Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

High power and energy density dynamic phase change materials using pressure-enhanced close contact melting


Phase change materials show promise to address challenges in thermal energy storage and thermal management. Yet, their energy density and power density decrease as the transient melt front moves away from the heat source. Here, we propose an approach that achieves the spatial control of the melt-front location of pure phase change materials using pressure-enhanced close contact melting. Using paraffin wax, we demonstrate effective energy density and power density of 230 J cm3 and 0.8 W cm3, respectively. Using gallium, we achieve effective energy density of 480 J cm3 and power density of 1.6 W cm3. Through experimentally validated physics-based analytical and finite element models, we show that our system enables the stabilization of surface temperatures at heat fluxes approaching 3 kW cm2. This approach uses pure and cost-effective materials, overcoming complexities and cost of composite phase change materials. We report design guidelines for integrating our approach in thermal management and thermal energy storage applications.

Your institute does not have access to this article

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Comparison of conventional and dynPCM.
Fig. 2: Thermal experiments.
Fig. 3: Simulation and analytical model of dynPCM performance.
Fig. 4: Melting and solidification cycling of a dynPCM.
Fig. 5: Performance of different dynPCMs.

Data availability

All data generated or analysed during this study are included in the published article and its Supplementary Information.

Code availability

All Python, COMSOL and ANSYS files generated for this work have been uploaded to a public repository at


  1. Moore, A. L. & Shi, L. Emerging challenges and materials for thermal management of electronics. Mater. Today 17, 163–174 (2014).

    Article  Google Scholar 

  2. van Erp, R., Soleimanzadeh, R., Nela, L., Kampitsis, G. & Matioli, E. Co-designing electronics with microfluidics for more sustainable cooling. Nature 585, 211–216 (2020).

    Article  Google Scholar 

  3. Wang, Q., Jiang, B., Li, B. & Yan, Y. A critical review of thermal management models and solutions of lithium-ion batteries for the development of pure electric vehicles. Renew. Sustain. Energy Rev. 64, 106–128 (2016).

    Article  Google Scholar 

  4. Hao, M., Li, J., Park, S., Moura, S. & Dames, C. Efficient thermal management of Li-ion batteries with a passive interfacial thermal regulator based on a shape memory alloy. Nat. Energy 3, 899–906 (2018).

    Article  Google Scholar 

  5. Fleischer, A. S. Cooling our insatiable demand for data. Science 370, 783–784 (2020).

    Article  Google Scholar 

  6. Wang, C. et al. A thermal management strategy for electronic devices based on moisture sorption-desorption processes. Joule 4, 435–447 (2020).

    Article  Google Scholar 

  7. Ling, Z. et al. Review on thermal management systems using phase change materials for electronic components, Li-ion batteries and photovoltaic modules. Renew. Sustain. Energy Rev. 31, 427–438 (2014).

    Article  Google Scholar 

  8. Chen, J. et al. Effects of different phase change material thermal management strategies on the cooling performance of the power lithium ion batteries: a review. J. Power Sources 442, 227228 (2019).

    Article  Google Scholar 

  9. Fan, L. & Khodadadi, J. M. Thermal conductivity enhancement of phase change materials for thermal energy storage: a review. Renew. Sustain. Energy Rev. 15, 24–46 (2011).

    Article  Google Scholar 

  10. Qureshi, Z. A., Ali, H. M. & Khushnood, S. Recent advances on thermal conductivity enhancement of phase change materials for energy storage system: a review. Int. J. Heat. Mass Transf. 127, 838–856 (2018).

    Article  Google Scholar 

  11. Yang, T., King, W. P. & Miljkovic, N. Phase change material-based thermal energy storage. Cell Rep. Phys. Sci. 2, 100540 (2021).

    Article  Google Scholar 

  12. Mohamed, S. A. et al. A review on current status and challenges of inorganic phase change materials for thermal energy storage systems. Renew. Sustain. Energy Rev. 70, 1072–1089 (2017).

    Article  Google Scholar 

  13. Liu, M., Saman, W. & Bruno, F. Review on storage materials and thermal performance enhancement techniques for high temperature phase change thermal storage systems. Renew. Sustain. Energy Rev. 16, 2118–2132 (2012).

    Article  Google Scholar 

  14. Yang, X.-H., Tan, S.-C., He, Z.-Z. & Liu, J. Finned heat pipe assisted low melting point metal PCM heat sink against extremely high power thermal shock. Energy Convers. Manag. 160, 467–476 (2018).

