electric motor concept, Applied Thermal Engineering, 276 (2025) 126918.
[28] X. Li, X. Zhao, Z. Zhang, S. Liu, C. Zhang, H. Guo, Experimental study on heat pipe performance and a case study on electric motor cooling, Case Studies in Thermal Engineering, 72 (2025) 106419.
[29] R. Regan, K. Saviers, A. Alahyari, A. Kuczek, J. Tangudu, J.A. Weibel, Two-phase flow distribution and stability of R-1233zd(E) in a system of heated parallel microchannels with a hierarchical manifold, Int. J. Heat Mass Transfer, 258 (2026) 128298.
[30] S. Luo, W. Li, B. Huang, J. Hong, L. Wang, H. Wang, Study on temperature distribution of permanent magnet synchronous motor for electric vehicles under three-port hybrid cooling structure, Case Studies in Thermal Engineering, 78 (2026) 107727.
[31] J. Song, J. Li, Z. Hu, K. Yan, L. Chen, M. Ouyang, Advance research of oil-water dual-jacket cooling system for PMSM motors used in heavy-duty trucks, Applied Thermal Engineering, 280 (2026) 129729.
[32] Z. Pan, L. Shi, J. Hu, Research on water-cooling heat dissipation of modular stator built-in waterway permanent magnet synchronous motor, Int. J. Thermal Sciences, 222 (2026) 110563.
[33] X. Sun, D. Zhang, Y. Wang, Z. Li, Z. Cheng, R. Ni, A hybrid oil cooling strategy for thermal management of high power density PMSMs, Case Studies in Thermal Engineering, 78 (2026) 107605.
[34] A.S. Fawzal, R.M. Cirstea, T.J. Woolmer, M. Dickison, M. Blundell, K.N. Gyftakis, Air inlet/outlet arrangement for rotor cooling application of axial flux PM machines, Applied Thermal Engineering, 130 (2018) 1520-1529.
[35] F. Li, J. Gao, X. Shi, F. Liang, K. Zhu, Experimental investigation of single loop thermosyphons utilized in motorized spindle shaft cooling, Applied Thermal Engineering, 134 (2018) 229-237.
[36] S.W. Chang, and W.L. Cai, Thermal impact of integrated bore cooling with impinging jets and turbulators in rotating shaft of interior permanent magnet electric motor, Thermal Science and Engineering Progress, 57 (2025) 103164.
[37] S.W. Chang, and W.L. Cai, Thermal performance of two-phase thermosyphon loop in rotating thin pad, Int. J. Thermal Sciences, 112 (2017) 270-288.
[38] T.-M. Liou, S.W. Chang, W.L. Cai, I-A. Lan, Thermal fluid characteristics of pulsating heat pipe in radially rotating thin pad, Int. J. Heat and Mass Transfer, 131 (2019) 273-290.
[39] H. Wang, C. Zhang, L. Guo, X. Li, Novel revolving heat pipe cooling structure of permanent magnet synchronous motor for electric vehicle, Applied Thermal Engineering, 236 (2024) 121641.
[40] D. Zhuang, Y. Tang, A. Yang , Y. Wu, X. Zhang, X. Li, S. Zheng, A numerical simulation of V shaped heat pipe in the PMSM rotor case, Int. J. Heat Mass Transfer, 256 (2026) 128176.
[41] S. Khandekar, N. Dollinger, M. Groll, Understanding operational regimes of closed loop pulsating heat pipes: An experimental study, International Journal of Heat and Mass Transfer, 46 (2003) 707–719.
[42] Y.J. Youn, S.J. Kim, Fabrication and evaluation of a silicon-based micro pulsating heat spreader, Sensors and Actuators A, 174 (2012) 189–197.
[43] J. Qu, H. Wu, P. Cheng, Start-up, heat transfer and flow characteristics of silicon-based micro pulsating heat pipes, International Journal of Heat and Mass Transfer, 55 (2012) 6109–6120.
[44] J. Wang, Z. Wang, M. Li, Thermal performance of pulsating heat pipes with different heating patterns, Applied Thermal Engineering, 64 (2014) 209–212.
[45] G.H. Kwon, S.J. Kim, Experimental investigation on the thermal performance of a micro pulsating heat pipe with a dual-diameter channel, International Journal of Heat and Mass Transfer, 89 (2015) 817–828.
