Numerical Study of Semi-Circular, Triangular, and Rectangular Roughness in Microchannels

1. Introduction

Continued miniaturization and performance scaling in electronics have driven substantial increases in local heat flux, with modern processors and power devices routinely dissipating hundreds to thousands of watts per square centimeter from compact footprints [1,2,14,15]. As power density rises, thermal management becomes a primary constraint on performance, reliability, and energy efficiency, because elevated temperatures accelerate material degradation, induce thermal stresses, and can lead to catastrophic failure. Traditional cooling solutions such as finned heat sinks with forced air convection are often unable to remove these large heat loads efficiently, especially when package size, weight, and noise must be minimized [3,4].

Microchannel heat sinks, first proposed by Tuckerman and Pease for high-performance VLSI cooling, exploit small hydraulic diameters to achieve very high surface-area-to-volume ratios and greatly enhanced convective heat transfer [5,19,33,39]. Their compact geometry, low thermal resistance, and compatibility with liquid coolants have led to widespread investigation for applications in CPUs, 3D integrated circuits, power electronic modules, and concentrator photovoltaics [6,7,8,9]. Under the predominantly laminar flow conditions typical of microchannels, velocity and temperature fields can be predicted with reasonable accuracy using continuum models, enabling careful optimization of both geometry and operating conditions.

In practice, the performance of microchannel heat sinks depends sensitively on geometric parameters such as channel length, width, height, aspect ratio, and manifold design, as well as on flow distribution and material properties [16,17,33,41]. Real fabrication techniques—including deep reactive ion etching, micromachining, molding, and additive manufacturing—introduce surface roughness and geometric deviations that modify friction factor and Nusselt number, sometimes in ways that differ from classical smooth-channel correlations [10,12,13,43]. Roughness can promote mixing and boundary-layer disruption, but it also increases pressure drop and can complicate flow stability, especially when roughness elements interact with developing hydrodynamic and thermal boundary layers [11,20,21,31].

A substantial literature addresses single-phase laminar heat transfer in smooth or ideally roughened microchannels, producing families of correlations for friction factor, Nusselt number, and entry-length behavior over a wide range of Prandtl number and aspect ratio [19,20,21,33]. Many studies focus on engineered geometric perturbations, such as ribs, cavities, wavy channels, or vortex generators, to intensify mixing and improve heat transfer, often relying on numerical simulations due to the experimental challenges of instrumenting microscale flows [24,25,26,27]. Several recent studies have reported complementary insights into thermal transport and evaporation phenomena in micro- and nanoscale systems using both numerical and molecular approaches [34,35,36,37,38]. Other works examine the use of nanofluids as working media, reporting performance gains that depend on nanoparticle concentration, stability, and viscosity penalties [28,29,30,44].

Despite this activity, relatively few studies directly compare multiple surface-roughness morphologies—such as semi-circular, triangular, and rectangular features—within a single, unified modeling framework that also includes conjugate heat transfer through a solid substrate. Furthermore, many numerical investigations idealize walls as perfectly smooth and do not explicitly account for fabrication-induced roughness scales or patterns [9,17,39,43]. This gap complicates attempts to generalize design rules or to anticipate how realistic roughness will shift the trade-off between heat transfer enhancement and pumping power in microchannel heat sinks.

The primary objective of this study is therefore two-fold: (i) to construct and validate a conjugate, laminar, nonisothermal microchannel model in COMSOL Multiphysics that reproduces expected smooth-wall behavior, and (ii) to use that validated framework to evaluate the thermal–hydraulic impact of three distinct roughness geometries: sinusoidal (modeled as semi-circular dimples), triangular protrusions, and rectangular protrusions. By applying identical operating conditions to all configurations, the study isolates the influence of roughness shape on velocity field, temperature distribution, pressure drop, and overall cooling performance, yielding practical guidance for microchannel designs that must tolerate or intentionally use surface roughness.

2. Methods and Materials

2.1. Microchannel Geometry

Four microchannel geometries were created in SolidWorks to define both three-dimensional representations and two-dimensional profiles suitable for import into COMSOL Multiphysics. Exporting CAD cross-sections as DXF files preserves geometric fidelity and is a standard workflow in microchannel and microfluidic simulations, where complex shapes are routinely constructed in mechanical design tools and then meshed in finite-element environments [22,23,31,32].

Each microchannel shares the same primary dimensions: a channel height of $0.18$ mm, a width of $0.06$ mm, and a length of 25 mm, which are consistent with high-performance liquid-cooled microchannel heat sinks used in electronic packaging [16,33,39,41]. Copper is used as the heat-sink material because of its high thermal conductivity and prevalence in microchannel coolers, where efficient in-plane heat spreading reduces peak chip temperatures and mitigates local hot spots [14,15,40,45]. Water serves as the coolant, reflecting its widespread use and well-characterized thermo-physical properties in electronics cooling applications [2,9,33,44].

