# Comparing the Performance of a Straight-Channel Heat Sink with Different Channel Heights: An Experimental and Numerical Study

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}/s and heat fluxes between 3.8 and 7.43 W/cm

^{2}. The comparison is carried out between channels with four different heights in terms of temperature distribution, local Nusselt number, velocity, and flow characteristic. The results indicate that lowering the height of the channel from 12.7 to 7 and 4 mm raises the highest temperature of the heat sink, whereas the change in height to 10 mm reduces the temperature. Furthermore, increasing the flow rate has a higher impact on improving the Nusselt number in channels with a height of 10 mm. When the height is decreased from 12.7 to 10 mm, the performance evaluation criterion is obtained higher than one for all flow rates.

## 1. Introduction

## 2. Experimental Apparatus and Procedure

#### 2.1. Experimental Apparatus

^{2}are three different heat fluxes used for each case. Once equilibrium conditions with a constant temperature are reached, a voltage regulator is used to apply an adjusted heat flux to the test area at a specified flow rate. Each test was carried out three times for straight channels with different heights. All tests were repeated three times.

#### 2.2. Experimental Procedure

#### 2.3. Measurement Uncertainty

## 3. Numerical Model Development

#### 3.1. Governing Equations

#### 3.2. Boundary Conditions

_{i}, and the outflow determines the temperature at the outlet. An adiabatic boundary condition (insulated walls) was applied for the remaining walls to generate a fully insulated outside surface for the system. In terms of thermal paste between the surface of the straight channel and the aluminum block, a thin layer was modeled in COMSOL. At the outflow, the open boundary was utilized due to the absence of normal stress at this boundary. Figure 4 depicts the schematic diagram of the channel with a straight design and 7 mm. In laminar flow, a non-slip boundary condition was applied to the wall, meaning that the normal component of the velocity vector was zero. Table 2 provides more information on the dimensional parameter.

#### 3.3. Mesh Sensitivity Analysis

## 4. Results and Discussion

#### 4.1. Temperature Difference Variations

^{2}for four different channel heights. Based on Figure 7, the lowest temperature was obtained for the first thermocouple that is located at the entrance of the heat sink for all heat sinks with different channel heights. By looking at all cases, it can be found that increasing the heat flux leads to higher temperatures. With the comparison of temperature differences in Figure 7, when the flow rate is $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ and the heat flux is 7.43 W/cm

^{2}, the highest temperature difference of the channel with 12.7 mm height is 33.58 $\mathrm{\mathbb{C}}$, which increases to 36.67 °C and 40.16 °C once the height is reduced to 7 and 4 mm, respectively. Meanwhile for a channel with a height of 10 mm, the temperature difference reduces to 23.54 $\mathrm{\mathbb{C}}$. The impact of changing the channel height and heat fluxes for the $13.25{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate is illustrated in Figure 8. Like the previous case, by decreasing the channel height from 12.7 mm to 7 mm and 4 mm, the temperature difference is boosted for the $13.25{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate and maximum 7.43 W/cm

^{2}heat flux, with the difference that the range of temperature has become higher. Thus, the maximum temperature difference of 36.22 °C increases to 39.07 °C for the former, and the latter reaches 47.89 °C. However, a 2.7 mm decrease in the channel height caused the drop in temperature difference so that the temperature difference reached 26.22 °C for the heat sink with a 10 mm channel height. It can also be noted that the other two heat fluxes, 3.8 and 5.17 W/cm

^{2}, reveal the same temperature trend over the lower temperature range. Figure 9 presents the temperature difference variation for flow rate $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ and three heat fluxes. Based on Figure 9a, the maximum temperature difference for the channel with a 12.7 mm height and minimum heat flux of 3.8 W/cm

^{2}is 18.38 °C. As presented in Figure 9c,d, decreasing the channel height to 7 mm leads to a 10% rise in temperature, while for the channel with the height of 4 mm, a 44.3% temperature difference rise was obtained in comparison to the height of 12.7 mm. However, Figure 9b shows a 19.2% decrement in the temperature difference for the heat sink with a 10 mm channel height.

