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Heat transfer and pressure drop in a ZrB2 microchannel heat sink: A numerical approach
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Heat transfer and pressure drop in a ZrB2 microchannel heat sink: A numerical approach Vajdi Mohammada, Sadegh Moghanlou Farhada,∗, Ranjbarpour Niari Elaheha, Shahedi Asl Mehdia, Mohammadreza Shokouhimehrb,∗∗ a b
Department of Mechanical Engineering, University of Mohaghegh Ardabili, Ardabil, Iran Department of Materials Science and Engineering, Research Institute of Advanced Materials, Seoul National University, Seoul, 08826, Republic of Korea
A R T I C LE I N FO
A B S T R A C T
Keywords: Microchannel Heat transfer ZrB2 Numerical method Reynolds number MEMS
Advances in micro-electro-mechanical systems (MEMS) resulted in the fabrication of electronic and optic devices which generate high amounts of heat in a small space. Microchannel heat sinks are a new type of heat exchangers which are capable to absorb such ultrahigh heat fluxes and ensure the proper function of such devices. In the present work, a microchannel heat sink made of ZrB2 ceramic is investigated numerically to evaluate its feasibility to operate at such harsh conditions. The governing equations of the liquid domain (water) and solid domain (ZrB2) were solved by the finite element method. The obtained results showed a considerable heat transfer rate from the heated surface. For example, at an ultra-high heat flux of 3.6 MW/m2, the maximum temperature didn't exceed ~360 K. The high heat transfer area per volume of the applied microchannel, as well as the remarkable thermal conductivity of ZrB2, are the main reasons for such a high heat transfer rate.
1. Introduction Advances in micro-electro-mechanical systems (MEMS) have resulted in manufacturing high-density integrated electronic circuits with higher operational frequencies. This new generation of electronic packs normally operates at very high heat fluxes. High temperatures may disrupt the function of these devices, thus for stable and reliable operations, the working temperature must be maintained below 403 K [1]. Consequently, it is very important to enhance the convectional cooling methods to absorb high heat fluxes at small spaces [2–11]. The cooling methods are divided into two major groups of active and passive enhancements. In the active method, external energies such as electric field, magnetic field, vibrating forces, etc. improve the heat transfer rate [12,13]. In a passive method, there is not any form of external energies. Instead, the heat transfer is generally enhanced by the changes in geometry of flow channels or fluid properties [13]. Miniaturization of flow passages is one of the passive techniques, which shows considerable heat transfer enhancement. As the flow channel size decreases the ratio of heat transfer area to occupied volume increases remarkably and results in ultra-high heat flux absorption [14]. Microchannel heat sinks (MCHS) as a group of miniaturized heat exchangers have some
particular specifications such as very high heat transfer surface to volume ratio, great convective heat transfer coefficient, small mass and volume, and small coolant inventory [14,15]. Tuckerman and Pease [16] for the first time proposed the concept of a liquid-cooled microchannel heat sinks. Their experimental data showed a heat flux absorption of 790 W/cm2 from a high power device. Rosa and Collins [17] investigate the importance of scaling effects on Single-phase heat transfer in microchannels. Xia et al. [18] investigated the effects of structural parameters on fluid flow and heat transfer in a microchannel. Chai et al. [19] performed numerical simulations for the fluid flow and heat transfer in a microchannel heat sink with cavities on sidewall. Wavy and straight micro-channels were compared by Sui et al. [20,21]. Their results showed that wavy heat sinks dissipate more heat than the straight ones. It is also shown that there is an optimum size for the heat transfer of the wavy channels [19,22]. The heat transfer performance of the microchannel heat sinks is influenced by several factors including the applied material properties, size, and cross-sectional shape of the channel [23–27]. The heat sink should be made of the materials that have high thermal conductivities. On the other hand, they should operate without any change in their shapes and structures. Ultra-high temperature ceramics (UHTCs) are a
∗
Corresponding author. Corresponding author. E-mail addresses: [email protected] (M. Vajdi), [email protected] (F. Sadegh Moghanlou), [email protected] (M. Shahedi Asl), [email protected] (M. Shokouhimehr). ∗∗
https://doi.org/10.1016/j.ceramint.2019.09.146 Received 28 July 2019; Received in revised form 16 September 2019; Accepted 16 September 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Please cite this article as: Vajdi Mohammad, et al., Ceramics International, https://doi.org/10.1016/j.ceramint.2019.09.146
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- Conservation of mass (continuity):
group of materials with considerably high strength and melting point, which offer very good chemical and physical stabilities at high temperatures [28–42]. Zirconium diboride (ZrB2) as one of the UHTCs family member has very good mechanical and thermal properties such as high hardness, great melting point (3519 K), high elastic modulus (500 MPa) and excellent thermal conductivity (60–120 W/m-K) [43–54] which makes it a promising candidate to tolerate harsh working environments e.g. impact, corrosion, wear and high temperatures. This material has been offered for multifarious applications at elevated temperatures including cutting tools, molten metal containment, and electrodes [55–69]. Considering the aforementioned unique properties and potential applications, there is a lack of studies for using UHTCs in microchannel heat sinks. In the present work, a ZrB2 made microchannel heat sink was investigated in a very high heat flux condition and the cooling ability was evaluated numerically by finite element method. The present work can be developed for cooling of ceramics, especially at ultrahigh temperature conditions.