The baseline geometry is a smooth rectangular microchannel without any internal surface texture. Three additional geometries incorporate periodic roughness along the bottom wall: (i) semi-circular dimples (approximating sinusoidal roughness), (ii) triangular protrusions, and (iii) rectangular protrusions. In each case, the characteristic roughness element has a width of $0.05$ mm, a height of $0.025$ mm, and a spacing of $0.05$ mm between adjacent features, so that the pitch and amplitude are directly comparable across geometries. These dimensions are chosen to be representative of roughness scales achievable by microfabrication or additive manufacturing methods while still being large enough to noticeably affect flow and heat transfer [10,12,43,44].

Figure 1 shows the 3D models of the four microchannels, while Figure 2, Figure 3, Figure 4 and Figure 5 present the corresponding 2D cross-sectional dimensions used for simulation.

2.2. Dimensionality and Domain Definition

To reduce computational cost while capturing the essential physics, a two-dimensional representation of the microchannel cross-section is used instead of a full three-dimensional model. This approach is widely adopted in microchannel research when the channel depth is uniform and much larger than the characteristic roughness scale, because spanwise variations are relatively small and the dominant gradients occur in the streamwise and wall-normal directions [20,21,41,42].

The computational domain is partitioned into a fluid region, representing the water-filled channel, and a solid region, representing the copper substrate and, where applicable, the added roughness geometry. Figure 6, Figure 7 and Figure 8 illustrate the selected domains for water and copper in the COMSOL model.

2.3. Meshing Strategy

The presence of numerous small roughness features increases geometric complexity and demands careful meshing to resolve local velocity and temperature gradients without excessive computational expense. A relatively coarse global mesh is adopted but refined near the channel walls and around roughness elements, using quadrilateral elements for the baseline geometry and primarily triangular elements for roughened configurations. This strategy balances accuracy and runtime, producing 6706 elements for the smooth channel, 65318 elements for the semi-circular channel, 22752 elements for the triangular channel, and 19908 elements for the rectangular channel. Figure 9 and Figure 10 show representative meshes for the baseline and semi-circular cases.

2.4. Governing Equations

The simulations employ COMSOL’s conjugate heat transfer interface, which couples laminar flow with heat transfer in both solids and fluids under nonisothermal conditions. The model solves the incompressible steady Navier–Stokes equations for the fluid region and the energy equation for both fluid and solid regions.

2.4.1. Heat Transfer in Solids and Fluids

The conductive heat flux in the solid and fluid domains is expressed as

$$\mathbf{q}=-k\nabla T,$$

(1)

where $\mathbf{q}$ is the heat flux vector, k is the thermal conductivity, and T is the temperature.

The corresponding volumetric energy balance for a control volume of characteristic thickness $\Delta z$ can be written in finite-volume form as

$$(\Delta z)\rho C_p\mathbf{u}·\nabla T+\Delta q=(\Delta z)Q+q_0+(\Delta z)Q_p+(\Delta z)Q_{vd},$$

(2)

where $\rho$ is the density, $C_p$ is the specific heat capacity, $\mathbf{u}$ is the velocity vector, Q is any volumetric heat source, $Q_p$ represents pressure-work contributions, $Q_{vd}$ captures viscous dissipation, $q_0$ is an externally imposed surface heat flux, and $\Delta q$ is the net conductive flux into the control volume. In the present simulations, volumetric sources are set to zero except for the imposed bottom-surface heat flux, and viscous dissipation is negligible under the studied conditions.[1,2,44]

On external boundaries where a heat flux is prescribed, the boundary condition takes the form

$$-\mathbf{n}·\mathbf{q}=q_0,$$

(3)

where $\mathbf{n}$ is the outward unit normal vector and $q_0$ is the applied heat flux.

2.4.2. Laminar Flow

The steady, incompressible Navier–Stokes equations governing the fluid flow are

$$\rho (\mathbf{u}·\nabla )\mathbf{u}=-\nabla p+\nabla ·\tau +\mathbf{F},$$

(4)

$$\nabla ·\left(\rho \mathbf{u}\right)=0,$$

(5)

where p is pressure, $\tau$ is the viscous stress tensor, and $\mathbf{F}$ is a body force per unit volume. For a Newtonian fluid, the stress tensor is

$$\tau =\mu \left(\nabla \mathbf{u}+\nabla {\mathbf{u}}^T\right),$$

(6)

with dynamic viscosity $\mu$. Under the low-Reynolds-number conditions considered, inertial terms remain modest, and the flow remains laminar and steady, as in many microchannel cooling applications.[19,33,44]

At the inlet, a uniform velocity boundary condition is imposed:

$$\mathbf{u}=U_0{\mathbf{n}}_{\mathrm{in}},$$

(7)

where $U_0$ is the prescribed mean inlet speed and ${\mathbf{n}}_{\mathrm{in}}$ is the inward normal vector. At the outlet, a fixed static pressure condition is applied:

$$p=p_0,$$

(8)

which corresponds to atmospheric pressure at the reference plane. No-slip conditions are enforced along all solid–fluid interfaces, ensuring that the fluid velocity vanishes at the walls [2,7,14].

