Experimental investigations on a variable channel width double layered minichannel heat sink

International Journal of Heat and Mass Transfer 165 (2021) 120633

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Experimental investigations on a variable channel width double layered minichannel heat sink Nirav Patel, Hemantkumar B. Mehta∗ Department of Mechanical Engineering, Sardar Vallabhbhai National Institute of Technology, Surat-395007, Gujarat, India

a r t i c l e

i n f o

Article history: Received 22 July 2020 Revised 15 October 2020 Accepted 19 October 2020

Keywords: Variable channel width MCHS Zero overlap Temperature non-uniformity Pressure drop Thermo-hydraulic performance

a b s t r a c t The persistent development in modern electronics and communication technologies leads to compact and efficient devices. Conversely, it is accompanied by the downside of enormous heat generation in the constrained space of microelectronic devices. One of the substitutes for the high heat flux dissipation is a liquid cooled Minichannel Heat Sink. However, the drawbacks of higher temperature non-uniformity and higher pressure drop penalty associated with MCHS obliges its all-encompassing utilization. In view of tailing off these issues, a Variable Channel Width Double Layered Minichannel Heat Sink was proposed by the authors and its applicability is experimentally investigated in the present study. A Variable Channel Width Double Layered Minichannel Heat Sink consisting of two layers of MCHS having channels with variable widths in the axial direction are positioned one atop the other in such a way that the denser channel regions of upper and lower layers do not overlap (Zero Overlap). The present research is aimed to develop a test setup to experimentally investigate the influence of various heat flux (11.44 W/cm2 - 30.09 W/cm2 ) and Reynolds number (46 – 138) on the thermal performance of a VWC DL-MCHS with zero overlap and to compare it with the numerical results. The performance of a Variable Channel Width Double Layered Minichannel Heat Sink was analysed in terms of major thermal performance parameters such as thermal resistance (Rth ), temperature non-uniformity in the substrate (TS ) and total pressure drop (Ptotal ). The overall thermo-hydraulic performance was evaluated in terms of COP. The agreed comparison between the present experimental and numerical results evidences the aptness of a VWC DL-MCHS geometry for real-life applications. Moreover, a Variable Channel Width Double Layered Minichannel Heat Sink shows significant improvement in overall thermal performance of about 1.53 to 2.35 times than the conventional DL-MCHS. Therefore, a Variable Channel Width Double Layered Minichannel Heat Sink has come out as an improved alternative for the thermal management of high heat flux electronic applications. © 2020 Elsevier Ltd. All rights reserved.

1. Introduction The incessant advancement of data and communication innovations in the 21st century brings up progressive technologies such as distributed computing, 5 G, the web of things and Artificial intelligence (AI). Contrary, the limit and thermal stacking regarding computing/exchange/handling/stockpiling for the advanced electronics and communication applications keep ascending exponentially. The developing interest of efficient, faster and compact electronic systems led to the miniaturization and integration of such electronic devices. The faster and advanced microelectronic components integrate a higher number of transistors in a con∗

Corresponding author. E-mail addresses: [email protected] (N. Patel), [email protected], [email protected] (H.B. Mehta).

https://doi.org/10.1016/j.ijheatmasstransfer.2020.120633 0017-9310/© 2020 Elsevier Ltd. All rights reserved.

strained space, which brings up the continuous and enormous heat generation in microelectronic chips. This heat is needed to be dissipated continuously to maintain the operating temperature of the microelectronic chips below the permissible limit (<85 °C) [1]. If this heat is not dissipated effectively, then the chip temperature keeps on increasing and resulting in deterioration of the performance and abbreviate the lifespan of the microelectronics components. In such a way, the continuous high heat dissipation requirements from the constrained space of electronic components make the thermal management to be a challenging task and necessitate the exploration of advanced heat dissipation techniques. For higher heat dissipation, ordinary cooling strategies (natural convection or fan-blown air cooling) have been outperformed by potential cooling methods such as Micro/Mini channel heat sinks (MCHS), jet impingement, flat micro heat pipes and phase change energy storage [2].