(1)
∇. v = 0
where the v is the velocity field and ∇ is the Nabla mathematical operator. - Conservation of momentum:
ρf v. ∇v = −∇p + ∇ . (μf ∇v )
(2)
where the ρf is fluid density, p is the pressure and μf is the fluid viscosity. - Conservation of energy for fluid:
ρf Cp, f . ∇T = ∇ . (kf ∇T )
(3)
where the Cp, f is the fluid specific heat, T is the temperature, kf is the fluid thermal conductivity. - Conservation of energy for solid
∇ . (ks ∇T ) = 0
(4)
where the ks is the solid thermal conductivity. - Thermal resistance equation Thermal resistant consists of three parts: conduction, convection, and capacity resistant that are defined as following [71,72]:
2. Mathematical formulation and numerical method A numerical investigation of fluid flow and heat transfer in a microchannel heat sink made by ZrB2 ceramic was simulated by the finite element method. Fig. 1 illustrates the geometry of applied MCHS in the present work which is based on an experimental sample introduced by Bhattacharya et al. [70]. The heat sink consists of 110 identical ZrB2 micro-channels with a dimension of 57 × 180 μm and a length of 11 mm. Because all channels of applied MCHS show similar heat transfer behavior, one of the representative channels was selected and considered as computational domain instead of investigating whole MCHS (as shown in Fig. 1). Water serves as a working fluid with the inlet temperature of T0 = 293K . A uniform heat flux of 0.9 MW/m2 was applied at the bottom of the heat sink [70]. The top wall of MCHS is insulated. The detailed geometrical information and applied boundary conditions are shown in Fig. 1.
Rtotal = R conduction + R convection + R capacity
(5)
R conduction =
H KA
(6)
R convection =
Tw − Tm − R conduction Q˙
(7)
R capacity =
Tm − Tin Q˙
(8)
where H is the thickness of heat sink, A is heat transfer area and Q˙ is heat power. Total thermal resistance can be calculated as Eq. (9):
3. Governing equations
Rtotal =
Tw − Tin Q˙
The governing equations for fluid flow and heat transfer in stationary condition are:
Fig. 1. The geometry of applied MCHS and boundary conditions. 2
(9)
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Fig. 3. Substrate wall temperature comparison between the present work and ref. [70].
Fig. 2. Applied mesh on MCHS.
