Pith. sign in

REVIEW 3 major objections 4 minor 34 references

Wall roughness and viscous dissipation effects in microchannel heat sinks with semicircular cross-section

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read In a semicircular microchannel heated only at its smooth flat wall, wall roughness raises the Poiseuille number but leaves the Nusselt number nearly unchanged; heat-transfer penalties appear only when viscous dissipation is strong.

desk verdict A sound, model-specific extension: roughness on an adiabatic curved wall barely affects heat transfer from a smooth wall except at higher Brinkman numbers; deserves peer review but needs a clearer range-of-validity statement. read the letter →

arxiv 2505.24398 v1 pith:H3YVKCBF submitted 2025-05-30 physics.flu-dyn

A. Barletta , M. Celli , P. V. Brandão This is my paper
classification physics.flu-dyn
keywords laminarforcedconvectionmicrochannelheatsinksemicircularcross-sectionwallroughnessviscousdissipationBrinkmannumberNusseltPoiseuille
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether wall roughness on the unheated part of a microchannel matters for cooling. Its answer is that, when the heated wall is perfectly smooth, roughness on the curved adiabatic wall has only a minor thermal effect: the Poiseuille number $Po$ increases with the roughness parameter $\gamma$, while the Nusselt number for the isothermal $T$ condition stays essentially constant. For the $H1$ and $H2$ heating conditions, the Nusselt number does decrease with roughness, but only when the Brinkman number is at least about 0.5, meaning viscous dissipation must be significant. The authors compare this with a previously studied circular microchannel where the heat-transfer surface itself was rough and conclude that roughness affects heat transfer mainly when it lies on the surface where heat actually enters the fluid.

What carries the argument

The central objects are the Poiseuille number $Po = u_0/u_m$ and the Nusselt number $Nu = 2 r_h q_w/(k(T_w-T_b))$, computed for random polygonal approximations of the semicircular boundary. Roughness is parameterized by $\gamma$, the maximum relative radial deviation of $N=45$ boundary nodes from the nominal semicircle, and each roughness level is represented by a population of 500 randomly generated cross-sections solved with a finite-element method. The argument runs on the Brinkman number $Br = \mu u_m^2/(2 r_h q_w)$, which weights the viscous dissipation term in the energy equation; the $T$ condition emerges as a special $Br$ value, $Br_T$, at which the wall temperature has no streamwise variation. The comparison case is the smooth semicircular duct, whose exact $Po = 8\pi^4/((\pi+2)^2(\pi^2-8)) \approx 15.7668$ validates the solver.

What would settle it

Repeat the statistical roughness study with a third-kind or conjugate-conduction boundary condition on the curved wall, or measure pressure drop and heat transfer in an etched semicircular microchannel whose curved wall has finite thermal conductivity, and check whether $Nu_{H1}$ and $Nu_{H2}$ depend on $\gamma$ at $Br=0$; a clear dependence would mean the adiabatic-curved-wall assumption, rather than the smoothness of the heated wall, is what makes roughness effects minor.

Watch

Extended reading notes

Core claim

For fully developed laminar flow in a semicircular microchannel whose diametrical flat wall is smooth and heated while the curved boundary is rough and adiabatic, the paper reports statistical results from 500 random geometries per roughness level. The mean Poiseuille number $Po$ grows with $\gamma$, while the $T$-condition Nusselt number $Nu_T = 3.95071$ for the smooth duct is statistically unaffected by roughness up to $\gamma = 0.1$, with relative scatter below about 2.3 percent. For $H1$ and $H2$ conditions, roughness has no statistically significant effect on $Nu$ at $Br = 0$ and $Br = 0.1$, but at $Br = 0.5$ and $Br = 1$ the Nusselt number decreases with $\gamma$, an effect attributed to the viscous-dissipation source term $2 Po^2 Br |\nabla^* u^*|^2$ being amplified by roughness spikes. The conclusion is that roughness effects are minor when heat transfer occurs from a smooth part of the boundary.