N. Patel and H.B. Mehta

International Journal of Heat and Mass Transfer 165 (2021) 120633

tsc

Nomenclature AI COP DAQ DI DL-MCHS DPT MARD MCHS NEPCM NI SEM SL-MCHS VWC DL-MCHS

Principal Ab Amp As Hhs Hc,l Hc,u ks kf kT P Lc1 Lc2 Lhs m˙ lower m˙ upper n1 n2 NTs NCOP N P Nuz PU pper PLower Ptotal Q q Qloss Qlower Qtotal Qupper Rth,total Rth Re TS,max TS,min Tc,z,lower T f,L,in T f,L,out T f,U,in T f,U,out T f,z,lower Ts,z ths tu

T S Uc1

Artificial intelligence Coefficient of Performance Data Acquisition System De-ionized Double Layered microchannel heat sink Differential Pressure Transmitter Mean Absolute Relative Deviation Mini/Microchannel heat sink Nano Encapsulated Phase Change Material National Instruments Scanning electron microscope Single Layered microchannel heat sink Variable Channel Width Double Layered Minichannel Heat Sink

Uc2 V V˙ lower V˙ total V˙ upper Wc1 Wc 2 W˙ Whs Ww

Symbols Base Area Ampere Total convective surface area Heat sink total Height Channel height in Lower Layer Channel height in Upper Layer Thermal conductivity of solid material Thermal conductivity of fluid Thermal conductivity of thermal paste Length of Channel in Upstream Region of Lower Layer Length of Channel in Downstream Region of Lower Layer Heat sink total Length Mass flow rate in lower layer Mass flow rate in upper layer Number of channels in upstream region Number of channels in upstream region Normalised temperature non-uniformity in the substrate Normalised Coefficient of Performance Normalised pressure drop Local Nusselt number Pressure drop in Upper Layer Pressure drop in Lower Layer Total pressure drop Total heat supplied Heat Flux Total heat loss heat dissipated by the coolant in the lower layer Total heat dissipated by a VWC DL-MCHS heat dissipated by the coolant in the upper layer Total thermal Resistance Thermal Resistance Reynolds number Maximum temperature in the substrate Minimum temperature in the substrate Local wall Temperature at lower channel Inlet fluid temperature in lower layer Outlet fluid temperature in lower layer Inlet fluid temperatures in upper layer Outlet fluid temperature in upper layer Local fluid Temperature in lower layer Local wall Temperature at substrate Thickness of substrate Thickness of middle rib

Distance between the substrate and base of lower channel Temperature Non-uniformity in the substrate Length of Channel in Upstream Region of Upper Layer Length of Channel in downstream Region of Upper Layer Voltage Volumetric flow rate in lower layer Total volumetric flow rate Volumetric flow rate in upper layer Channel width in Upstream Region Channel width in Downstream Region Total Pumping power Heat sink total Width Fin width

Single Layered microchannel heat sink (SL-MCHS) was first reported by Tuckerman and Pease [3] in 1981. It finds its applications in the field of military, nuclear, medical, concentrated photovoltaic thermal system and electronics industry. It offers several advantages such as compactness, reliability, lightweight, low coolant requirement and low operating cost [4]. However, a conventional SL-MCHS has the drawbacks of non-uniformity of the substrate temperature and high-pressure drop across the channels that lead to local hotspots, decreased reliability and shortened lifespan of the electronic components. To address these issues, Vafai and Zhu [5] came up with Double Layered MCHS (DL-MCHS) in 1999. With this geometry, they succeeded in reducing temperature non-uniformity in the substrate. However, the issue of the higher-pressure drop was found unresolved. Afterward, substantial numerical and analytical research on DL-MCHS was carried out [6]. The research efforts were majorly implemented for improvement in the thermal performance of DL-MCHS by modification in channel shapes [7–10], MCHS configurations [11,12], by introducing advanced coolants such as nanofluids [13–17] and optimizing the geometrical parameters [18–21]. For optimization, various techniques have been proposed and adopted by the researchers. Such as Mosavati et al. [22] have proposed a novel noniterative inverse boundary design regularized solution technique using the backward Monte Carlo method for solving the inverse radiation boundary problem in a 3-D furnace prevailing radiative equilibrium condition. Moreover, Mosavati et al. solved the inverse boundary design problem of natural convection–radiation by combining the backward MCM and the finite volume method (FVM) for unsteady free convection flow [23] and radiating-free convecting furnace filled with considering specular reflectivity and participating media [24]. Their reported results demonstrate the efficiency and accuracy of the proposed optimization methods. The mainstream research on DL-MCHS involved the improvement in cooling performance by rupturing the thermal and hydrodynamic boundary layers to lessen the issue of temperature non-uniformity in the substrate, which emanates the higher pressure drop penalty. Conversely, less emphasis was given to improve the overall thermal performance of DL-MCHS by reducing the total pressure drop across the channel. Based on the above facts, it is observed that there is a greater need to develop a compact, efficient and cost-effective DL-MCHS that can overcome the issues of temperature non-uniformity in the substrate and high pressure drop simultaneously. Moreover, the majority of the research reported on DL-MCHS was carried out by adopting numerical and analytical techniques that involved assumptions and could not give insight into the real-life applications. The experimental investigations on DL-MCHS were rare and performed for conventional DL2