Mass flow rate is considered as the inlet boundary condition. The pressure at the exit of channels is set to zero (atmospheric relative pressure). The inlet temperature is 293 K and the outflow heat transfer boundary condition is considered for the fluid leaving the channels. The bottom of the heat sink exposed to a heat flux of 0.9 MW/m2 and the top side of the channel is considered to be insulated. The symmetry boundary condition is used for sidewalls of the solid and fluid domains as depicted in Fig. 1. The thermal conductivity of ZrB2 is chosen as Ref. [73] and the specific heat is given by Ref. [74]:
Cp (
J ) = 0.704 + 2.52 × 10−5T − 80.2 × T −1 gK
(10)
where, T is in Kelvin. 4. Solution methodology The governing equations were solved by finite element method using COMSOL Multiphysics software. The model consists of solid and fluid domains. The applied mesh is shown in Fig. 2. In order to obtain accurate results at the lower time, the fluid cross-section was meshed by mapped square elements and the solid face by triangular ones. The selected faces were swept along the channel length to form uniform mesh elements. The mesh independency was investigated at different mesh sizes and 27850 elements were selected for simulations. 5. Results and discussion A series of numerical simulations were carried out to investigate the cooling of an electronic chip using a ZrB2–made microchannel heat sink. The simulations were carried out on a geometry according to the method proposed by Bhattacharya et al. [70]. In order to validate the obtained results, the same geometry and materials were applied similar to the procedure reported by them. The substrate wall temperature was obtained and the results are compared in Fig. 3. This comparison studies acquired at Re = 250 and q” = 0.9 MW/m2 show very good agreement with the experimental data of ref [70]. Therefore, the present simulation method can be expanded to investigate different materials or boundary conditions at the same geometry. In the next step, the simulations were developed for ZrB2 made micro-channel heat sink. Fig. 4 shows the temperature contours at four different heat fluxes at Reynolds number of 250. It can be seen that at a
Fig. 4. Temperature contours of microchannel wall for different heat fluxes at the Reynolds number of 250.
heat flux of 0.9 MW/m2, a small temperature change is observable. As the heat flux increases, the temperature of both solid domain and working fluid increases. The temperature contour related to q” = 3.6 MW/m2 shows that the highest temperature occurs at the bottom of the heat sink. This is the place of applied external heat flux (CPU surface) which is far from the working fluid. The substrate temperature versus applied heat flux at the Reynolds number of 250 is shown in Fig. 5. It can be seen that in all Reynolds numbers, the temperature increases along the channel length. By increasing the applied 3
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Fig. 8. Pressure drop in microchannel versus Reynolds number. Fig. 5. Wall Temperature at different heat fluxes and Reynolds number of 250.
fixed heat flux of 0.9 MW/m2 for different Reynolds numbers. As mentioned before, the thermal resistance decreases by an increase in Reynolds number and result in enhanced heat transfer. The result of Fig. 7 is consistent with Fig. 5 which states that by increasing Reynolds number the wall temperature decreases. Pressure drop is another characteristic of fluidics systems which shows the necessity of pumping power to circulate the working fluid. Fig. 8 shows the pressure drop in the microchannel heat sink at different Reynolds numbers. A 1.66 bar pressure drop at Re = 250 indicates very high-pressure drop at microchannels. This value increases dramatically as the Reynolds number increases. This is because of small dimensions of microchannel compared to common ones. Microchannels generally have higher pressure drops and this is a negative aspect of using microchannels. On the other hand, working at high pressures increases the danger of leakages.
Fig. 6. Convective heat transfer versus Reynolds number.
6. Conclusions Micro-channels have dramatic heat transfer characteristics which can absorb ultra-high heat fluxes at very small spaces. ZrB2 as ultrahigh temperature ceramic has interesting thermal properties as well as high strength properties. At the very high heat flux microchannel heat sink made by ZrB2 is investigated numerically by means of finite element method. The maximum wall temperature at the very high heat flux of 3.6 MW/m2 was obtained to be 360 K. The high heat transfer area of microchannels heat sinks compared to conventional devices as well as the very high convective heat flux of microchannels are the main reasons for ultra-high heat flux absorption of microchannels. The results also show that using microchannels impose too pressure drop which is a negative aspect of using microchannels. Fig. 7. Thermal resistance in the heat sink versus Reynolds numbers.
