Microchannel heat sinks cooled by subcooled flow boiling can be geometrically optimized (e.g. by constructal design) for a target heat flux, but the actual thermal limit of the optimized design is its critical heat flux (CHF), the onset of departure from nucleate boiling (DNB). A 2020 CFD study by Ariyo and Bello Ochende [ref 1] predicted CHF values of 800–950 W/cm² for rectangular microchannels optimized at 300–500 W/cm² design fluxes, showing large but unquantified margins, and left open — in the authors' own account of the programme — how sensitive CHF and the safe operating margin are to the distinct global optima produced by the optimization procedure, and whether the same constructal CFD workflow and the resulting CHF account extend to other microchannel heat sink configurations. Later work has only partially approached this core: the same authors extended the framework to stacked and triangular channels without CHF analysis across optima, and adjacent experimental and review literature (2022–2024) still identifies optimal design and transient flow-boiling analysis of microchannel evaporators as open needs. The problem — a validated, quantitative account of the CHF limits of optimized two-phase microchannel heat sinks across the optimization family — remains open.

Background

A microchannel heat sink is a block of millimetre- or sub-millimetre-scale channels through which a coolant is forced, used to remove very high heat fluxes (hundreds of W/cm²) from electronic and power devices. In flow boiling the coolant partially evaporates, exploiting latent heat; in subcooled flow boiling the bulk liquid remains below its saturation temperature while bubbles form at the heated wall. The upper limit of safe operation is the critical heat flux (CHF): the heat flux at which vapour blankets the heated wall and heat transfer deteriorates sharply — for highly subcooled conditions this occurs as departure from nucleate boiling (DNB) — driving a sudden wall-temperature excursion. Because a design is only usable with a known margin between its operating flux and its CHF, the CHF of a given optimized channel is itself a quantity of first-order engineering interest.

Constructal design is a geometric-optimization methodology in which the channel geometry and flow parameters are varied under fixed volume constraints to minimize an objective such as the total thermal resistance; different optimization runs can return distinct global optima (different channel widths, heights, and inlet velocities) with nearly equal thermal performance. The wall heat flux partitioning model (RPI model, after Rensselaer Polytechnic Institute) treats the heat leaving a boiling heated wall as the sum of a single-phase convection term qCq_C, an evaporation term qEq_E driving bubble growth, and a wall-quenching term qQq_Q accounting for liquid refilling the wake of a departing bubble. Near CHF the wall becomes covered by vapour, so the classical three-term partition is incomplete; commercial solvers (here ANSYS Fluent's non-equilibrium boiling model) add a fourth term qCv=hCv(Tw−Tv)q_{Cv}=h_{Cv}(T_w-T_v) for convection from the wall to a contiguous vapour layer, giving qW=qC+qE+qQ+qCvq_W=q_C+q_E+q_Q+q_{Cv}.

Ariyo and Bello Ochende (2020) [ref 1] combined these ingredients: they validated an Eulerian two-phase CFD implementation of the extended RPI model against the microchannel boiling-incipience experiments of Qu and Mudawar (2002), then simulated six rectangular microchannel configurations optimized (by constructal design, following their 2020 optimization study [ref 2]) at design heat fluxes of 300, 400, and 500 W/cm² with optimized inlet-velocity ranges of 1.0–1.5 and 1.5–2.0 m/s, using water at 25 °C inlet temperature. Incrementing the heat flux in 50 W/cm² steps, they located CHF at 800–950 W/cm² — far above the design points — with outlet temperatures staying in the 85–90 °C window commonly cited for electronics cooling. However, the study did not analyze how these limits depend on which optimum the optimization returns, and it considered only horizontal rectangular channels. In the first author's doctoral thesis account of the same programme, the CHF computations are described as stable — the heat flux was ramped in 50 W/cm² steps until the last stable outlet temperature, and runs that became unstable and could not be resolved were terminated — while static and dynamic instabilities appear only as an unstudied topic, a potential concern for microchannels operating off their optimal values that stacked or v-grooved configurations might alleviate.