N. Patel and H.B. Mehta

International Journal of Heat and Mass Transfer 165 (2021) 120633

Fig. 1. Schematic and Photographic view of VWC DL-MCHS experimental setup.

MCHS with straight channels which offer higher pressure drop [25,26]. In synopsis, the investigations on the effective design of a DL-MCHS, which offers less pressure drop and reduces the temperature non-uniformity without much heat transfer forfeit, are still untouched. Therefore, systematic experimental investigations along with the development of a novel DL-MCHS to understand the thermal instabilities associated with DL-MCHS, are greatly expected. In order to circumvent the aforementioned research issues, the authors had proposed the novel design of Variable channel Width Double Layered Minichannel Heat Sink (VWC DL-MCHS) [27]. In the VWC DL-MCHS geometry, the continuous flow channels of conventional DL-MCHS were replaced with stepwise variable width channels in both the upper and lower layers. This, in turn, decreased the hydraulic diameter of flow channels in the streamwise direction. The authors performed the numerical studies on a VWC DL-MCHS and compared the obtained results with conventional SL- and DL-MCHS [28]. The results showed that counterflow VWC DL-MCHS with zero overlap performed better and gave overall improvement in thermal performance of 8.68 times as compared to conventional SL-MCHS and 3.73 times higher than the conventional DL-MCHS. The temperature non-uniformity in the substrate of a VWC DL-MCHS with zero overlap (λ = 0.8 in the lower layer) was observed to decrease by 58.84% as compared to a conventional SL-MCHS and 53.67% as compared to a conventional DL-MCHS. Moreover, the pressure drop of a VWC DL-MCHS with zero overlap (λ = 0.8 in the lower layer) was observed to decrease by 44.04% as compared to a conventional SL-MCHS and 42.14% as compared to a conventional DL-MCHS. The water-based numerical investigations on VWC DL-MCHS were then extended with efficient coolants such as water-based nanofluids (CuO-water and Al2 O3 -water) and Nano Encapsulated Phase Change Material (NEPCM) slurries [29]. The obtained results confirmed the potential of a VWC DL-MCHS with zero overlap and gave a maximum improvement in thermal performance of about 2.27 to 3.22 times higher than the conventional DL-MCHS. Overall pressure drop penalty of a VWC DL-MCHS with zero overlap using

advanced coolants is decreased by 42.4% to 47.84% as compared to advanced coolant based conventional DL-MCHS. In a nutshell, VWC DL-MCHS with zero overlap emerged as the prominent configuration. However, the applicability of this geometry is essential to be explored experimentally to obtain real-life insight as well as to validate the numerical hypothesis. The present study is the authors’ ongoing research project work and aimed to experimentally validate the potential of this VWC DL-MCHS geometry. The experimental setup was developed to investigate the influence of different heat flux and coolant Re on the thermohydraulic performance of a VWC DL-MCHS with zero overlap. The research findings of the experimental work were compared with the numerical investigations performed. The authors believe that the research work on this VWC DL-MCHS geometry has excellent potential and will serve as benchmark results for MCHS based cooling systems. 2. Experimental setup The experimental setup was developed to investigate the thermal and hydraulic characteristics of a VWC DL-MCHS. The schematic diagram is shown in Fig. 1. It consists of a flow circuit (solid line), a heating circuit (dash-dot line), Data Acquisition System (DAQ) (dotted line) and test section assembly. The specifications of the experimental components are tabulated in Table 1. The flow circuit consists of a constant temperature cooling bath, programmable Gear pumps and micron-sized filters. De-ionized (DI) water was used as a working fluid. The inlet temperature of DI water was kept 20 °C for all the experiments performed and was maintained constant using a cooling bath (Accuracy= ±1 °C). The cooling bath is a recirculation type bath with a total capacity of 30 L. Lexpure make Filters were used to remove dirt and/or impurities from DI water. Cole Parmer make two Gear pumps (Accuracy: ±2 %) were used to supply and control the flow rates of DI water separately for the upper layer and lower layer of a VWC DL-MCHS. The inbuilt continuous mode was adopted to provide continuous 3

N. Patel and H.B. Mehta

International Journal of Heat and Mass Transfer 165 (2021) 120633

Table 1 specification of experimental components. Sr. No.