References heat flux, the wall temperature increases. It is interesting that the maximum temperature of the wall doesn't exceed 310 K at the heat flux of 0.9 MW/m2. This value is about 103 times higher than sun radiation on earth. This is one of the attractive aspects of using microchannel heat sinks in the cooling of hot surfaces. The reason for ultra-high heat flux absorption of microchannels comes back to the high heat transfer area to the occupied volume. The maximum wall temperature at the flux of 3.6 MW/m2 is 360 K. The convective heat transfer coefficient at different Reynolds numbers is given in Fig. 6. The obtained results show considerable convective heat transfer in all Reynolds numbers. The high heat transfer coefficient is another interesting characteristic of using microchannels. As the Reynolds number increases, the fluid velocity increase and subsequently results in higher cooling rates. On the other hand, increasing Reynolds number decreases the thermal resistance and subsequently, increases the heat transfer rate. Thermal resistance is a parameter that shows the resistance of a device against heat transfer. The thermal resistance in the applied heat sink is shown in Fig. 7 at the
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Heat transfer and pressure drop in a ZrB2 microchannel heat sink: A numerical approach Vajdi Mohammada, Sadegh Moghanlou Farhada,∗, Ranjbarpour Niari Elaheha, Shahedi Asl Mehdia, Mohammadreza Shokouhimehrb,∗∗ a b
Department of Mechanical Engineering, University of Mohaghegh Ardabili, Ardabil, Iran Department of Materials Science and Engineering, Research Institute of Advanced Materials, Seoul National University, Seoul, 08826, Republic of Korea
A R T I C LE I N FO
A B S T R A C T
Keywords: Microchannel Heat transfer ZrB2 Numerical method Reynolds number MEMS
Advances in micro-electro-mechanical systems (MEMS) resulted in the fabrication of electronic and optic devices which generate high amounts of heat in a small space. Microchannel heat sinks are a new type of heat exchangers which are capable to absorb such ultrahigh heat fluxes and ensure the proper function of such devices. In the present work, a microchannel heat sink made of ZrB2 ceramic is investigated numerically to evaluate its feasibility to operate at such harsh conditions. The governing equations of the liquid domain (water) and solid domain (ZrB2) were solved by the finite element method. The obtained results showed a considerable heat transfer rate from the heated surface. For example, at an ultra-high heat flux of 3.6 MW/m2, the maximum temperature didn't exceed ~360 K. The high heat transfer area per volume of the applied microchannel, as well as the remarkable thermal conductivity of ZrB2, are the main reasons for such a high heat transfer rate.
1. Introduction Advances in micro-electro-mechanical systems (MEMS) have resulted in manufacturing high-density integrated electronic circuits with higher operational frequencies. This new generation of electronic packs normally operates at very high heat fluxes. High temperatures may disrupt the function of these devices, thus for stable and reliable operations, the working temperature must be maintained below 403 K [1]. Consequently, it is very important to enhance the convectional cooling methods to absorb high heat fluxes at small spaces [2–11]. The cooling methods are divided into two major groups of active and passive enhancements. In the active method, external energies such as electric field, magnetic field, vibrating forces, etc. improve the heat transfer rate [12,13]. In a passive method, there is not any form of external energies. Instead, the heat transfer is generally enhanced by the changes in geometry of flow channels or fluid properties [13]. Miniaturization of flow passages is one of the passive techniques, which shows considerable heat transfer enhancement. As the flow channel size decreases the ratio of heat transfer area to occupied volume increases remarkably and results in ultra-high heat flux absorption [14]. Microchannel heat sinks (MCHS) as a group of miniaturized heat exchangers have some
particular specifications such as very high heat transfer surface to volume ratio, great convective heat transfer coefficient, small mass and volume, and small coolant inventory [14,15]. Tuckerman and Pease [16] for the first time proposed the concept of a liquid-cooled microchannel heat sinks. Their experimental data showed a heat flux absorption of 790 W/cm2 from a high power device. Rosa and Collins [17] investigate the importance of scaling effects on Single-phase heat transfer in microchannels. Xia et al. [18] investigated the effects of structural parameters on fluid flow and heat transfer in a microchannel. Chai et al. [19] performed numerical simulations for the fluid flow and heat transfer in a microchannel heat sink with cavities on sidewall. Wavy and straight micro-channels were compared by Sui et al. [20,21]. Their results showed that wavy heat sinks dissipate more heat than the straight ones. It is also shown that there is an optimum size for the heat transfer of the wavy channels [19,22]. The heat transfer performance of the microchannel heat sinks is influenced by several factors including the applied material properties, size, and cross-sectional shape of the channel [23–27]. The heat sink should be made of the materials that have high thermal conductivities. On the other hand, they should operate without any change in their shapes and structures. Ultra-high temperature ceramics (UHTCs) are a
∗
Corresponding author. Corresponding author. E-mail addresses: [email protected] (M. Vajdi), [email protected] (F. Sadegh Moghanlou), [email protected] (M. Shahedi Asl), [email protected] (M. Shokouhimehr). ∗∗
https://doi.org/10.1016/j.ceramint.2019.09.146 Received 28 July 2019; Received in revised form 16 September 2019; Accepted 16 September 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Please cite this article as: Vajdi Mohammad, et al., Ceramics International, https://doi.org/10.1016/j.ceramint.2019.09.146
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- Conservation of mass (continuity):
group of materials with considerably high strength and melting point, which offer very good chemical and physical stabilities at high temperatures [28–42]. Zirconium diboride (ZrB2) as one of the UHTCs family member has very good mechanical and thermal properties such as high hardness, great melting point (3519 K), high elastic modulus (500 MPa) and excellent thermal conductivity (60–120 W/m-K) [43–54] which makes it a promising candidate to tolerate harsh working environments e.g. impact, corrosion, wear and high temperatures. This material has been offered for multifarious applications at elevated temperatures including cutting tools, molten metal containment, and electrodes [55–69]. Considering the aforementioned unique properties and potential applications, there is a lack of studies for using UHTCs in microchannel heat sinks. In the present work, a ZrB2 made microchannel heat sink was investigated in a very high heat flux condition and the cooling ability was evaluated numerically by finite element method. The present work can be developed for cooling of ceramics, especially at ultrahigh temperature conditions.