[46] A. Takawale, S. Abraham, A. Sielaff, et al., A comparative study of flow regimes and thermal performance between flat plate pulsating heat pipe and capillary tube pulsating heat pipe, Applied Thermal Engineering, 149 (2019) 613–624.
[47] G. Rouaze, J.B. Marcinichen, et al., Simulation and experimental validation of pulsating heat pipes, Applied Thermal Engineering, 196 (2021) 117271.
[48] S. Rudresha, E.R. Babu, R. Thejaraju, Experimental investigation and influence of filling ratio on heat transfer performance of a pulsating heat pipe, Thermal Science and Engineering Progress, 38 (2023) 101649.
[49] L. Pagliarini, N. Iwata, F. Bozzoli, Pulsating heat pipes: Critical review on different experimental techniques, Experimental Thermal and Fluid Science, 148 (2023) 110980.
[50] E.R. Babu, N.C. Reddy, A. Babbar, et al., Characteristics of pulsating heat pipe with variation of tube diameter, filling ratio, and SiO₂ nanoparticles: Biomedical and engineering implications, Case Studies in Thermal Engineering, 55 (2024) 104065.
[51] D. Zhang, L. Wang, B. Xu, et al., Experimental and simulation study on flow heat transfer characteristics of flat pulsating heat pipe with wide and narrow interphase channels, Applied Thermal Engineering, 245 (2024) 122806.
[52] Y. Dai, R. Zhang, Z. Qin, et al., Research on the thermal performance and stability of three-dimensional array pulsating heat pipe for active/passive coupled thermal management application, Applied Thermal Engineering, 245 (2024) 122793.
[53] A.K. Shukla, S. Kumar, A novel method for introducing asymmetry in pulsating heat pipes to enhance performance, International Journal of Heat and Mass Transfer, 238 (2025) 126436.
[54] Y. Hu, G. Meng, Y. Yao, et al., Experimental investigation on the start-up and thermal performance of nanofluid-based pulsating heat pipe, Applied Thermal Engineering, 259 (2025) 124897.
[55] Y. Xu, Y. Xue, S. Tang, et al., Experimental investigation on thermal characteristics and performance enhancement of pulsating heat pipe with ultra-maximum hydraulic diameter, Applied Thermal Engineering, 267 (2025) 125702.
[56] Y. Liu, M. Wei, D. Dan, et al., Experimental study on flow and heat transfer characteristics of a pulsating heat pipe under vertical vibration conditions, Applied Thermal Engineering, 267 (2025) 125701.
[57] J. Lee, S.J. Kim, Effect of channel geometry on the operating limit of micro pulsating heat pipes, International Journal of Heat and Mass Transfer, 107 (2017) 204–212.
[58] A. Bakhirathan, G.K.K. Lachireddi, Performance evaluation of branched micro heat pipes with different branch angles for electronic thermal management, Thermal Science and Engineering Progress, 54 (2026) 102811.
[59] F. Song, D. Ewing, C.Y. Ching, Fluid flow and heat transfer model for high-speed rotating heat pipes, International Journal of Heat and Mass Transfer, 46 (2003) 4393–4401.
[60] T.-M. Liou, S.W. Chang, W.L. Cai, I.-A. Lan, Thermal fluid characteristics of pulsating heat pipe in radially rotating thin pad, International Journal of Heat and Mass Transfer, 131 (2019) 273–290.
[61] S. Fang, C. Zhou, Y. Zhu, Z. Qian, C. Wang, Review on research progress of pulsating heat pipes, Inventions, 9 (2024) 86.
[62] J.S. Peh, S.J. Kim, A review on advancements in structural design of pulsating heat pipe, Thermal Science and Engineering Progress, 59 (2025) 103361.
[63] F. Luo, C. Ma, J. Liu, L. Zhang, S. Wang, Theoretical and experimental study on rotating heat pipe towards thermal error control of motorized spindle, International Journal of Thermal Sciences, 185 (2023) 108095.
[64] L. Zhu, L. Zhu, S. Wang, Experimental investigation on rotational oscillating heat pipe for in-wheel motor cooling of urban electric vehicle, International Communications in Heat and Mass Transfer, 151 (2024) 107209.
[65] Z. Chen, Z. Yu, J. Fu, J. Yang, Analysis and design of air-heat pipe composite cooling of high power density motor, Applied Thermal Engineering, 236 (2024) 121495.
[66] J. Einolander, R. Lahdelma, Multivariate copula procedure for electric vehicle charging event simulation, Energy, 238 (2022) 121718.
[67] A. Nikulin, M. Bernagozzi, N. Miche, Y. Grosu, M. Marengo, E. Palomo del Barrio, Pulsating heat pipe performance enhancement through porous metallic surfaces produced via physical dealloying, International Journal of Heat and Mass Transfer, 234 (2024) 126045.
[68] H. Aziza, R. Boubaker, N. Iwata, V. Dupont, S. Harmand, Assessment of thermal performance in novel pulsating heat pipes for cooling a five-phase permanent magnet synchronous machine, Applied Thermal Engineering, 274 (2025) 126662.
[69] J. Lee, and S.J. Kim, Effect of channel geometry on the operating limit of micro pulsating heat pipes, Int. J. Heat and Mass Transfer, 107 (2017) 204-212.
[70] S.J. Kline, F.A. McClintock, Describing uncertainties in single sample experiments, Mech. Eng. 75, pp. 3-8, 1953.
[71] S.W. Chang, P.-S. Wu, Y.-S. Hong, Y.-C. Hsu, S.-H. Huang, Thermal characterization of an interior permanent magnet electric motor, Results in Engineering, 20 (2023) 101540.
[72] W.L. Cai, S.W. Chang, W.N. Liu, Y.S. Li, Hydrothermal characteristic of pulsating heat pipe arranged in tubular loop, The 10th International Conference on New Energy and Future Energy System (NEFES 2025), July 21-24, 2025, Matsue, Japan.
[73] Y. Zhang, A. Faghri, M.B. Shafii, Analysis of liquid–vapor pulsating flow in a U-shaped miniature tube, Int. J. Heat Mass Transfer, 45 (2002) 2501-2508.
[74] D. Koutsoyiannis, D. Clausius–Clapeyron equation and saturation vapour pressure: simple theory reconciled with practice, European Journal of Physics, 33 (2012) 295-305.
[75] K. On-ai, N. Kammuang-lue, P. Terdtoon, P. Sakulchangsatjatai, Implied physical phenomena of rotating closed-loop pulsating heat pipe from working fluid temperature, Applied Thermal Engineering, 148, (2019) 1303-1309.
[76] J. Wang, Z. Wang, M. Li, Thermal performance of pulsating heat pipes with different heating patterns, Applied Thermal Engineering, 64 (2014) 209–212.
[77] E.R. Babu, N.C. Reddy, A. Babbar, A. Chandrashekar, R. Kumar, P.S. Bains, M. Alsubih, S. Islam, S.K. Joshi, A. Rizal, M.I. Ammarullah, Characteristics of pulsating heat pipe with variation of tube diameter, filling ratio, and SiO2 nanoparticles: Biomedical and engineering implications, Case Studies in Thermal Engineering, 55 (2024) 104065.
[78] D. Zhang, L. Wang, B. Xu, Q. Li, S. Wang, Z. An, Experimental and simulation study on flow heat transfer characteristics of flat pulsating heat pipe with wide and narrow interphase channels, Applied Thermal Engineering, 245 (2024) 122806.
[79] Y. Bao, H. Wang, S. Shao, Experimental study on heat transfer characteristics of a novel pulsating heat pipe with shunt-confluence structure, International Communications in Heat and Mass Transfer, 162 (2025) 108616.
[80] N. Qian, M. Marengo, F. Jiang, X. Chen, Y. Fu, J. Xu, Pulsating heat pipes filled with acetone and water under radial rotation conditions: Heat transfer performance and semi-empirical correlation, International Communications in Heat and Mass Transfer, 150 (2024) 107172.
[81] M. Ebrahimi Dehshali, M.A. Zazari, M.B. Shafii, Thermal performance of rotating closed-loop pulsating heat pipes: Experimental investigation and semi-empirical correlation, International Journal of Thermal Sciences, 123 (2018) 14–26.
[82] T.J. Shimokusu, B. Drolen C. Wilson, J. Didion, G. Wehmeyer, Strain gauge measurements of an oscillating heat pipe from startup to stable operation, Applied Thermal Engineering, 233 (2023) 121118.