Load-bearing premise

The load-bearing premise is that the rough curved boundary is perfectly adiabatic, so all heat enters through the smooth flat wall; if that curved wall conducts heat appreciably, roughness would change the actual heat-transfer area and the conclusion that roughness hardly affects cooling could collapse.

Editorial extensions

If this is right

  • In heat-sink designs where the cooled plate is polished, etching roughness on the curved channel walls can be tolerated from a thermal standpoint, but the required pressure gradient for a given flow rate will be larger.
  • Roughness-induced degradation of the Nusselt number under $H1$ and $H2$ heating appears only when viscous dissipation is significant ($Br \gtrsim 0.5$), so low-dissipation microchannel coolers should be nearly immune to this effect.
  • The standard deviation of $Po$ and $Nu$ grows with $\gamma$, so manufacturing tolerance translates into a spread of thermal-hydraulic performance even when the mean values are stable.
  • Comparing the semicircular result with the fully rough circular duct implies that surface roughness on the heat-exchange wall, not on the adiabatic wall, governs the thermal roughness penalty.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the etched solid layer has finite thermal conductivity, heat can leak through the rough curved boundary; a third-kind boundary condition would then likely make $Nu$ depend on $\gamma$ even at $Br=0$, because the rough surface changes the effective heat-exchange area. The paper acknowledges this as a possible model improvement.
  • A three-dimensional roughness pattern that varies along the flow could generate local recirculation and extra mixing, an effect excluded by the present streamwise-invariant geometry; one testable extension is to compare the 2D fully developed predictions with 3D simulations at matched root-mean-square roughness.
  • The claim that normal distributions fit the population statistics is based on 500 samples; larger ensembles or bootstrap resampling could sharpen whether the tails of $Po$ and $Nu$ matter for design margins at high $\gamma$.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper presents a numerical-statistical study of fully developed laminar forced convection in a semicircular microchannel whose diametrical wall is smooth and heated, while the curved wall is adiabatic and rough. Roughness is generated as random polygonal perturbations controlled by a dimensionless parameter γ, with 500 realizations per case and N=45 nodes. The authors solve the local momentum and energy equations with viscous dissipation by finite elements, compute the Poiseuille number and Nusselt numbers for the T, H1, and H2 thermal conditions, and compare the results with their earlier circular-duct analysis. They find that Po increases with γ, Nu_T is essentially unchanged, and Nu_H1/Nu_H2 are roughness-independent at small Brinkman number but decrease when Br is at least 0.5, leading to the conclusion that roughness effects are minor when heat transfer occurs through the smooth wall.

Significance. If accepted within its stated modeling assumptions, the paper is a useful counterpoint to the circular-duct study [26]: it separates roughness-induced changes in hydraulic resistance from changes in the actual heat-transfer surface. The clean benchmark against the exact smooth-channel Poiseuille number (Table 1, converging to 15.7668) and the internally consistent derivation of σ, Po, and Nu are genuine strengths. The numerical protocol is otherwise straightforward, and the comparison with [26] is informative. The main result is falsifiable and of practical interest for etched microchannel heat sinks, provided the adiabatic-curved-wall assumption is respected. The principal weakness is that the central claim is stated more broadly than the model supports, and the statistical evidence is presented without formal significance testing.

major comments (3)
  1. [Section 2 (Eq. 6) and Section 6] The conclusion that roughness effects are "definitely minor" is load-bearing on the assumption that the rough boundary P1 is perfectly adiabatic. Under Eq. (6), heat can enter only through the smooth diametrical wall, so roughness can affect Nu only indirectly through the velocity field and the dissipation term; this is exactly why Nu_H1 and Nu_H2 are roughness-independent at Br=0. The authors acknowledge in Section 6 that a third-kind boundary condition would be more realistic, but the abstract and the closing bullet state the result without that qualifier. As written, the central claim does not cover etched layers of finite thermal conductivity, in which the rough boundary itself participates in heat transfer and the heat-transfer area changes with γ. Please restrict the conclusions to the adiabatic-wall model, or add a finite-conductivity/third-kind test and report whether the "minor effects" conclusion survives.
  2. [Section 5, Figures 4 and 5] The claims that roughness has "no statistically significant effect" at Br=0 and Br=0.1, and a "weak, though indisputable, decrease" at Br=0.5 and Br=1, are inferred from one-standard-deviation error bars. With 500 samples per γ, the standard error of the mean is roughly σ/√500, so visual overlap or non-overlap of ±σ intervals is not a valid significance criterion. Please report the standard error of the mean or confidence intervals, and state whether the mean differences were tested formally (for example, a two-sample test or a regression of Nu on γ) before using the words "statistically relevant" or "indisputable".
  3. [Section 2, Eqs. (1)-(2)] The statistical model is incompletely specified. The text gives only the admissible ranges of δrn and θn, but never states their probability distributions. If δrn and θn are not uniform, the population means and standard deviations of Po and Nu, and the comparison with the circular-duct results in [26], are not reproducible. Please state the distributions, clarify whether the random variables are independent at each node, and justify the fixed value N=45, for example through a sensitivity test.
minor comments (4)
  1. [Section 3, after Eq. (14)] The sentence beginning "In fact, we denote with S∗, P∗ and P∗1 are the nondimensional objects" is ungrammatical and should be revised.
  2. [Section 4, Table 2] Mesh convergence is reported for Po only; a short convergence check for Nu_T and Nu_H1/Nu_H2 in the smooth case would strengthen confidence in the Nusselt numbers reported in Eq. (20) and Table 2.
  3. [Section 5, Figure 6] The caption should state explicitly that each histogram uses 500 samples and that the gray curve is a normal distribution with the same mean and standard deviation as the data; currently this information appears only in the main text.
  4. [Nomenclature and Eq. (17)] The Brinkman number is defined with qw positive for heating of the fluid, but Br_T in Eq. (17) is negative; a brief sentence explaining the sign convention for the T condition would help readers avoid confusion when comparing with Table 2.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the results are obtained by solving the governing PDEs numerically and are validated against an independent analytical result, with self-citations used only for comparison and methodology.

full rationale

The paper contains no fitted parameters presented as predictions. The Poiseuille number for the smooth duct is checked against the independent analytic expression (18), and the rough-channel results are obtained by finite-element solution of the momentum and energy equations (13)-(14) with no-slip and prescribed thermal boundary conditions. The roughness parameter gamma only enters the geometry generation (1)-(2), while the Brinkman number is prescribed externally, so neither Po nor Nu is fit to a target. Self-citations [26] and [27] are used to describe the statistical approach and to compare trends, but they are not invoked as premises that force the conclusions; the central claim about minor roughness effects when heat transfer occurs from the smooth diametrical wall follows from the numerical statistics in Figs. 4 and 5, not from a self-referential definition. The adiabatic rough-boundary condition (6) is a modeling assumption and a stated limitation, not a circular input; it constrains the physical scenario but does not by itself determine the magnitude of the roughness effect on Nu, which is computed and found to be small. Thus no circular step is present.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The computation relies on standard continuum fluid mechanics and a set of explicit modeling simplifications. The only hand-chosen discretization parameter is N=45. The most consequential assumptions are the adiabatic curved wall and the two-dimensional, streamwise-invariant roughness representation; both are acknowledged in the text as simplifications. No new physical entities are introduced.

free parameters (1)
  • Number of polygon vertices N = 45
    The rough boundary is built from N=45 random vertices; no convergence study with respect to N is reported, and the roughness statistics depend on this discretization choice.
assumptions (5)
  • domain assumption Fully developed laminar flow: velocity has only the axial component and is independent of z, and the streamwise temperature gradient is constant.
    Invoked in Section 2, Eqs. (3)-(4). This reduces the three-dimensional problem to a two-dimensional cross-section and is standard, but it excludes developing-flow effects that can be important in short microchannels.
  • domain assumption No-slip boundary condition and continuum hypothesis at the rough wall.
    Stated in Eq. (5). For hydraulic diameters below 100 micrometers, rarefaction or slip may be non-negligible; the paper does not model slip, though it cites slip-flow work [27] from the same group.
  • domain assumption The curved semicircular boundary is perfectly adiabatic; all heat transfer occurs through the smooth diametrical boundary.
    Stated in Section 2 before Eq. (6). The central conclusion that roughness has minor heat-transfer effects depends on this assumption: if the curved wall conducts heat, roughness would directly alter the heat-transfer area.
  • ad hoc to paper Roughness is represented by random polygonal paths with N=45 vertices, with radial deviations in [-gamma*r0, gamma*r0] and angular positions in prescribed intervals; the probability distributions of the random variables are not specified.
    Section 2, Eqs. (1)-(2). The statistical outputs depend on these distributions, so the missing distribution specification is a load-bearing modeling choice.
  • ad hoc to paper Roughness is streamwise invariant; the cross-section does not change along the channel axis.
    Section 6 acknowledges that a three-dimensional roughness model is more realistic. The two-dimensional roughness model is an assumption, not derived from manufacturing data.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Wall roughness and viscous dissipation effects in microchannel heat sinks with semicircular cross-section." pith.science (2026). https://pith.science/paper/H3YVKCBF

@misc{pith2026250524398,
  author       = {Pith},
  title        = {Pith review of: Wall roughness and viscous dissipation effects in microchannel heat sinks with semicircular cross-section},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H3YVKCBF}},
  note         = {Machine review of arXiv:2505.24398}
}
read the original abstract

A statistical analysis of the wall roughness effect is carried out to determine the impact of the shape uncertainty on the Poiseuille number and Nusselt number of laminar forced convection. The focus is on the fully developed regime in a semicircular microchannel where the heat transfer occurs from the diametrical plane boundary, modelled as a perfectly smooth surface. On the other hand, the curved semicircular boundary is devised as rough and with a negligible wall heat flux. Three types of thermal boundary conditions are implemented: the T condition, the H1 condition and the H2 condition. The T condition serves to model a case where the fluid temperature does not undergo any change in the streamwise direction, while the H1 and H2 conditions are employed to describe a net heating of the fluid. A statistical sample of several different rough microchannels is used to detect the actual effects of roughness on the Poiseuille number and on the Nusselt number, through the evaluation of their average values and standard deviations. The governing local momentum and energy balance equations are solved numerically by a finite element method taking into account the viscous dissipation contribution to the local energy balance.

Figures

Figures reproduced from arXiv: 2505.24398 by the authors.

Figure 1
Figure 1. Cross-sectional view of an array of semicircular microchannels employed to cool a heated [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Sketch of the microchannel nominal cross-section [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. A typical domain S (a), obtained with N = 45 and γ = 0.02, and one of its possible unstructured meshes (b) for the finite-element solver yields the velocity profile u(x, y) and, by employing (4), the average velocity um. After having determined u(x, y), the second equation (3) leads to the determination of T(x, y, z). The solution process of the second equation (3) requires the statement of boundary conditions at th… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Plots of Po (a) and NuT (b) versus γ. The dots indicate the mean value over the statistical population, while the segments show the uncertainties in a one standard deviation range from the mean value a precise Brinkman number, namely Br = BrT. On the other hand, NuH1 a…
Figure 5
Figure 5. Figure 5: Plots of NuH1 (in blue) and NuH2 (in red) versus γ for Br = 0 (a), Br = 0.1(b), Br = 0.5 (c) and Br = 1 (d). The dots indicate the mean value over the statistical population, while the segments show the uncertainties in a one standard deviation range from the mean valu…
Figure 6
Figure 6. Figure 6: Probability density plots with the actual data for Po and Nu [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

  1. [26]

    Barletta, M

    A. Barletta, M. Celli, L. A. Sphaier, P. V. Brand˜ ao, S. Lazzari, E. Ghedini, Shape uncertainty analysis of laminar forced convection in a round microchannel with viscous dissipation, Applied Thermal Engineering 265 (2025) 125536

    work page 2025

  2. [1]

    M. G. Khan, A. Fartaj, A review on microchannel heat exchangers and potential applications, International Journal of Energy Research 35 (2011) 553–582. 14

    work page 2011

  3. [2]

    S. G. Kandlikar, History, advances, and challenges in liquid flow and flow boiling heat transfer in microchannels: A critical review, ASME Journal of Heat Transfer 134 (2012) 034001

    work page 2012

  4. [3]

    O. K. Siddiqui, S. M. Zubair, Efficient energy utilization through proper design of microchan- nel heat exchanger manifolds: A comprehensive review, Renewable and Sustainable Energy Reviews 74 (2017) 969–1002

    work page 2017

  5. [4]

    Gilmore, V

    N. Gilmore, V. Timchenko, C. Menictas, Microchannel cooling of concentrator photovoltaics: A review, Renewable and Sustainable Energy Reviews 90 (2018) 1041–1059

    work page 2018

  6. [5]

    D. Deng, L. Zeng, W. Sun, A review on flow boiling enhancement and fabrication of enhanced microchannels of microchannel heat sinks, International Journal of Heat and Mass Transfer 175 (2021) 121332

    work page 2021

  7. [6]

    Harris, H

    M. Harris, H. Wu, W. Zhang, A. Angelopoulou, Overview of recent trends in microchannels for heat transfer and thermal management applications, Chemical Engineering and Processing – Process Intensification 181 (2022) 109155

    work page 2022

  8. [7]

    Heidarshenas, A

    B. Heidarshenas, A. El-Shafay, S. M. Sajadi, Y. Yuan, Enhancing efficiency in microscale systems with microchannels: A review, Journal of Thermal Analysis and Calorimetry (2024) 1–26

    work page 2024

Show all 34 references
  1. [8]

    B. Dash, J. Nanda, S. K. Rout, The role of microchannel geometry selection on heat transfer enhancement in heat sinks: A review, Heat Transfer 51 (2022) 1406–1424

    2022

  2. [9]

    Yu, M.-T

    Z.-Q. Yu, M.-T. Li, B.-Y. Cao, A comprehensive review on microchannel heat sinks for electronics cooling, International Journal of Extreme Manufacturing 6 (2024) 022005

    2024

  3. [10]

    W. Dong, X. Zhang, B. Liu, B. Wang, Y. Fang, Research progress on passive enhanced heat transfer technology in microchannel heat sink, International Journal of Heat and Mass Transfer 220 (2024) 125001

    2024

  4. [11]

    B. Xu, K. T. Ooi, C. Mavriplis, M. E. Zaghloul, Evaluation of viscous dissipation in liquid flow in microchannels, Journal of Micromechanics and Microengineering 13 (2002) 53

    2002

  5. [12]

    J. Koo, C. Kleinstreuer, Viscous dissipation effects in microtubes and microchannels, Inter- national Journal of Heat and Mass Transfer 47 (2004) 3159–3169

    2004

  6. [13]

    Croce, P

    G. Croce, P. D’Agaro, Numerical analysis of roughness effect on microtube heat transfer, Superlattices and Microstructures 35 (2004) 601–616

    2004

  7. [14]

    Croce, P

    G. Croce, P. D’Agaro, Numerical simulation of roughness effect on microchannel heat transfer and pressure drop in laminar flow, Journal of Physics D: Applied Physics 38 (2005) 1518–1530

    2005

  8. [15]

    Bruus, Theoretical Microfluidics, Oxford University Press, 2007

    H. Bruus, Theoretical Microfluidics, Oxford University Press, 2007

    2007

  9. [16]

    Croce, P

    G. Croce, P. D’Agaro, C. Nonino, Three-dimensional roughness effect on microchannel heat transfer and pressure drop, International Journal of Heat and Mass Transfer 50 (2007) 5249– 5259. 15

    2007

  10. [17]

    Van Rij, T

    J. Van Rij, T. Ameel, T. Harman, The effect of viscous dissipation and rarefaction on rect- angular microchannel convective heat transfer, International Journal of Thermal Sciences 48 (2009) 271–281