(1)
∇. v = 0
where the v is the velocity field and ∇ is the Nabla mathematical operator. - Conservation of momentum:
ρf v. ∇v = −∇p + ∇ . (μf ∇v )
(2)
where the ρf is fluid density, p is the pressure and μf is the fluid viscosity. - Conservation of energy for fluid:
ρf Cp, f . ∇T = ∇ . (kf ∇T )
(3)
where the Cp, f is the fluid specific heat, T is the temperature, kf is the fluid thermal conductivity. - Conservation of energy for solid
∇ . (ks ∇T ) = 0
(4)
where the ks is the solid thermal conductivity. - Thermal resistance equation Thermal resistant consists of three parts: conduction, convection, and capacity resistant that are defined as following [71,72]:
2. Mathematical formulation and numerical method A numerical investigation of fluid flow and heat transfer in a microchannel heat sink made by ZrB2 ceramic was simulated by the finite element method. Fig. 1 illustrates the geometry of applied MCHS in the present work which is based on an experimental sample introduced by Bhattacharya et al. [70]. The heat sink consists of 110 identical ZrB2 micro-channels with a dimension of 57 × 180 μm and a length of 11 mm. Because all channels of applied MCHS show similar heat transfer behavior, one of the representative channels was selected and considered as computational domain instead of investigating whole MCHS (as shown in Fig. 1). Water serves as a working fluid with the inlet temperature of T0 = 293K . A uniform heat flux of 0.9 MW/m2 was applied at the bottom of the heat sink [70]. The top wall of MCHS is insulated. The detailed geometrical information and applied boundary conditions are shown in Fig. 1.
Rtotal = R conduction + R convection + R capacity
(5)
R conduction =
H KA
(6)
R convection =
Tw − Tm − R conduction Q˙
(7)
R capacity =
Tm − Tin Q˙
(8)
where H is the thickness of heat sink, A is heat transfer area and Q˙ is heat power. Total thermal resistance can be calculated as Eq. (9):
3. Governing equations
Rtotal =
Tw − Tin Q˙
The governing equations for fluid flow and heat transfer in stationary condition are:
Fig. 1. The geometry of applied MCHS and boundary conditions. 2
(9)
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Fig. 3. Substrate wall temperature comparison between the present work and ref. [70].
Fig. 2. Applied mesh on MCHS.
Mass flow rate is considered as the inlet boundary condition. The pressure at the exit of channels is set to zero (atmospheric relative pressure). The inlet temperature is 293 K and the outflow heat transfer boundary condition is considered for the fluid leaving the channels. The bottom of the heat sink exposed to a heat flux of 0.9 MW/m2 and the top side of the channel is considered to be insulated. The symmetry boundary condition is used for sidewalls of the solid and fluid domains as depicted in Fig. 1. The thermal conductivity of ZrB2 is chosen as Ref. [73] and the specific heat is given by Ref. [74]:
Cp (
J ) = 0.704 + 2.52 × 10−5T − 80.2 × T −1 gK
(10)
where, T is in Kelvin. 4. Solution methodology The governing equations were solved by finite element method using COMSOL Multiphysics software. The model consists of solid and fluid domains. The applied mesh is shown in Fig. 2. In order to obtain accurate results at the lower time, the fluid cross-section was meshed by mapped square elements and the solid face by triangular ones. The selected faces were swept along the channel length to form uniform mesh elements. The mesh independency was investigated at different mesh sizes and 27850 elements were selected for simulations. 5. Results and discussion A series of numerical simulations were carried out to investigate the cooling of an electronic chip using a ZrB2–made microchannel heat sink. The simulations were carried out on a geometry according to the method proposed by Bhattacharya et al. [70]. In order to validate the obtained results, the same geometry and materials were applied similar to the procedure reported by them. The substrate wall temperature was obtained and the results are compared in Fig. 3. This comparison studies acquired at Re = 250 and q” = 0.9 MW/m2 show very good agreement with the experimental data of ref [70]. Therefore, the present simulation method can be expanded to investigate different materials or boundary conditions at the same geometry. In the next step, the simulations were developed for ZrB2 made micro-channel heat sink. Fig. 4 shows the temperature contours at four different heat fluxes at Reynolds number of 250. It can be seen that at a
Fig. 4. Temperature contours of microchannel wall for different heat fluxes at the Reynolds number of 250.