^{2}heat flux, when the flow rates decrease from $19.56$ to $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$, the maximum temperature increases from 33.85 °C to 40.8 °C. That means a 21.5% rise in the heat sink’s temperature.

^{2}heat flux, whereas with a 2.7 mm decrement in channel heights under the same condition, the maximum temperature decreases to 26.22 °C. However, a further drop in channel height resulted in a higher temperature difference in such a way that a 5.7 mm decrease in channel height increased the temperature difference to 39.07 °C; the maximum temperature difference reached 47.89 °C with a reduction of 8.7 mm in channel height. It can be ascertained that decreasing the channel height in a straight-channel heat sink provides an open space on the top of the channel that ameliorates the heat transfer and reduces the temperature difference along the heat sink, but the height of the channel limits this enhancement. For all cases, the minimum temperature differences were obtained for the channel with a height of 10 mm.

^{2}. Under the same condition, for the channel height of 10 mm, an 11.91% rise in maximum temperature is obtained by reducing the flow rate.

#### 4.2. Local Nusselt Number Variation

^{2}heat flux. It should be noted that two different flow rates are compared, which are 6.94 and $13.25{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$. As expected, there is a descending trend for the local Nu number along the heat sink for all tests. Moreover, when the flow rate increases to $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$, the coolant capacity of the heat sink rises, which causes a higher Nusselt number than $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rates. When the flow rate increases from 6.94 to $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$, the highest Nu number in the channel with a 10 mm height increases by 27.95%, from 89.24 to 114.19. However, by increasing the flow rate to $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ for the channel with a height of 12.7 mm, the maximum Nu number shows a 19.42% rise and changes from 62.24 to 74.32. That result demonstrates that the impact of increased flow rates on heat transfer enhancement is more significant for channels with a height of 10 mm compared to 12.7 mm. Once the channel height is decreased from 12.7 to 10 mm, the maximum Nu number rises from 74.2 to 114.19 for the $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate. As expected, open space above the channel enhances mixing flow and results in a higher convective heat transfer coefficient, although the convective heat transfer area reduces as channel height lowers. The maximum local Nu number is 20% higher for the channel with a height of 10 mm and a $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate compared to the channel with a height of 12.7 mm and a $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate. Figure 11b compares heat sinks with heights of 7 and 4 mm for flow rates of 6.94 and $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$. When the flow rate increases to $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ for the channel with a height of 7 mm, the maximum local Nu number increases by 23.15%, changing from 55.91 to 68.85. In comparison to a channel with a height of 7 mm, the average Nu number falls by 16.66% as the channel’s height is decreased to 4 mm. Moreover, it has also been observed that a channel with 7 mm height indeed has a higher Nu number than a channel with 4 mm height for both working fluid flow rates of 6.94 and $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$, respectively.

^{2}in Figure 12a,b. With a flow rate of $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$, Figure 12a illustrates that the heat sink with a 10 mm channel height provides better heat transfer and possesses a higher Nu number when compared to the other heat sinks. The average Nu number of this channel is 76.2, while under the same circumstances, the average Nu number for the channel with a height of 12.7, 7, and 4 mm is 66.68, 56.68, and 44.64, respectively. Moreover, as presented in Figure 12b, increasing the flow rate to $13.25{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ enhances heat transfer with a higher Nusselt number for all channels. By illustration, a 10 mm channel height has a 3.6% higher average Nu number when the flow rate changes to $13.25{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$. However, the higher Nusselt number corresponds to the 10 mm channel height heat sink. The channel with a height of 4 mm yields the lowest average Nu number of 54.78. As expected, further diminishing the channel height reduces the convective heat transfer area and achieves a lower Nu number.