Problem Statement

For microchannel heat sinks optimized by the constructal response-surface CFD optimization of Ariyo and Bello-Ochende (2020) [ref 2] for subcooled flow-boiling cooling, establish a validated, quantitative description of their actual thermal limits, where "validated" carries the sense fixed in the Background: the predictive model is checked against available experimental benchmark data, such as the boiling-incipience measurements of Qu and Mudawar (2002) used in the source study. Concretely: (1) determine how the critical heat flux and the safe operating margin (allowable overflux above the design heat flux and the wall/outlet temperature rise before departure from nucleate boiling) vary across the distinct global optimal geometric and flow parameter sets that the optimization procedure produces — the authors note that different global optima "could affect the response of optimal microchannel heat sinks to critical heat fluxes"; and (2) establish whether the same constructal/response-surface CFD workflow and the resulting CHF account extend to microchannel heat sink configurations beyond the horizontal rectangular channels studied; demonstrating the workflow and its CHF account on one representative additional configuration, together with an explicit statement of what that demonstration establishes and leaves open for the remaining configurations, counts as resolving this component. The two components share one objective — a predictive account of the CHF limits of optimized two-phase microchannel heat sinks sufficient to define safe operating envelopes for the whole family of optima the optimization procedure produces, and for configurations beyond the horizontal rectangular channels studied, rather than for single designs.

References

  1. David O. Ariyo and Tunde Bello Ochende, 2020, 'Critical heat fluxes for subcooled flow boiling in optimised microchannels', International Journal of Hydromechatronics 3(2), 140, DOI: 10.1504/IJHM.2020.107786, https://doi.org/10.1504/IJHM.2020.107786
  2. David O. Ariyo and Tunde Bello-Ochende, 2020, 'Constructal design of subcooled microchannel heat exchangers', International Journal of Heat and Mass Transfer 146, 118835, DOI: 10.1016/j.ijheatmasstransfer.2019.118835, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118835
  3. David O. Ariyo and Tunde Bello-Ochende, 2021, 'Constructal design of two-phase stacked microchannel heat exchangers for cooling at high heat flux', International Communications in Heat and Mass Transfer 125, 105294, DOI: 10.1016/j.icheatmasstransfer.2021.105294, https://doi.org/10.1016/j.icheatmasstransfer.2021.105294
  4. David Olugbenga Ariyo and Tunde Bello-Ochende, 2021, 'Optimal design of subcooled triangular microchannel heat sink exchangers with variable heat loads for high performance cooling', Journal of Physics: Conference Series 2116, 012052, DOI: 10.1088/1742-6596/2116/1/012052, https://doi.org/10.1088/1742-6596/2116/1/012052
  5. Weilin Qu and Issam Mudawar, 2002, 'Prediction and measurement of incipient boiling heat flux in micro-channel heat sinks', International Journal of Heat and Mass Transfer 45(19), 3933-3945, DOI: 10.1016/S0017-9310(02)00106-0, https://doi.org/10.1016/s0017-9310(02)00106-0
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  7. Lixin Cheng and Guodong Xia, 2022, 'High Heat Flux Cooling Technologies Using Microchannel Evaporators: Fundamentals and Challenges', Heat Transfer Engineering 44(16-18), 1470-1497, DOI: 10.1080/01457632.2022.2140639, https://doi.org/10.1080/01457632.2022.2140639
  8. M. B. Darshan, M. Magnini and O. K. Matar, 2024, 'Numerical modelling of flow boiling inside microchannels: A critical review of methods and applications', Applied Thermal Engineering 257, 124464, DOI: 10.1016/j.applthermaleng.2024.124464, https://doi.org/10.1016/j.applthermaleng.2024.124464
  9. Zhen Tian, Kun Li, Yuan Zhang, Zhikang Huang, Shuming Xu and Wenzhong Gao, 2023, 'Numerical simulation of microchannel flow boiling and critical heat flux under rolling motion', International Journal of Refrigeration 145, 118-128, DOI: 10.1016/j.ijrefrig.2022.08.025, https://doi.org/10.1016/j.ijrefrig.2022.08.025