heat flux of 0.9 MW/m2, a small temperature change is observable. As the heat flux increases, the temperature of both solid domain and working fluid increases. The temperature contour related to q” = 3.6 MW/m2 shows that the highest temperature occurs at the bottom of the heat sink. This is the place of applied external heat flux (CPU surface) which is far from the working fluid. The substrate temperature versus applied heat flux at the Reynolds number of 250 is shown in Fig. 5. It can be seen that in all Reynolds numbers, the temperature increases along the channel length. By increasing the applied 3
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Fig. 8. Pressure drop in microchannel versus Reynolds number. Fig. 5. Wall Temperature at different heat fluxes and Reynolds number of 250.
fixed heat flux of 0.9 MW/m2 for different Reynolds numbers. As mentioned before, the thermal resistance decreases by an increase in Reynolds number and result in enhanced heat transfer. The result of Fig. 7 is consistent with Fig. 5 which states that by increasing Reynolds number the wall temperature decreases. Pressure drop is another characteristic of fluidics systems which shows the necessity of pumping power to circulate the working fluid. Fig. 8 shows the pressure drop in the microchannel heat sink at different Reynolds numbers. A 1.66 bar pressure drop at Re = 250 indicates very high-pressure drop at microchannels. This value increases dramatically as the Reynolds number increases. This is because of small dimensions of microchannel compared to common ones. Microchannels generally have higher pressure drops and this is a negative aspect of using microchannels. On the other hand, working at high pressures increases the danger of leakages.
Fig. 6. Convective heat transfer versus Reynolds number.
6. Conclusions Micro-channels have dramatic heat transfer characteristics which can absorb ultra-high heat fluxes at very small spaces. ZrB2 as ultrahigh temperature ceramic has interesting thermal properties as well as high strength properties. At the very high heat flux microchannel heat sink made by ZrB2 is investigated numerically by means of finite element method. The maximum wall temperature at the very high heat flux of 3.6 MW/m2 was obtained to be 360 K. The high heat transfer area of microchannels heat sinks compared to conventional devices as well as the very high convective heat flux of microchannels are the main reasons for ultra-high heat flux absorption of microchannels. The results also show that using microchannels impose too pressure drop which is a negative aspect of using microchannels. Fig. 7. Thermal resistance in the heat sink versus Reynolds numbers.
References heat flux, the wall temperature increases. It is interesting that the maximum temperature of the wall doesn't exceed 310 K at the heat flux of 0.9 MW/m2. This value is about 103 times higher than sun radiation on earth. This is one of the attractive aspects of using microchannel heat sinks in the cooling of hot surfaces. The reason for ultra-high heat flux absorption of microchannels comes back to the high heat transfer area to the occupied volume. The maximum wall temperature at the flux of 3.6 MW/m2 is 360 K. The convective heat transfer coefficient at different Reynolds numbers is given in Fig. 6. The obtained results show considerable convective heat transfer in all Reynolds numbers. The high heat transfer coefficient is another interesting characteristic of using microchannels. As the Reynolds number increases, the fluid velocity increase and subsequently results in higher cooling rates. On the other hand, increasing Reynolds number decreases the thermal resistance and subsequently, increases the heat transfer rate. Thermal resistance is a parameter that shows the resistance of a device against heat transfer. The thermal resistance in the applied heat sink is shown in Fig. 7 at the
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