#### 4.3. Velocity and Flow Characteristics

#### 4.4. Performance Evaluation Criterion

## 5. Conclusions

- When the height of the channel is reduced from 12.7 to 10 mm, the temperature distribution along the heat sink is diminished at all flow rates. When the maximum heat flow of 7.43 W/cm
^{2}is combined with a heat flux of $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$, the maximum temperature drops from 33.85 °C to 23.54 °C. Under the same circumstances, the temperature of the channels with 7 and 4 mm heights reaches 36.67 °C and 40.16 °C, respectively. - When the lowest heat flux and flow rate are 3.8 W/cm
^{2}and $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$, reducing the channel heights to 7 mm and 4 mm results in a 10% and 44.3% increase in maximum temperature compared to 12.7 mm channel heights. In contrast, reducing the height to 10 mm corresponds to a 19.2% decrease in temperature. - The local Nu number descends along the flow direction and has a rising trend with increasing flow rates. Increasing the flow rate from 6.94 to $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ in a channel with a height of 10 mm yields a 27.95% growth in the maximum local Nusselt number. For channels with heights of 12.7 mm, 7 mm, and 4 mm, the exact change in flow rate has a 19.42%, 23.15%, and 16.66% influence on increasing the maximum local Nu number.
- Decreasing the channel height to 10 mm ameliorates the heat sink’s heat transfer performance with the average Nu number of 76.2 with $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate and 3.86 W/cm
^{2}heat flux. However, reducing the channel height from 12.7 mm to 7 and 4 mm results in a declining Nu number; thus, the average Nu number decreases from 66.68 to 55.68 for the former and reaches 44.64 for the latter. - Reducing the channel height to 7 and 4 mm leads to a higher velocity area in the open space above the channel and a decreased velocity distribution between the channel area, affecting heat transfer performance. However, with a 10 mm channel height, the higher velocity distribution increases between the channel with more flow mixing in the open space above the heat sink.
- As the channel height lowers from 12.7 to 10 mm, the highest performance evaluation criterion is attained at 1.44, 1.22, and 1.34, respectively, for flow rates of 6.94, 13.25, and $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$. Except for the 7 mm height with a $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate, all other designs with lower heights resulted in a PEC of less than 1.0, indicating inferior thermal performance when compared to a full-height channel with 12.7 mm height.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${\mathrm{C}}_{\mathrm{p}}$ | Specific heat capacity (J/kg·K) |

$\mathrm{D}$ | Diameter (m) |

${\mathrm{D}}_{\mathrm{h}}$ | Hydraulic diameter (m) |

$\mathrm{f}$ | Friction factor (dimensionless) |

F | Body force (N) |

$\mathrm{h}$ | Heat transfer coefficient (W/m^{2}·K) |

H | Height (m) |

${\mathrm{H}}_{\mathrm{c}}$ | Channel height (m) |

${\mathrm{H}}_{\mathrm{t}}$ | Heat sink height (m) |

${\mathrm{k}}_{\mathrm{w}}$ | Water thermal conductivity (W/m·K) |

$\mathrm{L}$ | Heat sink length (m) |

${\mathrm{N}\mathrm{u}}_{\mathrm{x}}$ | Local Nusselt number (dimensionless) |

$\overline{\mathrm{N}\mathrm{u}}$ | Average Nu number (dimensionless) |

$\mathrm{P}$ | Pressure (Pa) |

${\mathrm{q}}^{\u2033}$ | Heat flux (W/m^{2}) |

r | Measured variable |

${\mathrm{R}}_{\mathrm{c}}$ | Converge criterion |

$\mathrm{R}\mathrm{e}$ | Reynolds number (dimensionless) |

s | Iteration number |

$\mathrm{T}$ | Temperature (°C) |

${\mathrm{T}}_{\mathrm{b}}$ | Bulk temperature (°C) |

u | Velocity in x-direction (m/s) |

${\mathrm{U}}_{\mathrm{i}}$ | Combined standard uncertainty |

${\mathrm{U}}_{\mathrm{r}}$ | Measurement error |

v | Velocity in y-direction (m/s) |

w | Velocity in z-direction (m/s) |

W | Width (m) |

${\mathrm{W}}_{\mathrm{h}}$ | Channel width (m) |

${\mathrm{W}}_{\mathrm{t}}$ | Heat sink width (m) |

${\mathrm{X}}_{\mathrm{i}}$ | Measured variables |

Greek symbols | |

$\mathsf{\rho}$ | Density (kg/m^{3}) |

$\mathsf{\mu}$ | Dynamic viscosity (Pa·s) |

Subscripts | |

$\mathrm{i}$ | Unit vector in x-direction |

$\mathrm{j}$ | Unit vector in y-direction |

$\mathrm{k}$ | Unit vector in z-direction |

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**Figure 7.**Temperature difference variation for flow rate of $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$: (