2.4.3. Nonisothermal Coupling

The nonisothermal flow problem couples the velocity and temperature fields through convective transport in the energy equation and, if desired, temperature-dependent properties in the momentum equation. The viscous dissipation term $Q_{vd}$ in Equation (2) can be written as

$$Q_{vd}=\tau :\nabla \mathbf{u},$$

(9)

but this contribution is generally small for the laminar, moderate-velocity flows studied here and is not the dominant source of heating. The fully coupled solution yields spatially varying temperature and velocity profiles that reflect both fluid convection and solid conduction, which is essential for realistic prediction of microchannel heat-sink performance [22,40,44,45].

2.5. Boundary Conditions and Operating Parameters

A uniform heat flux of 1000 W/m² is applied to the bottom surface of the copper substrate to approximate heating from an active semiconductor device bonded beneath the heat sink. Constant heat-flux boundary conditions are commonly used in microchannel heat-sink simulations because they mimic the nearly uniform power dissipation across a chip footprint and simplify comparison across different channel geometries.[14,44,45,47] Reported heat fluxes in modern microprocessors and power modules span several hundred to several thousand watts per square centimeter when measured directly at the chip level, but the effective flux through the heat-spreading substrate can be considerably lower due to thermal spreading and packaging details [1,15,33,46]. The value used in this work lies in a representative low-to-moderate range for compact electronic systems.

At the channel inlet, a uniform velocity of $1.5$ m/s is specified, with water at an inlet temperature consistent with typical coolant conditions in laboratory demonstrations and compact liquid-cooling loops. The outlet is set to atmospheric pressure (1 atm), and all solid–fluid interfaces use the no-slip boundary condition. The channel is modeled as a shallow structure with an effective depth equal to the out-of-plane thickness, which is incorporated as a parameter in the COMSOL formulation; this treatment has been successfully used in prior microchannel and corrugated-channel CFD studies to represent 3D effects in a reduced-dimensional model [29,30,42,48].

Figure 11 shows the heat-flux boundary selection, while Figure 12 and Figure 13 illustrate the inlet and outlet conditions in the COMSOL environment.

3. Results and Discussion

3.1. Baseline Smooth Microchannel Behavior

The baseline smooth-walled microchannel is simulated first to validate the modeling approach and to provide a reference for subsequent comparisons. As expected for laminar flow entering a narrow channel, the velocity profile develops from a relatively uniform inlet condition toward a fully developed shape, accompanied by a modest entrance-region acceleration due to the geometric contraction and viscous effects.[Lee2005,Rosa2009] The pressure drop between inlet and outlet is on the order of 1000 Pa under the specified conditions, consistent with trends predicted by laminar duct-flow correlations for similar dimensions and Reynolds numbers [19,20,47].

Figure 14 shows the velocity field in the baseline channel, and Figure 15 presents the corresponding temperature distribution. The temperature gradually increases from inlet to outlet along the heated bottom wall, while the unheated top wall remains cooler, creating a transverse temperature gradient and a developing thermal boundary layer. These qualitative features agree with classical analyses of laminar forced convection with constant heat flux in rectangular ducts, supporting the validity of the simplified two-dimensional model [33,44,47].

3.2. Effect of Roughness on Velocity Fields

Introducing periodic roughness elements along the bottom wall alters the local velocity distribution by creating acceleration zones around protrusions or cavities and by generating recirculation regions that disturb the boundary layer. Such geometric perturbations are known to enhance convective transport by increasing surface renewal and thinning the thermal boundary layer, though they also increase frictional losses and therefore pumping power [24,25,26,27].

Figure 16, Figure 17 and Figure 18 display the velocity fields for the semi-circular, triangular, and rectangular roughness geometries. The semi-circular case exhibits the highest peak velocity near the channel entrance and around the curved surfaces, as the flow accelerates to negotiate the reduced local cross-sectional area while maintaining volumetric flow rate. However, the average velocity over the channel length is lower than in the triangular and rectangular cases because the smoother curvature induces less persistent mixing and weaker flow disturbance downstream [11,24,43].

In contrast, the triangular roughness generates sharp corners that cause pronounced local accelerations and stronger recirculation zones behind the features, leading to more sustained flow disturbance and elevated shear near the wall. The rectangular protrusions also perturb the flow, but their blunt geometry can promote larger wake regions with slower-moving fluid, which may reduce the net enhancement compared to the triangular case [Kose2022,Gonul2025,Salamatbakhsh2023].