Components

Make (Model No.)

1.

2.

DAQ system (a) Chassis (a) Temperature module (a) Pressure module Gear pumps

National Instruments NI cDAQ-9189 NI-9213, Channels: 16 NI-9203, Channels: 08 Cole Parmer (CX 74,014–32)

3.

DPT sensor

Siemens (SITRANS P410)

4. 5. 6.

Thermocouples Cartridge Heaters Constant Temperature Bath

Tempsens Instruments Tempsens Instruments Mechmatics

7.

Heating Controlling Unit

Apex, Multispan

8.

Filters

Lexpure

flow without any pulsation and inbuilt calibration mode was used to calibrate the gear pumps for accurate flow rates of DI water. A digital balance (make: ScaleTec, accuracy: ±1 mg) was also used to measure the flow rate of coolant before the dispersion into the constant temperature bath. The volumetric flow rate was measured after one minute and the weight of the accumulated volume was measured from the digital balance. The flow rate was measured twice i.e., before and after the temperature and pressure data logging for each experiment. The heating circuit consists of a heating controller unit and a servo voltage stabilizer as shown in Fig. 1. Amar make servo voltage stabilizer was used to supply constant voltage at the inlet of the control panel. Input heat supplied was set through a Dimmerstat (Make: Apex, Range: 0–2 Amp, 0–230 V AC, Accuracy: ± 2%), a voltmeter (Make: Multispan, Range: 0–230 V, Resolution: 1 V) and an ammeter (Make: Multispan, Range: 0–5 Amp, Resolution: 0.01 Amp). The maximum variations observed for Dimmerstat was about ± 2%. The power supply to the control panel was supplied from the voltage stabilizer, which minimized the variation in the heat supply to the heaters by minimizing the variation in input voltage to the controller. Novus communication converters were used to connect the control panel with the computer storage device, which is used to communicate the data and to operate the controller directly from the computer through virtual interface software. National Instruments (NI) based DAQ system with a high sampling rate was used for the data logging and communication of experimental data. It involves compact chassis (NI cDAQ-9189, Accuracy: ±0.1%), temperature module (NI cDAQ-9213, Accuracy: ±0.1%) and pressure module (NI cDAQ-9203, Accuracy: ±0.1%). DAQ system was attached to the computer to transfer the temperature and pressure data through Ethernet cable effectively. Standard LabVIEW17 software was used for automatic controlling and operation of the DAQ system and to develop real data view and various plots for the post-processing of the experiment data. The test section assembly consists of upper layer and lower layer of a VWC DL-MCHS, inlet and outlet plenums, heater and insulation block (housing), thermocouples and Differential Pressure Transmitter (DPT). The assembled and exploded view of a test section is shown in Fig. 2. The upper and lower layers are placed one atop the other, as shown in Fig. 3. The size of the substrate, i.e., the heat sink base (Whs x Lhs ) is 25 × 25 mm2 , which is in accordance with the actual size of the microprocessors used in the electronic applications. The flow channels are separated by solid

Specifications Accuracy: ±0.1%

Flow range: 33 ml/min to 3300 ml/min Accuracy: ±2 %, Repeatability: ±5 % Accuracy: ±0.1%, Measuring Range: 0.25–25 kPa Accuracy: ±0.5 °C Accuracy: ± 5% Accuracy= ±1 °C, Controllable Temperature Range: 10 °C to 40 °C Voltage: 0–230 V, Current: 0–5 Amp Accuracy: ±2% 10 microns

fins. The solid fin width (Ww ) is 0.25 mm in both the layers. The flow channel width is kept variable in such a way that the hydraulic diameter (Dh ) is decreased in the flow direction. The denser fin region is provided at the downstream region of each layer. The channel width (Wc,2 ) in the downstream region is 0.25 mm. However, channel width in the upstream region is chosen in such a way that the number of channels in the upstream region remains half as compared to the number of channels in the downstream region. Therefore, the channel width in the upstream region (Wc,1 ) is 0.75 mm. The height of both the channels Hc, l and Hc, u is 2.5 mm. The geometrical dimensions of a VWC MCHS with zero overlap are tabulated in Table 2. Here, zero overlap means the denser and/or coarser region of each layer don’t overlap each other. The overlapping of different regions is set using λ, which is defined as the ratio of the length of the stepped fin in the downstream region (Lc2 or Uc2 ) to the total length of a heat sink (Lhs ). For the present geometry with zero overlap, the value of λ is 0.8 in the lower layer and 0.2 in the upper layer. Therefore, for the lower layer, the length of the denser fin region (Lc2 ), i.e., downstream of the lower layer is 20 mm and the length of the coarser fin region (Lc1 ), i.e., upstream of the lower layer is 5 mm. In the upper layer, the length of the denser fin region (Uc2 ) and coarser fin region (Uc1 ) are 5 mm and 20 mm, respectively. The test section material is Aluminium and was fabricated using the Wire-cut EDM machining process. The Scanning Electron Microscope (SEM) images of the denser and coarser region of fabricated VWC DL-MCHS is shown in Fig. 4 (a) and (b), respectively. As shown in Fig. 4(a), the rounded edge corners were created at the bottom of the channels. It is worth to note that the Wirecut EDM machine forms rounded edge corners for the rectangular slots. However, it is reported that when the channel aspect ratio (AR = Hc /Wc ) is higher, then there is a minuscule influence of rounded edge corners on the thermo-hydraulic performance of a MCHS [26]. In the present experiments, AR is 10 and hence flow channels with rounded edge corners can be treated as rectangular channels. The applicability of the rounded edge corner increases the manufacturing feasibility and minimizes the fabrication cost and machining time. The parameters of a wire cut EDM machining process were kept similar, as reported by Seder et al. [30]. The surface roughness of the MCHS is found 2 μm. The heater block was developed from Aluminium material and directly embedded to the bottom of the substrate. To minimize the contact resistance and to remove air gap between the substrate and heater block, a high thermal conductive paste was used.

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N. Patel and H.B. Mehta

International Journal of Heat and Mass Transfer 165 (2021) 120633

Fig. 2. Schematic of a VWC DL-MCHS test section assembly (a) Assembled view (b) Exploded view.

Fig. 3. CAD view of a VWC DL-MCHS with Zero Overlap.

The size of a heater block is 50 × 50 mm2 . A total of 12 holes were drilled in the heater block to accommodate 12 number of heaters. Tempsens make high watt density cartridge heaters (each of 100 W, Accuracy: ± 5%) were used to heat the substrate of the MCHS. The arrangement of heaters and the detailed dimensions

of the heater block is shown in Fig. 2(b). The heater block and VWC DL-MCHS are press-fitted and hold fixed with the lower layer plenum using the clamps and bolts. As shown in Fig. 2(b), the upper and lower layer of a VWC DL-MCHS was separated by an aluminum sheet having a thickness of 0.2 mm. This aluminum sheet

5

N. Patel and H.B. Mehta

International Journal of Heat and Mass Transfer 165 (2021) 120633 Table 2 Geometrical dimension of a VWC MCHS with Zero overlap. Dimensions (in mm) material Heat sink total Width, Whs Heat sink total Length, Lhs Heat sink total Height, Hhs Thickness of substrate, ths Thickness of middle rib tu Channel height in Upper Layer, Hc,u Channel height in Lower Layer, Hc,l Fin width, Ww Channel width in Upstream Region, Wc1 Channel width in Downstream Region, Wc 2 Length of Channel in Upstream Region of Lower Layer, Lc1 Length of Channel in Downstream Region of Lower Layer, Lc2 Length of Channel in Upstream Region of Upper Layer, Uc1 Length of Channel in downstream Region of Upper Layer, Uc2 Number of channels in upstream region, n1 Number of channels in upstream region, n2

Aluminum 25.00 25.00 08.50 02.00 0.50 2.50 2.50 0.25 0.75 0.25 05.0 20.00 20.00 05.00 25.00 50.00

Fig. 4. SEM Images of a VWC DL-MCHS channels.