**a**) channel height 12.7 mm; (

**b**) channel height 10 mm; (

**c**) channel height 7 mm; (

**d**) channel height 4 mm.

**Figure 8.**Temperature difference variation for flow rate $13.25{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$: (

**a**) channel height 12.7 mm; (

**b**) channel height 10 mm; (

**c**) channel height 7 mm; (

**d**) channel height 4 mm.

**Figure 9.**Temperature difference variation for flow rate $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$: (

**a**) channel height 12.7 mm; (

**b**) channel height 10 mm; (

**c**) channel height 7 mm; (

**d**) channel height 4 mm.

**Figure 10.**Temperature counter for straight-channel heat sink with 12.7 mm and maximum heat flux: (

**a**) $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate; (

**b**) $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate.

**Figure 11.**The comparison of Nusselt number along the heat sink for 7.43 W/cm

^{2}heat flux: (

**a**) heat sink with 12.7 and 10 mm heights and flow rates of 6.94 and $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$; (

**b**) heat sink with 7 and 4 mm height and flow rates of 6.94 and $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$.

**Figure 12.**The Nu number variation along the heat sink with 3.86 W/cm

^{2}heat flux for different channel heights: (

**a**) $6.94{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate; (

**b**) minimum flow rate of $13.25{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$.

**Figure 13.**Velocity contour in X–Y planes for straight-channel heat sinks with indium heat flux and $13.25{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate: (

**a**) channel height 12.7 mm; (

**b**) channel height 10 mm; (

**c**) channel height 7 mm; (

**d**) channel height 4 mm.

**Figure 14.**Pressure changes with flow rate for straight-channel heat sink with 12.7, 10, 7.5, and 4 mm height.

**Figure 15.**Streamlines for straight-channel heat sink with $19.56{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$ flow rate: (

**a**) 12.7 mm height; (

**b**) 10 mm height.

**Figure 16.**Velocity vectors along straight-channel heat sink cross-sections for the flow rate of $13.25{\mathrm{c}\mathrm{m}}^{3}/\mathrm{s}$: (

**a**) 12.7 mm channel height; (

**b**) 10 mm channel height.

**Figure 17.**Performance evaluation criterion for different flow rates and channel heights compared to the height of 12.7 mm.

Parameters | Components | Uncertainty |
---|---|---|

Temperature | T-type thermocouple | $\pm $0.75% |

Flow rate | Digital flow meters | $\pm $0.44% |

Nu number | - | $\pm 2.44$% |

Components | Height (mm) | Width (mm) | Length (mm) |
---|---|---|---|

Heat sink | 12.7 | 37.5 | 37.5 |

Channel | 12.7, 10, 7, 4 | 1.88 | 37.5 |

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## Share and Cite

**MDPI and ACS Style**

Hajialibabaei, M.; Saghir, M.Z.; Bicer, Y.
Comparing the Performance of a Straight-Channel Heat Sink with Different Channel Heights: An Experimental and Numerical Study. *Energies* **2023**, *16*, 3825.
https://doi.org/10.3390/en16093825

**AMA Style**

Hajialibabaei M, Saghir MZ, Bicer Y.
Comparing the Performance of a Straight-Channel Heat Sink with Different Channel Heights: An Experimental and Numerical Study. *Energies*. 2023; 16(9):3825.
https://doi.org/10.3390/en16093825

**Chicago/Turabian Style**

Hajialibabaei, Mahsa, Mohamad Ziad Saghir, and Yusuf Bicer.
2023. "Comparing the Performance of a Straight-Channel Heat Sink with Different Channel Heights: An Experimental and Numerical Study" *Energies* 16, no. 9: 3825.
https://doi.org/10.3390/en16093825