Although all roughness geometries increase local velocities relative to the smooth channel, the overall hydraulic penalty differs by shape. The triangular configuration tends to maintain higher average velocities and more persistent mixing, whereas the rectangular case can suffer larger effective blockage and wake-induced stagnation, increasing pressure drop without proportionally improving heat transfer.[Lu2020,Kose2022,Gong2025] These trends align qualitatively with prior studies on ribbed and vortex-generator-based microchannels, where sharper or more streamlined features are often tuned to balance enhancement against added drag [24,25,26,27].

3.3. Effect of Roughness on Temperature Fields

The modified velocity fields directly influence the temperature distributions by altering convective transport and boundary-layer structure. Figure 19, Figure 20 and Figure 21 show the temperature fields for the semi-circular, triangular, and rectangular roughness geometries under the same heat-flux and inlet conditions used for the baseline.

All roughened channels exhibit lower maximum fluid temperatures compared with the smooth channel, confirming that surface roughness enhances heat removal by promoting mixing and surface renewal near the heated wall. Among the tested configurations, the triangular roughness yields the lowest peak temperature, reaching approximately 295 K, indicating the most effective cooling performance under the studied conditions. The semi-circular geometry also reduces the maximum temperature relative to the baseline, but its improvement is somewhat more modest than that of the triangular case, reflecting differences in how each shape disturbs the boundary layer [Lu2020,Zhou2016,Gonul2025].

The rectangular roughness provides the weakest thermal enhancement, with maximum temperatures rising to around 345 K, only modestly better than (or in some regions comparable to) the baseline channel. This outcome suggests that the rectangular protrusions create regions of slow-moving fluid and thicker thermal boundary layers on their lee sides, which partially offset the benefits of increased surface area and localized acceleration [20,31,33,43].

3.4. Thermal–Hydraulic Performance Trade-Offs

A central goal in microchannel design is to maximize heat-transfer performance while limiting the associated increase in pressure drop and pumping power [2,21,39,44]. The present simulations illustrate this trade-off by demonstrating that all roughness shapes improve cooling compared with the smooth channel, but they also introduce additional flow resistance whose magnitude depends sensitively on geometry.

The triangular roughness case offers the most favorable balance among the configurations considered, combining strong boundary-layer disruption and mixing with a manageable pressure drop that remains within a practical range for microchannel pumping systems. The semi-circular case achieves good local enhancement near the entrance but allows the flow to adapt relatively quickly, leading to a situation where the channel behaves almost as if the effective wall location has shifted upward, with limited further gains downstream. The rectangular case, by contrast, incurs a comparatively high hydraulic penalty and exhibits large wake regions with elevated temperatures, making it less attractive from a system-level perspective.

These observations echo broader findings in the literature, where optimized roughness and vortex-generator designs often rely on streamlined or tapered shapes to maintain momentum while still thinning the thermal boundary layer [24,25,26,27]. Further work could quantify these trade-offs using performance metrics such as the thermal–hydraulic performance factor or entropy generation minimization, as commonly used in advanced microchannel design studies [21,31,32,44].

4. Conclusion

This study developed and applied a conjugate, laminar, nonisothermal COMSOL Multiphysics model to investigate how idealized surface-roughness geometries influence thermal–hydraulic performance in a copper microchannel heat sink cooled by water. A baseline smooth channel was first simulated to establish reference behavior and to verify that the model captured expected trends in pressure drop, velocity development, and wall temperature distribution under a uniform bottom heat flux. Three additional configurations—semi-circular, triangular, and rectangular roughness along the heated wall—were then evaluated under identical operating conditions to isolate the influence of roughness shape on flow and heat transfer.

The results show that all roughened channels reduce maximum fluid temperature relative to the smooth baseline, confirming that geometric perturbations can enhance convective cooling by disturbing laminar boundary layers and promoting mixing. Among the studied geometries, the triangular roughness provided the best thermal performance, achieving a minimum peak temperature of around 295 K with a moderate increase in pressure drop, while the rectangular roughness produced the weakest enhancement and the highest peak temperatures, on the order of 345 K. The semi-circular geometry delivered intermediate performance, with strong local acceleration near the entrance but less sustained disturbance farther downstream.

These findings highlight the importance of carefully tailoring roughness morphology, amplitude, and spacing when designing microchannel heat sinks that must either tolerate or exploit fabrication-induced surface textures [11,21,31,43]. Future work could extend the present two-dimensional analysis to fully three-dimensional geometries, explore a wider range of Reynolds numbers and heat fluxes, and incorporate temperature-dependent fluid properties, thereby providing a more comprehensive picture of how realistic surface roughness impacts microchannel cooling in next-generation electronic systems [22,29,30,45].