DOI : 10.5281/zenodo.23054645
- Open Access
- Authors : Engr. Imran Hussain
- Paper ID : IJERTV15IS090593
- Volume & Issue : Volume 15, Issue 09 , September – 2026
- Published (First Online): 30-09-2026
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Computational Fluid Dynamics Modelling and Thermal Performance Analysis of an Aluminium Microchannel
Engr. Imran Hussain
Convener Mechanical Engineers Committee Pakistan Engineers Association, Pakistan
Abstract – This study investigates flow behaviour and heat transfer in an open rectangular aluminium microchannel conveying deionized water using computational fluid dynamics. The aluminium microchannel was analysed for mass flow rates of 20, 40, and 80 g/s and heating powers of 250, 500, and 1000 W applied at the bottom wall. The study evaluates temperature distribution, velocity, pressure drop, wall heat flux, and thermal performance under the different operating conditions. A three dimensional model was developed using aluminium 2024-T4 as the solid material and deionized water as the fluid domain. Mesh independence was assessed using skewness and aspect ratio, and the CFD simulations were conducted for the selected operating conditions. The results show that increasing mass flow rate improves convective heat transfer and cooling effectiveness but also increases pressure losses. The results indicate balanced thermal and hydraulic performance at the intermediate mass flow rate, while the highest mass flow rate produces higher velocity and pressure penalties with comparatively small additional thermal improvement.
Keywords – computational fluid dynamics; aluminium microchannel; deionized water; heat transfer; mass flow rate; pressure drop; wall heat flux
-
INTRODUCTION
Enhancing thermal management in small systems like heat exchangers, microreactors, and electronic components requires research into single-phase heat transport in microchannels that are the flow properties of deionized water through an open rectangular aluminium microchannel (Aluminium 2024-T4), where controlled thermal gradients are produced by selective heating of the bottom wall, are the main focus of this study. The study intends to simulate and optimize heat transfer performance by altering flow rates and thermal inputs, which is essential for enhancing dependability and efficiency in contemporary engineering applications. In- depth examination of the heat transfer and fluid dynamics in this configuration offers important information for improving the microchannel design for increased cooling capacity and operational stability.
-
OBJECTIVE
-
To analyse temperature distribution and flow behaviour at varying flow rates (20, 40, 80 g/s) and heating powers (250, 500, 1000 W) using CFD.
-
To evaluate the thermal efficiency and heat transfer performance of the system under different operating conditions.
-
-
LITERATURE REVIEW
According to Sahar et al., ignoring wall conduction in microscale heat exchangers can lead to significant inaccuracies in heat transfer predictionup to 50%. Additionally, the study noted a non-uniform distribution of Nusselt numbers along the channel, highlighting how important it is to appropriately simulate solid wall conduction in CFD simulations (Sahar, Madi et al., 2025). Yu and associates (2018): Solid wall conduction significantly pre-heats the fluid upstream, which lowers the local heat transfer rate, according to research on the impact of axial conduction in low Peclet number regimes. In microchannels with a high solid-to-fluid thermal conductivity ratio, this is especially important (Li & Tu, 2009).
In order to provide a conservative standard for heat transfer research, Bergman et al. (2011) offered analytical solutions for external laminar flow over a homogeneous flat plate. Even though they are idealized, these solutions might be used as a starting point, particularly when the model is first being validated. However, actual performance in this project is projected to be higher due to 3D effects and side wall conduction In 2024, Anjaneya et al. CFD results for a microchannel layout akin to Design 0 in this research
were presented by Alnaimat et al. (2024). Pressure drops, wall temperature gradients, and Nusselt number profiles were all analysed in the study. Additionally, it covered non-uniform grid space and mesh refinement methodologies, both of which are crucial for guaranteeing numerical correctness in the current investigation. offered a conservative standard for heat transfer research by providing analytical approaches for external laminar circulation over a homogeneous flat plate. Even though they are idealized, these solutions might be used as a starting point, particularly when the model is first being validated. However, because of side wall conduction and 3D effects, actual efficiency in this project should be higher.