    Article  Google Scholar 

  15. Mahmoud, S., Tang, A., Toh, C., Al-Dadah, R. & Soo, S. L. Experimental investigation of inserts configurations and PCM type on the thermal performance of PCM based heat sinks. Appl. Energy 112, 1349–1356 (2013).

    Article  Google Scholar 

  16. Wang, C., Lin, T., Li, N. & Zheng, H. Heat transfer enhancement of phase change composite material: copper foam/paraffin. Renew. Energy 96, 960–965 (2016).

    Article  Google Scholar 

  17. Yang, T. et al. A composite phase change material thermal buffer based on porous metal foam and low-melting-temperature metal alloy. Appl. Phys. Lett. 116, 071901 (2020).

    Article  Google Scholar 

  18. Mills, A., Farid, M., Selman, J. R. & Al-Hallaj, S. Thermal conductivity enhancement of phase change materials using a graphite matrix. Appl. Therm. Eng. 26, 1652–1661 (2006).

    Article  Google Scholar 

  19. Ji, H. et al. Enhanced thermal conductivity of phase change materials with ultrathin-graphite foams for thermal energy storage. Energy Environ. Sci. 7, 1185–1192 (2014).

    Article  Google Scholar 

  20. Shamberger, P. J. & Bruno, N. M. Review of metallic phase change materials for high heat flux transient thermal management applications. Appl. Energy (2020).

  21. Tao, Y. B., Lin, C. H. & He, Y. L. Preparation and thermal properties characterization of carbonate salt/carbon nanomaterial composite phase change material. Energy Convers. Manag. 97, 103–110 (2015).

    Article  Google Scholar 

  22. Li, T., Lee, J.-H., Wang, R. & Kang, Y. T. Enhancement of heat transfer for thermal energy storage application using stearic acid nanocomposite with multi-walled carbon nanotubes. Energy 55, 752–761 (2013).

    Article  Google Scholar 

  23. Li, M. A nano-graphite/paraffin phase change material with high thermal conductivity. Appl. Energy 106, 25–30 (2013).

    Article  Google Scholar 

  24. Bejan, A. in Advances in Heat Transfer Vol. 24, 1–38 (Elsevier, 1994).

  25. Rozenfeld, T., Kozak, Y., Hayat, R. & Ziskind, G. Close-contact melting in a horizontal cylindrical enclosure with longitudinal plate fins: demonstration, modeling and application to thermal storage. Int. J. Heat. Mass Transf. 86, 465–477 (2015).

    Article  Google Scholar 

  26. Saito, A., Utaka, Y., Shinoda, K. & Katayama, K. Basic research on the latent heat thermal energy storage utilizing the contact melting phenomena. Bull. JSME 29, 2946–2952 (1986).

    Article  Google Scholar 

  27. Saito, A., Hong, H. & Hirokane, O. Heat transfer enhancement in the direct contact melting process. Int. J. Heat. Mass Transf. 35, 295–305 (1992).

    Article  Google Scholar 

  28. Moallemi, M. K., Webb, B. W. & Viskanta, R. An experimental and analytical study of close-contact melting. J. Heat Transf. (1986).

  29. Woods, J. et al. Rate capability and Ragone plots for phase change thermal energy storage. Nat. Energy 6, 295–302 (2021).

    Article  Google Scholar 

  30. Hirata, T., Makino, Y. & Kaneko, Y. Analysis of close-contact melting for octadecane and ice inside isothermally heated horizontal rectangular capsule. Int. J. Heat. Mass Transf. 34, 3097–3106 (1991).

    Article  Google Scholar 

  31. Hu, N., Zhang, R.-H., Zhang, S.-T., Liu, J. & Fan, L.-W. A laser interferometric measurement on the melt film thickness during close-contact melting on an isothermally-heated horizontal plate. Int. J. Heat. Mass Transf. 138, 713–718 (2019).

    Article  Google Scholar 

  32. Moore, F. E. & Bayazitoglu, Y. Melting within a spherical enclosure. J. Heat Transf. (1982).

  33. Fomin, S. A. & Saitoh, T. S. Melting of unfixed material in spherical capsule with non-isothermal wall. Int. J. Heat. Mass Transf. 42, 4197–4205 (1999).

    Article  Google Scholar 

  34. Mansouri, L., Balistrou, M. & Baudoin, B. One-dimensional time-dependent modeling of conductive heat transfer during the melting of an initially subcooled semi-infinite PCM. In 23ème Congrès Français de Mécanique (CFM, 2017).

