{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T21:34:49Z","timestamp":1770413689162,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T00:00:00Z","timestamp":1770336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/00285\/2025"],"award-info":[{"award-number":["UID\/00285\/2025"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["LA\/P\/0112\/2020"],"award-info":[{"award-number":["LA\/P\/0112\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/50022\/2025"],"award-info":[{"award-number":["UID\/50022\/2025"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["LA\/P\/0079\/2020"],"award-info":[{"award-number":["LA\/P\/0079\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>The continuous increase in electronic power densities demands thermal management solutions that surpass the conventional heat sink designs. This study introduces a synergistic approach that combines constructal design principles with Friction Stir Processing (FSP) to create next-generation heat sinks featuring an optimized geometry and locally enhanced thermal conductivity. Constructal design provides a physics-based framework for routing heat through preferential paths, whereas FSP enables the fabrication of these paths by refining the microstructure and reducing defect density, thereby improving thermal transport properties. Experimental validation on the AA6082-T651 aluminum alloy demonstrated a 21% increase in thermal conductivity within the FSP-processed regions, as confirmed through electrical resistivity measurements and thermal step-response tests. Microstructural analysis revealed significant grain refinement (from ~150 \u03bcm to 3\u20135 \u03bcm), which correlated with enhanced heat diffusion rates. A constructal scale-based model was developed to establish the relationship between the conductivity ratio and optimal geometric configuration, showing that a higher local conductivity shifts the design toward denser thermal pathways. These findings substantiate the feasibility of integrating geometry optimization with property tailoring, paving the way for scalable, high-efficiency heat sinks for advanced cooling systems.<\/jats:p>","DOI":"10.3390\/app16031640","type":"journal-article","created":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T10:05:47Z","timestamp":1770372347000},"page":"1640","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Constructal Design and Friction Stir Processing Synergy: Towards Next-Generation High-Efficiency Heat Sinks"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7133-2331","authenticated-orcid":false,"given":"Joel de","family":"Jesus","sequence":"first","affiliation":[{"name":"CEMMPRE, ARISE, Department of Mechanical Engineering, University of Coimbra, Rua Lu\u00eds Reis Santos, 3030-788 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9561-9268","authenticated-orcid":false,"given":"Miguel","family":"Pan\u00e3o","sequence":"additional","affiliation":[{"name":"ADAI, LAETA, Department of Mechanical Engineering, University of Coimbra, Polo II, Rua Luis Reis Santos, 3030-788 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2471-1125","authenticated-orcid":false,"given":"Ricardo","family":"Branco","sequence":"additional","affiliation":[{"name":"CEMMPRE, ARISE, Department of Mechanical Engineering, University of Coimbra, Rua Lu\u00eds Reis Santos, 3030-788 Coimbra, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/0017-9310(96)00175-5","article-title":"Constructal-theory network of conducting paths for cooling a heat generating volume","volume":"40","author":"Bejan","year":"1997","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"124568","DOI":"10.1016\/j.ijheatmasstransfer.2023.124568","article-title":"Generalizing multi-branching radial symmetric flow structures","volume":"216","author":"Clemente","year":"2023","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhang, F., Feng, H., Chen, L., You, J., and Xie, Z. (2020). Constructal Design of an Arrow-Shaped High Thermal Conductivity Channel in a Square Heat Generation Body. Entropy, 22.","DOI":"10.3390\/e22040475"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhu, H., Chen, L., Ge, Y., Shi, S., and Feng, H. (2022). Multi-Objective Constructal Design for Quadrilateral Heat Generation Body with Vein-Shaped High Thermal Conductivity Channel. Entropy, 24.","DOI":"10.3390\/e24101403"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"10341","DOI":"10.1016\/j.aej.2022.03.018","article-title":"Novel design of a liquid-cooled heat sink for a high-performance processor based on constructal theory: A numerical and experimental approach","volume":"61","author":"Sakamatapan","year":"2022","journal-title":"Alex. Eng. J."},{"key":"ref_6","unstructured":"Mishra, R.S., and Mahoney, M.W. (2007). Friction Stir Welding and Processing, ASM International."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.scriptamat.2007.09.062","article-title":"Microstructural refinement and property enhancement of cast light alloys via friction stir processing","volume":"58","author":"Ma","year":"2008","journal-title":"Scr. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Mishra, R.S., De, P.S., and Kumar, N. (2014). Friction Stir Processing. Friction Stir Welding and Processing, Springer.","DOI":"10.1016\/B978-0-12-800150-9.00006-6"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1969","DOI":"10.1007\/s12541-015-0256-1","article-title":"Effects of friction stir processing on the thermal conductivity of a strain-hardened Al\u2013Mg alloy","volume":"16","author":"Jeong","year":"2015","journal-title":"Int. J. Precis. Eng. Manuf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"127437","DOI":"10.1016\/j.matlet.2020.127437","article-title":"Development of high strength and high electrical conductivity Cu\/Gr composites through friction stir processing","volume":"265","author":"Naik","year":"2020","journal-title":"Mater. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s11706-021-0541-0","article-title":"Recent progress in graphene-reinforced aluminum matrix composites","volume":"15","author":"Su","year":"2021","journal-title":"Front. Mater. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Chen, G., Yu, M., Dong, H., and Liu, J. (2024). Experimental Investigation into the Preparation Process of Graphene-Reinforced Aluminum Matrix Composites by Friction Stirring Processing. Materials, 17.","DOI":"10.3390\/ma17163918"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"119223","DOI":"10.1016\/j.energy.2020.119223","article-title":"Thermal management and temperature uniformity enhancement of electronic devices by micro heat sinks: A review","volume":"216","author":"He","year":"2021","journal-title":"Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.ijheatmasstransfer.2017.10.099","article-title":"Optimization of thermal design of heat sinks: A review","volume":"118","author":"Hamdi","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Li, Y., Xie, Z., Lin, D., Lu, Z., and Ge, Y. (2023). Constructal Optimizations of Liquid-Cooled Channels with Triangle or Square Sections in a Cylindrical Heating Body. Mathematics, 11.","DOI":"10.3390\/math11020357"},{"key":"ref_16","unstructured":"Halliday, D., Resnick, R., and Walker, J. (2013). Fundamentals of Physics, John Wiley & Sons."},{"key":"ref_17","unstructured":"Kittel, C. (2005). Introduction to Solid State Physics, John Wiley & Sons."},{"key":"ref_18","unstructured":"Taylor, J. (1997). An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, University Science Books."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2418","DOI":"10.1038\/s41598-025-86744-y","article-title":"Improving mechanical properties and electrical conductivity of Al-Cu-Mg matrix composites by GNPs and sc additions","volume":"15","author":"Yuan","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1140\/epjp\/s13360-021-01303-4","article-title":"Accounting for the resistivity contribution of grain boundaries in metals: Critical analysis of reported experimental and theoretical data for Ni and Cu","volume":"136","author":"Bakonyi","year":"2021","journal-title":"Eur. Phys. J. Plus"}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/16\/3\/1640\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T10:27:37Z","timestamp":1770373657000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/16\/3\/1640"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,6]]},"references-count":20,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["app16031640"],"URL":"https:\/\/doi.org\/10.3390\/app16031640","relation":{},"ISSN":["2076-3417"],"issn-type":[{"value":"2076-3417","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,6]]}}}