CFD results for the microchannel layout akin to Design 0 in this research were presented by Alnaimat et al. (2024). Pressure drops, temperature at the wall variations, and Nusselt coefficient profiles were all analysed in the study. Additionally, it covered non- uniform grid spacing and mesh refinement techniques, both of which are crucial for guaranteeing numerical correctness in the current investigation. investigated methods for improving heat transfer in microchannel heat sinks and determined the impact of flows maldistribution and surface roughness. Their research supports the incorporation of geometry-specific thermal resistance modelling and sheds light on the effects of manufacturing in the real world (Ekkad & Singh, 2023). Minea (2012): Examined several CFD techniques used for transitioning and laminar flows in microchannels. According to the study, simulation reliability is significantly impacted by mesh quality, thermal boundary parameters, and conjugate heat transfer modelling (Zhang et al., 2023).
-
COMPUTATIONAL FLUID DYNAMICS MODELLING
An aluminium microchannel was subjected to CFD simulations in order to examine flow behavior and heat transfer. Three distinct mass flow rates20, 40, and 80 g/swere taken into account in the investigation. At the bottom wall, heated power levels of 250 W, 500 W, and 1000 W were applied. Under each circumstance, the Nusselt number, pressure drop, and temperature distribution were assessed. The findings support the evaluation of the system's thermal efficiency and design optimization for a range of operating circumstances.
-
Geometry Model
Using the draw, edit, and extrusion commands in Ansys Design Modeler, the geometry of a microchannel conveying deionized water in an open channel was modelled using aluminium 2024-T4 as a solid material. After that, the components were designated as solid and fluid parts for additional CFD processing. The channel's dimensions and shape are as follows
-
Solid part Aluminium
Width 12mm Hight 06mm Depth 60mm
-
Fluid Domain deionised water
Width 6mm Hight 2mm Depth 60mm
Figure 1 model
-
-
Mesh Metrics
ANSYS meshing tools were used to create a 3D mesh for the current CFD study, with a definite preference for fluid flow analysis. With an element size of 0.0004, 0.0003, and 0.00025 m, important flow areas and temperature barriers may be finely resolved. With roughly 50778, 76599, 142746 nodes and 245765, 377754, 714509 elements, the final mesh ensured a fair trade-off between computational cost and precision. The technique known as Sweep meshing, which works well with structured, extrudable geometries like microchannels, was used. This mesh configuration offersenough information to faithfully represent wall interactions, heat profiles, and velocity gradients in the simulation.
Table 1 Course Meshing Details
Mesh type
3D
Level
Course
Preference
CFD
Element size
0.0005m
Nodes
50778
Elements
245765
Figure 2 Front view coarse mesh
Figure 3 Side view coarse mesh
Figure 4 Isometric view Coarse mesh
Table 2 Medium Meshing Details
Mesh type
3D
Level
medium
Preference
CFD
Element size
0.0004m
Nodes
76599
Elements
377754
Figure 5 Medium mesh Front view
Figure 6 Medium mesh side view
Mesh type
3D
Level
Fine
Preference
CFD
Element size
0.00025m
Nodes
142746
Elements
714509
Figure 7 Medium mesh isometric view Table 3 Fine mesh details
Figure 8 Fine mesh front view
Figure 9 Fine mesh topside view
Figure 10 Fine mesh top view
-
Mesh independence test based on skewness and aspect ratio
The skewness histogram chart shows average skewness of 0.2314 and most of the elements are below 0.4 level of skewness element size was taken as 0.5mm for this mesh type. At edge sizing bias factor was take as 2 and no of divisions as 30.
Figure 11 edge sizing details
Figure 12 Skewness histogram plots Coarse Mesh
Medium mesh was created with element size 0.4mm and skewness was find as 0.2367 as average bias factor was again taken as 2 with 30 divisions
Figure 13 Skewness histogram plots medium mesh
Fine mesh was created with element size of 0.25 mm. the edge sizing was taken as 0.2mm and bias factor again as 2 with same number of divisions as 30. The average skewness was 0.225 which is good mesh quality.
Figure 14 Skewness histogram plots fine mesh
It is evident from the skewness histograms for coarse medium and fine mesh that more than 99% of the elements have skewness index less than 0.02 skewness value and the meshing successfully passes the mesh test to conduct flow and heat transfer simulations in ANSYS WORKBENCH 25R2
Figure 15 Aspect ratio Histogram Coarse Mesh
Figure 16 Aspect ratio Histogram Medium mesh
Figure 17 Aspect ratio Histogram plot fine mesh
The histogram charts in figure 14, 15 and 16 indicate the aspect ratio where all the element are below skewness index of 5 in coarse, medium and fine mesh which provides the basis to conduct CFD simulations on fine non uniform mesh.