  35. Boucíguez, A. C., Lozano, R. F. & Lara, M. A. About the exact solution in two phase-stefan problem. Rev. Eng. Térmica 6, 70–75 (2007).

    Google Scholar 

  36. Shamberger, P. J. Cooling capacity figure of merit for phase change materials. J. Heat Transf. (2016).

  37. Schlichting, H. & Gersten, K. Boundary-Layer Theory (Springer, 2016).

  38. Churchill, S. W. & Bernstein, M. A correlating equation for forced convection from gases and liquids to a circular cylinder in crossflow. J. Heat Transf. (1977).

  39. Oró, E., De Gracia, A., Castell, A., Farid, M. M. & Cabeza, L. F. Review on phase change materials (PCMs) for cold thermal energy storage applications. Appl. Energy 99, 513–533 (2012).

    Article  Google Scholar 

  40. Ji, H. et al. Ultrahigh power and energy density in partially ordered lithium-ion cathode materials. Nat. Energy 5, 213–221 (2020).

    Article  Google Scholar 

  41. López-Navarro, A. et al. Experimental investigation of the temperatures and performance of a commercial ice-storage tank. Int. J. Refrig. 36, 1310–1318 (2013).

    Article  Google Scholar 

  42. Seddegh, S., Wang, X., Henderson, A. D. & Xing, Z. Solar domestic hot water systems using latent heat energy storage medium: a review. Renew. Sustain. Energy Rev. 49, 517–533 (2015).

    Article  Google Scholar 

  43. Suberu, M. Y., Mustafa, M. W. & Bashir, N. Energy storage systems for renewable energy power sector integration and mitigation of intermittency. Renew. Sustain. Energy Rev. 35, 499–514 (2014).

    Article  Google Scholar 

  44. Ali, H. M. et al. Thermal management of electronics: an experimental analysis of triangular, rectangular and circular pin-fin heat sinks for various PCMs. Int. J. Heat. Mass Transf. 123, 272–284 (2018).

    Article  Google Scholar 

  45. Farzanehnia, A., Khatibi, M., Sardarabadi, M. & Passandideh-Fard, M. Experimental investigation of multiwall carbon nanotube/paraffin based heat sink for electronic device thermal management. Energy Convers. Manag. 179, 314–325 (2019).

    Article  Google Scholar 

  46. Zhao, L., Xing, Y., Wang, Z. & Liu, X. The passive thermal management system for electronic device using low-melting-point alloy as phase change material. Appl. Therm. Eng. 125, 317–327 (2017).

    Article  Google Scholar 

  47. Mann, A., Germann, T., Ruiter, M. & Groche, P. The challenge of upscaling paraffin wax actuators. Mater. Des. 190, 108580 (2020).

    Article  Google Scholar 

  48. Mann, A., Bürgel, C. M. & Groche, P. A. in Actuators Vol. 7, 81 (Multidisciplinary Digital Publishing Institute, 2018).

  49. Stovall, T. K. CALMAC Ice Storage Test Report (Oak Ridge National Laboratory, 1991).

Download references


We gratefully acknowledge fruitful discussions with R. Crawford as well as A. Mahvi and J. Woods at the National Renewable Energy Laboratory. We gratefully acknowledge the help from N. Liu of Naperville North High School for helping with the PCM charging experiments. We gratefully acknowledge funding support from the Air Conditioning and Refrigeration Center. X.Y. and N.M. gratefully acknowledge funding support from the National Science Foundation under award no. 1554249. Y.G., W.P.K. and N.M. gratefully acknowledge funding support from the National Science Foundation Engineering Research Center for Power Optimization of Electro-Thermal Systems with cooperative agreements EEC-1449548. N.M. gratefully acknowledges funding support from the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology.

Author information

Authors and Affiliations



N.M. conceived the idea for this work. W.F., Y.G. and X.Y. fabricated all samples. W.F., Y.G. and X.Y developed the experimental test set-up. W.F. and X.Y performed the experiments. Y.G., W.F. and V.S.G. performed the numerical and analytical simulations. W.F., N.M. and W.P.K performed the experimental and numerical data analysis. W.F., N.M. and W.P.K. wrote the paper. N.M. supervised the project.

Corresponding author

Correspondence to Nenad Miljkovic.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Energy thanks Philip Eames, Kyle Gluesenkamp and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Notes 1–11, Figs. 1–19, Tables 1–9 and References.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fu, W., Yan, X., Gurumukhi, Y. et al. High power and energy density dynamic phase change materials using pressure-enhanced close contact melting. Nat Energy 7, 270–280 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing