International Journal of Heat and Mass Transfer 136 (2019) 324–354 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Review Review of single-phase and two-phase nanofluid heat transfer in macro-channels and micro-channels ⇑ Gangtao Liang a, Issam Mudawar b, a Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, China b Purdue University Boiling and Two-Phase Flow Laboratory (PU-BTPFL), School of Mechanical Engineering, 585 Purdue Mall, West Lafayette, IN 47907, USA article info abstract Article history: This paper provides a comprehensive review of published literature concerning heat transfer benefits of Received 2 January 2019 nanofluids for both macro-channels and micro-channels. Included are both experimental and numerical Received in revised form 14 February 2019 findings concerning several important performance parameters, including single-phase and two-phase Accepted 25 February 2019 heat transfer coefficients, pressure drop, and critical heat flux (CHF), each being evaluated based on pos- Available online 7 March 2019 tulated mechanisms responsible for any performance enhancement or deterioration. The study also addresses issues important to heat transfer performance, including entropy minimization, hybrid Keywords: enhancement methodologies, and nanofluid stability, as well as the roles of Brownian diffusion and ther- Nanofluid mophoresis. Published results point to appreciable enhancement in single-phase heat transfer coefficient Flow boiling Heat transfer coefficient realized in entrance region, but the enhancement subsides downstream. And, while some point to the Heat transfer enhancement ability of nanofluids to increase CHF, they also emphasize that this increase is limited to short duration Critical heat flux (CHF) boiling tests. Overall, studies point to many important practical problems associated with implementa- tion of nanofluids in cooling situations, including clustering, sedimentation, and precipitation of nanopar- ticles, clogging of flow passages, erosion to heating surface, transient heat transfer behavior, high cost and production difficulties, lack of quality assurance, and loss of nanofluid stability above a threshold temperature. Ó 2019 Elsevier Ltd. All rights reserved. Contents 1. Introduction ......................................................................................................... 325 1.1. High heat flux cooling background and applications . ............................................................ 325 1.2. Two-phase cooling solutions . ............................................................................ 326 1.3. Heat transfer enhancement techniques . ............................................................................ 326 1.4. Nanofluid definition and preparation methods . ............................................................ 326 1.5. Prior nanofluid heat transfer reviews . ............................................................................ 327 1.6. Macro-channel versus micro-channel flow . ............................................................ 327 1.7. Objectives of present review . ............................................................................ 327 2. Single-phase convective heat transfer. ...................................................................... 327 2.1. Heat transfer in macro-channels . ............................................................................ 327 2.1.1. Laminar flow. ................................................................................. 327 2.1.2. Turbulent flow . ................................................................................. 330 2.2. Heat transfer in micro-channels (D <1mm).......................................................................... 332 2.2.1. Entrance effects . ................................................................................. 332 2.2.2. Heat transfer enhancement and pressure drop penalty. .............................................. 332 2.2.3. Predictive models . ................................................................................. 333 ⇑ Corresponding author. E-mail address: [email protected] (I. Mudawar). URL: https://engineering.purdue.edu/BTPFL (I. Mudawar). https://doi.org/10.1016/j.ijheatmasstransfer.2019.02.086 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved. G. Liang, I. Mudawar / International Journal of Heat and Mass Transfer 136 (2019) 324–354 325 Nomenclature c1,c2 empirical constants u velocity D channel hydraulic diameter x axial distance d nanoparticle diameter p Greek symbols f friction factor a G mass velocity thermal diffusivity dþ dimensionless thickness of laminar sub-layer h heat transfer coefficient v l dynamic viscosity k thermal conductivity q m ,m empirical exponents density 1 2 / m_ mass flow rate nanoparticle volume concentration Nu Nusselt number Subscripts P pressure f liquid Pe Peclet number out channel outlet Pr Prandtl number p particle 00 q heat flux sat saturation 00 q CHF critical heat flux sub subcooling Re Reynolds number v laminar sub-layer T temperature w wall D Tsat surface superheat water pure water 2.3. Numerical approaches. ......................................................................................... 334 2.3.1. Single-phase models. .............................................................................. 334 2.3.2. Eulerian-Eulerian two-phase models. ........................................................... 334 2.3.3. Eulerian- Lagrangian two-phase models . ........................................................... 335 2.4. Entropy analysis . ......................................................................................... 336 2.4.1. Macro-channel flow . .............................................................................. 336 2.4.2. Micro-channel flow . .............................................................................. 336 2.5. Hybrid enhancement techniques . ......................................................................... 337 2.5.1. Use of inserts . .............................................................................. 337 2.5.2. Helical channels . .............................................................................. 337 2.5.3. Corrugated channels. .............................................................................. 338 2.5.4. Ribbed channels . .............................................................................. 338 2.5.5. Other techniques . .............................................................................. 338 2.6. Important anomalies and concerns . ......................................................................... 338 2.6.1. Nanofluid destabilization . .............................................................................. 338 2.6.2. Inconsistent criteria in performance evaluation . ........................................................... 339 3. Flow boiling heat transfer . ................................................................................... 340 3.1. Flow boiling in macro-channels . ......................................................................... 340 3.1.1. Bubble dynamics . .............................................................................. 340 3.1.2. Heat transfer coefficient. .............................................................................. 340 3.1.3. Critical heat flux . .............................................................................. 342 3.2. Flow boiling heat transfer in micro-channels (D <1mm)............................................................... 343 3.2.1. Heat transfer coefficient. .............................................................................. 343 3.2.2. Critical heat flux . .............................................................................. 344 4. Concluding remarks . ................................................................................... 345 Conflicts of interest . ................................................................................... 346 Acknowledgement . ................................................................................... 346 Appendix A. Supplementary material................................................................................... 346 References . ...................................................................................................... 346 1. Introduction coolants, using a variety of single-phase cooling schemes that relied entirely on the coolant’s sensible heat rise to remove the 1.1. High heat flux cooling background and applications heat. However, by the mid-1980s, heat dissipation from devices used in supercomputers began to exceed 100 W/cm2, well beyond During the past three decades, aggressive micro- and nano- the capabilities of single-phase liquid cooling schemes [1].In miniaturization in the development of computer electronic compo- response, cooling system developers shifted their attention to nents has created an urgent need for innovative cooling schemes two-phase cooling schemes in an effort to capitalize on the cool- aimed at maintaining device temperatures safely below limits that ant’s both sensible and latent heat, which allowed rejection of far are dictated by both material constraints and device reliability. By greater amounts of heat than single-phase