Table 4 Zone wise mesh details
Sr No
Cell zone
No of nodes
Behaviour
1
Bottom Wall
2880
hard
2
Side Wall-1
1440
hard
3
Side Wall-2
1440
hard
5
Front Wall
240
hard
6
Back Wall
240
hard
7
Top Wall-1
720
hard
8
Top Wall-2
720
hard
9
Convection Wall
1440
soft
10
Inlet
48
soft
11
Outlet
48
soft
Table 5 Comparative Mesh table
Mesh type
Elements
Nodes
Coarse
245765
50778
Medium
377754
76599
Fine
714509
142746
Table 6 Nusselt number table
Mesh type
Nusselt number
%error
Coarse
4.974856322
0.5054%
Medium
4.962883142
0.2654%
Fine
4.949712644
0
Table 7 Velocity changes with Meshing
Mesh type
Vmin
Error
Vmax
Error
Coarse
0
0
1.6696721
0.599%
Medium
0
0
1.6796721
1.191%
Fine
0
0
1.6596721
0
Figure 18 Name Selection for Boundary Conditions
-
Material selection
The properties of Aluminium 2024-T4 and deionised water such as thermal conductivity, heat capacity density and thermal coefficients were provided to create these materials in CFD design modeler materials the cell zones were then assigned to solid as well as fluid materials.
-
Aluminium Properties
Density
2750
3
Heat capacity
0.875
Thermal conductivity
121
Expansion coefficient
23.2*10-6 1
-
Denoised water properties
Density
1000
3
Heat capacity
4180
Thermal conductivity
58
Expansion coefficient
210*10-6 1
-
-
Boundary conditions
Table 8 Boundary conditions at cell zones
SR No
Cell zone
Boundary Condition
1
Bottom Wall
Heat Power: 250, 500,1000 W
Temperature 295K
2
Side Wall-1
Insulated Temperature 295K Momentum:
Wall Motion: Stationary Wall
3
Side Wall-2
Insulated Temperature 295K Momentum:
Wall Motion: Stationary Wall
5
Front Wall
Insulated Temperature 295K Momentum:
Wall Motion: Stationary Wall
6
Back Wall
Insulated Temperature 295K Momentum:
Wall Motion: Stationary Wall
7
Top Wall-1
Insulated Temperature 295K Momentum:
Wall Motion: Stationary Wall
Shear condition: No slip at the fluid wall interface
8
Top Wall-2
Insulated Temperature 295K Momentum:
Wall Motion: Stationary Wall
Shear condition: No slip at the fluid wall interface
9
Convection Wall
Heat transfer coefficient 200 W/MK Wall Motion: Stationary Wall
Temperature 295
10
Inlet
Mass flow: 20 g/s,40 g/s, 80 g/s Temperature 291K
11
Outlet
Pressure Ambient
Temperature 295
12
Symmetry
Type: symmetry
-
Reasons and justifications for mesh and boundary condition selection
Based on the project requirements and relevant research articles, the selections for mesh size and boundary conditions were carefully chosen to ensure accurate simulation results in the CFD analysis of microchannel heat transfer. Two criteria were applied on all the three-mesh metrics for final selection of mesh. First Criteria was based o skewness level if 96% of the elements are in one group of sizing the mesh is taken as appropriate mesh sizing for accurate results. This criterion was fulfilled in fine meshing used for current study. 2nd criteria were based on aspect ratio as in the fine mesh the element size is smaller as compared to coarse and medium so minimum aspect ratio with a value of 0.1-0.2 was observed for 95% of the elements. At the fulfilment of both criteria a 3D mesh type was selected with an element size of 0.00025m, resulting in 305106 nodes and 276480 elements. This finer mesh resolution is essential for capturing detailed flow characteristics and thermal gradients within the microchannel, aligning with best practices recommended in similar studies ([1], [2]).
Boundary conditions were set to simulate realistic operating conditions of the microchannel. Distilled water was chosen as the working fluid with mass flow rates of 20, 40, and 80 g/s to investigate varying flow regimes. The fluid inlet temperature was fixed at 18°C (291K), reflecting typical laboratory conditions for experimental validation and ensuring consistency with previous studies (Reference: [3]). Heat flux values of 250, 500, and 1000 W applied to the bottom wall simulate different heat transfer intensities encountered in practical applications, facilitating a comprehensive analysis of thermal behaviour (Reference: [4]). Additionally, ambient temperature was set to 22°C to simulate standard laboratory environments, and a convective heat transfer coefficient of 200 W/m²K was applied to model heat exchange with the surroundings. The no-slip condition at the walls ensures that fluid velocity is zero relative to the wall, which is typical for microscale flows. These selections were made to optimize the accuracy and reliability of the CFD simulations, ensuring that the results effectively characterize the heat transfer performance and fluid dynamics within the microchannel under varying operational parameters.
Table 9 Solution methods
1
Formulation Type
Pressure based
2
Gravity
9.81m/s2
3
Velocity Formulation
absolute
4
Time
Steady
5
Planner
2D
6
Viscous model
Laminar
7
Energy
on
8
Gradient
Least Squares Cell Based
9
Scheme
Coupled
10
Pressure
2nd order upwind
11
Momentum
2nd order upwind
12
Energy
2nd order upwind
-
Convergence Residual Criteria
Continuity
0.001
x-velocity
0.001
y-velocity
0.001
z-velocity
0.001
Energy
1e-06
Convergence of residuals
iter
continuity
x-velocity
y-velocity
z-velocity
energy
time/iter
177
1.1220e-03
4.2088e-07
4.1721e-07
1.7255e-06
1.6861e-08
0:01:19 23
178
1.1020e-03
4.1592e-07
4.1166e-07
1.6928e-06
1.6888e-08
0:01:16 22
179
1.0813e-03
4.1033e-07
4.0465e-07
1.6670e-06
1.6865e-08
0:01:12 21
180
1.0630e-03
4.0476e-07
3.9823e-07
1.6415e-06
1.6859e-08
0:01:09 20
181
1.0437e-03
3.9970e-07
3.9243e-07
1.6205e-06
1.6815e-08
0:01:05 19
182
1.0239e-03
3.9444e-07
3.8722e-07
1.5985e-06
1.6885e-08
0:01:02 18
183
1.0044e-03
3.8845e-07
3.8136e-07
1.5767e-06
1.6898e-08
0:01:00 17
184
9.8598e-04
3.8003e-07
3.7545e-07
1.5543e-06
1.6927e-08
0:00:57 16
! 184 solution is converged
Writing "| gzip -2cf > SolutionMonitor.gz"…
-
-
-
CFD Simulation results at 20 g/s
Using an aluminium microchannel with water entering at 291 K, ambient temperature at 295 K, and a heat transfer coefficient of 200 W/m-K, a CFD analysis was performed to assess thermal performance under various mass flow rates (20, 40, and 80 g/s) and heat fluxes (250, 500, and 1000 W). The findings demonstrated that convective heat transfer was much improved by raising the mass flow rate, which decreased wall temperatures and increased cooling effectiveness. Similar to this, larger heat fluxes produced larger thermal gradients, which accelerated the rate of heat dissipation because of the stronger temperature differentials but also raised the demands for heat removal. In order to maintain stable temperature profiles, the heat transfer coefficient was essential in controlling the interaction between the microchannel and its surroundings. All things considered, the study shows that heat flux and mass flow rate are important determinants of microchannel thermal behaviour, providing insightful information for improving microscale cooling systems.
Table 10 Console computed results at 20g/s
250 W
500W
1000W
Zone
Total Pressure
Pa
Velocity m/s
Temperatu re K
Heat flux
W/M^2
K
Temperatu re K
Heat flux
W/M^2
K
Temperatu re K
Heat flux W/M^2K
Back
0
0
295
15570.35
1
294.99611
15291.92
5
294.76563
2.6890354
e-05
Cold wall
802.6635
2
0
291.06543
0
291.07767
0
291.07761
0
contact_regio
n1
0
0
294.6996
24246.62
7
294.70863
24268.00
4
294.68868
24144.262
contact_regio
n2
767.5057
9
0
294.69907
24246.61
9
292.30927
24267.99
5
292.3017
24144.252
Front
0
0
295
9592.991
4
294.99764
9304.314
294.99755
9617.4965
Hot wall
0
0
294.84561
31.77651
5
294.85291
500
294.83002
8.3317453
e-05
inlet
2647.152
8
1.6696721
291
0
290.99998
0
290.99991
0
outlet
1522.358
3
1.6713782
291.27217
0
291.27239
0
291.27125
0
sidewall1
0
0
295
10014.37
7
294.99736
9664.534
7
294.99702
10905.741
sidewall2
0
0
295
9988.400
4
294.99732
9638.484
1
294.99697
10877.567
topwall1
0
0
295
16136.12
4
294.99611
16029.61
1
294.9959
16839.947
topwall2
0
0
295
16166.44
4
294.99605
16059.86
5
294.99584
16869.717
Net
228.1668
0.01144195
3
294.43461
4151.865
6
294.02864
4155.525
7
294.01517
4134.3533
-
Discussion on simulation results at 20 g/s and 250, 500,1000W
Across all heat flux levels, the maximum velocity stayed comparatively consistent at around 2.23 at the mass flow rate of 20 g/s. Pressure was observed as 1.359kPa by maximum for mass flow rate of 20 g/s. This suggests that at this ow flow rate, the additional thermal input had no impact on the flow resistance. It is interesting to note that as the applied heat flux increased, the maximum wall heat flux declined somewhat from 9.35×105 to 9.750×10 W/m²K. This is probably because of localized temperature saturation and diminished thermal gradients at the wall. Constrained convective enhancement at lower flow rates was indicated by this flow regime's overall reduced ability to respond dynamically to increasing thermal loads.
Figure 19 Pressure At 20 g/s, 250W
Figure 20 Pressure At 20 g/s, 500W
Figure 21 Pressure at 20 g/s 1000W
Figure 22 Heat flux at 20 g/s, 250W
Figure 23 Heat flux at 20 g/s, 500W
Figure 24 Heat flux at 20 g/s, 1000W
Figure 6 Veloicty Streams-1 at 20 g/s, 250w
Figure 25 Velocity at 20 g/s and 500W
Figure 26 Velocity at 20 g/s and 1000
Figure 27 Temperature at 250w, 20 G/S
Figure 28 Temperature at 20 g/s and 500W
Figure 29 Temperature at 20 g/s and 1000 W
-
Discussion on simulation results at 40 g/s and 250, 500,1000W
-
The maximum velocity rose dramatically to roughly 4.14 m/s at a medium mass flow rate of 40 g/s, demonstrating that doubling the flow rate from 20 g/s resulted in an essentially proportionate increase in velocity. Additionally, the pressure drops increased significantly to 3.5KPa, as compared to pressure at 20 g/s indicating stronger flow resistance brought on by increased turbulence and velocity. The maximum wall heat flux, in contrast to the 20 g/s instance, reduced marginally at 1000 was 10.13×10 W/m²K but increased slightly with higher thermal loads, from 9.57×10 W/m²K at 250 W to 9.551×10 W/m²K at 500 W. This behaviour points
to more effective convective heat transfer at this flow rate, with the system better able to handle higher heat inputs without sacrificing performance. As a result, 40 g/s is the ideal balance between hydrodynamic effectiveness and heat evacuation.
Figure 30 Pressure at 40 G/S and 250W
Figure 31 Pressure 40 g/s 500W
Figure 32 Pressure 40 g/s 1000W
Figure 33 velocity at 40 g/s 1000W
Figure 34 Velocity at 40 g/s
Figure 35 Velocity-3 AT 40 g/s 1000W
Figure 36 Heat Flux-1 At 40 G/S
Figure 37 Figure 23 Heat Flux-2 At 40 G/S
Figure 38 Heat Flux-3 At 40 G/S
Figure 39 Temperature at 40 g/s and 500W
Figure 40 Temperature at 40 g/s and 500W
Figure 41 Temperature at 40 g/s and 1000W
5.3 Discussion on simulation Results at 80 g/s and 250, 500,1000W
The system showed a peak flow velocity of 71.6 m/s at the maximum mass flow rate of 80 g/s, which was constant at all heat flux levels, suggesting the flow was probably close to its saturation point. A considerable hydraulic cost for operating at such a high flow rate was shown by the pressure drop, which doubled from the 40 g/s instance to 7.69 kPa. The maximum wall heat flux, on the other hand, stayed comparatively constant, increasing marginally from 10.31×10 W/m²K at 250 W to 10.86×10 W/m²K at 500 W before significantly declining to 10.06×10 W/m²K at 1000 W. These findings indicate declining returns in thermal efficiency at very high
flow rates, even though thermal performance improved marginally. The benefits in heat transfer do not offset the sharp increase in pressure losses.
Figure 42 PRESSURE-1 AT 80 G/S and 250W
Figure 43 PRESSURE-2 AT 80 G/S and 500W
Figure 44 PRESSURE-3 AT 80 G/S and 1000W
Figure 45 Wall Heat Flux At 80 G/S and 250w
Figure 46 Wall Heat Flux At 80 G/S and 5000w
Figure 47 Wall Heat Flux At 80 G/S and 10000w
Figure 48 Temperature at 80 g/s and 250W
Figure 49 Temperature at 80 g/s and 500W
Figure 50 Temperature at 80 g/s and 1000W
Figure 51 velocity at 80 g/s and 250W
Figure 52velocity at 80 g/s and 500W
Figure 53 velocity at 80 g/s and 1000W
Table 11 minimum and maximum values
|
Sr No |
Pressure Pa |
Velocity |
Temperature |
Wall Heat flux |
|||||
|
maximum |
minimum |
maximum |
minimum |
maximum |
minimum |
maximum |
minimum |
||
|
1 |
1599 |
71 |
2.089 |
0.0115 |
291.1 |
291 |
788.2 |
43.78 |
|
|
2 |
1598 |
70.6 |
2.089 |
0.0116 |
291.1 |
291 |
788.2 |
43.79 |
|
|
3 |
1598 |
70.6 |
2.089 |
0.0116 |
291.2 |
291 |
995 |
55.28 |
|
|
4 |
4608 |
209.6 |
3.98 |
0.2216 |
291.12 |
291 |
790.4 |
43.91 |
|
|
5 |
4611 |
209.6 |
3.99 |
0.2216 |
291.12 |
291 |
790.4 |
43.91 |
|
|
6 |
4611 |
209.6 |
3.99 |
0.2216 |
291.12 |
291 |
995 |
55.28 |
|
|
7 |
14150 |
631.6 |
7.71 |
0.4286 |
291.15 |
291 |
792.4 |
44.01 |
|
|
8 |
14160 |
632 |
7.72 |
0.4294 |
291.15 |
291 |
792.4 |
44.02 |
|
|
9 |
14160 |
632 |
7.72 |
0.4294 |
291.15 |
291 |
995 |
55.28 |
|
-
CONCLUSION
Important details about the aluminium microchannel's thermal and hydraulic performance were uncovered by the CFD simulation conducted under various heat fluxes (250 W, 500 W, and 1000 W) and mass flow rates (20 g/s, 40 g/s, and 80 g/s). The maximum velocity and pressure drop across the channel increased dramatically as the mass flow rate increased, suggesting both higher hydraulic resistance and improved convective transport. With little change in flow characteristics and a slight drop in wall heat flux at 20 g/s, the system demonstrated limited reactivity to greater heat flux, indicating decreased heat removal efficiency at low flow rates. The channel's ideal working point was determined by its balanced performance at 40 g/s, which included enhanced heat dissipation and a modest pressure drop. On the other side, the 80 g/s condition resulted in severe pressure losses and just small thermal improvements, although offering the highest velocities and marginally improved heat flux handling. In general, heat transmission is improved by increasing mass flow rate up to a certain point, after which the advantages are diminished by increasing pressure penalties. These results are useful for microchannel cooling system optimization, where pumping power and thermal efficiency must be taken into account.
-
REFERENCES
-
Anjaneya, G., Sunil, S., K, M., Santhosh, A., Patil, S., Prasad C, D., Aden, A., & G, G. (2024). Study of Impact of Nano Fluids on Performance of Microchannel Heat Exchangers Using CFD. International Journal of Thermofluids, 24, 100836. https://doi.org/10.1016/j.ijft.2024.100836
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Ekkad, S. V, & Singh, P. (2023). Chapter Six – Recent advancements in single-phase liquid-based heat transfer in microchannels (J. P. Abraham, J. M. Gorman, & W. J. Minkowycz (eds.); Vol. 55, pp. 239293). Elsevier. https://doi.org/https://doi.org/10.1016/bs.aiht.2022.12.001
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Li, J.-X., & Tu, S.-T. (2009). Boundary analysis of fluid laminar forced flow over an isothermal plate in porous medium considering the local non-equilibrium. Huadong Ligong Daxue Xuebao /Journal of East China University of Science and Technology, 35, 481485.
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