    2009

  11. [18]

    M. B. Turgay, A. G. Yazicioglu, Effect of surface roughness in parallel-plate microchannels on heat transfer, Numerical Heat Transfer, Part A: Applications 56 (2009) 497–514

    2009

  12. [19]

    Nonino, S

    C. Nonino, S. Del Giudice, S. Savino, Temperature-dependent viscosity and viscous dissipation effects in microchannel flows with uniform wall heat flux, Heat Transfer Engineering 31 (2010) 682–691

    2010

  13. [20]

    Pelevi´ c, T

    N. Pelevi´ c, T. H. van der Meer, Heat transfer and pressure drop in microchannels with random roughness, International Journal of Thermal Sciences 99 (2016) 125–135

    2016

  14. [21]

    Mukherjee, P

    S. Mukherjee, P. Biswal, S. Chakraborty, S. DasGupta, Effects of viscous dissipation during forced convection of power-law fluids in microchannels, International Communications in Heat and Mass Transfer 89 (2017) 83–90

    2017

  15. [22]

    D. Jing, Y. Pan, X. Wang, Joule heating, viscous dissipation and convective heat transfer of pressure-driven flow in a microchannel with surface charge-dependent slip, International Journal of Heat and Mass Transfer 108 (2017) 1305–1313

    2017

  16. [23]

    H. Lu, M. Xu, L. Gong, X. Duan, J. C. Chai, Effects of surface roughness in microchannel with passive heat transfer enhancement structures, International Journal of Heat and Mass Transfer 148 (2020) 119070

    2020

  17. [24]

    Barletta, Fully developed laminar forced convection in circular ducts for power-law fluids with viscous dissipation, International Journal of Heat and Mass Transfer 40 (1996) 15–26

    A. Barletta, Fully developed laminar forced convection in circular ducts for power-law fluids with viscous dissipation, International Journal of Heat and Mass Transfer 40 (1996) 15–26

    1996

  18. [25]

    H. Wang, Y. Wang, Influence of three-dimensional wall roughness on the laminar flow in microtube, International Journal of Heat and Fluid Flow 28 (2007) 220–228

    2007

  19. [27]

    L. A. Sphaier, A. Barletta, M. Celli, P. V. Brand˜ ao, E. Ghedini, Laminar forced convection in circular microchannels with slip-flow: Analysis of randomly distributed roughness, Interna- tional Communications in Heat and Mass Transfer 162 (2025) 108615

    2025

  20. [28]

    R. K. Shah, A. L. London, Laminar Flow Forced Convection in Ducts, in: Advances in Heat Transfer, Academic Press, 1978

    1978

  21. [29]

    Wolfram Research, Inc., Mathematica, Version 14.2,https://www.wolfram.com/mathematica,

  22. [30]

    R. M. Manglik, A. E. Bergles, Laminar flow heat transfer in a semi-circular tube with uniform wall temperature, International Journal of Heat and Mass Transfer 31 (1988) 625–636

    1988

  23. [31]

    E. M. Languri, K. Hooman, Slip flow forced convection in a microchannel with semi-circular cross-section, International Communications in Heat and Mass Transfer 38 (2011) 139–143. 16

    2011

  24. [32]

    R. S. Alassar, Fully developed forced convection through semicircular ducts, Journal of Thermophysics and Heat Transfer 28 (2014) 560–565

    2014

  25. [33]

    Mukherjee, A

    S. Mukherjee, A. K. Gupta, R. P. Chhabra, Laminar forced convection in power-law and Bingham plastic fluids in ducts of semi-circular and other cross-sections, International Journal of Heat and Mass Transfer 104 (2017) 112–141

    2017

  26. [34]

    Kyritsi-Yiallourou, G

    S. Kyritsi-Yiallourou, G. C. Georgiou, Newtonian Poiseuille flow in ducts of annular-sector cross-sections with Navier slip, European Journal of Mechanics-B/Fluids 72 (2018) 87–102. 17

    2018

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.