was sandwiched between two Teflon sheets, having cut out portion for housing the VWC DL-MCHS. Teflon sheets (melting temp: 327 °C) were provided to ensure that the flow came in contact with the Aluminium within the MCHS area only and no heat transfer can take place between the upper- and lower-layer plenums while DI water passes through plenums. In such a way, Teflon sheets having a thermal conductivity of 0.25 W/m-K works as an insulator between the plenums. The thickness of the Teflon sheets is 0.5 mm. Moreover, at the side periphery of MCHS, i.e., the interface of plenums and MCHS, RTV silicon rubber (k = 0.2 W/m-K and melting temp: 255 °C) was used to prevent any leakage. Inlet and outlet plenums are developed from Acrylic glass block (melting temp: 160 °C) in order to minimize the maldistribution of DI water through flow channels of upper and lower layers. The detailed cut section view is shown in Fig. 5. The deep and shallow sections of plenum and housing for VWC DL-MCHS in both the layers were carefully slotted by VMC machining. The edges of the plenums were made smooth and rounded to minimize any abrupt change in the pressure drop penalty. As the flow perturbation can majorly influence the performance of MCHS, it was minimized by providing deep and shallow plenums before the entrance to the test section flow channels. The major perturbation at the inlet of the plenum was diminished by using deep plenum as it fills initially and after that, it enters into the shallow plenum and provides the uniform distribution of flow at the entrance of each channel.

The height of the shallow plenum is kept identical as of channel height (2.5 cm). The inlet and outlet plenums were made identical, having mirrored configuration. The pressure tapings were provided in each plenum to measure the pressure drop of each layer of a VWC DL-MCHS. These pressure tapings were enclosed with the non-return valve. Temperature and pressure measurements are essential for experimental investigations of any thermal system. Tempsens make twelve (12) T-type thermocouples with 1 mm bid diameter were used to measure the temperature of the system. The thermocouples were calibrated first and the accuracy was found within ±0.5%. Six (06) thermocouples were placed equidistance at the heat sink base to measure axial substrate temperature, as shown in Fig. 2(b). Four (04) thermocouples were placed at the inlet and outlet of each plenum to measure the inlet and outlet DI water temperature. One thermocouple was placed on the top cover to determine the heat loss and one thermocouple was kept open to the atmosphere to sense the surrounding temperature. Temperature data were sensed and logged by the NI-9213 temperature module. Pressure drop measurement was carried out using Siemens make DPT. The pressure measurement tapings are shown in Fig. 6. The outlet signal of the DPT is 4–20 mA. The pressure data were acquired to the computer by the NI-9203 pressure module. The DPT was first calibrated for flow through the tube. The tube dimensions were 4 mm ID and 58 mm in length. The flow rates for the cali-

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International Journal of Heat and Mass Transfer 165 (2021) 120633

Fig. 5. Cut section view of a VWC DL-MCHS test section.

Fig. 6. VWc DL-MCHS assembly.

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International Journal of Heat and Mass Transfer 165 (2021) 120633

bration of DPT were considered as 100 ml/min to 1400 ml/min. The accuracy of DPT was found within ±0.5%. The test section assembly of VWC DL-MCHS was placed and fixed in the acrylic box, which was completely filled with the glass wool insulation sheets and foams (k = 0.04 W/m-K and melting point:1713 °C) and this insulator block ensures that no heat loss can take place. The size of this insulation box is 200 × 150 × 130 mm3 .

T f,U,in and T f,U,out are the fluid temperatures at the inlet and outlet of the upper layer, respectively. The Reynold number is determined using Eq. (5)

Re =

ρvDh μ

(5)

Total heat dissipated by the coolant in a VWC DL-MCHS was calculated by Eq. (6)

Qtotal = Qlower + Qupper

2.1. Experimental procedure

(6)

Heat loss was calculated by Eq. (7) [26].

The experiments were performed carefully to investigate the influence of different heat flux and Reynolds Number on the overall thermal performance of a VWC DL-MCHS with zero overlap. Firstly, the computer, DAQ system and main power supply were switched on. The DAQ system was configured and verified using an in-built self-testing facility. Constant temperature bath was turned on and the desired temperature of 20 °C was set. After that, both the pumps were switched on and initial priming was carried out using in-built priming assistance mode. The valves attached to DPT were also opened to remove any air bubbles trapped in the pressure measurement line. Afterward, the desired flow rate was set in the flow controlling gear pump. The flow rate was measured using weight balance and verified before and after each experiment. Later on, the temperature and pressure drop data were monitored for the adiabatic flow condition and the stability and uniformity of temperature were verified. The voltage stabilizer and heating controller circuit were turned on. The desired heat input was set and varied using the heating controller unit and the temperature and pressure drop data were acquired through a DAQ system and logged using LabVIEW17 software. The data were analysed after the steady-state was reached (20–30 minutes for each experiment). The collected data were post-processed and plotted in the graphical form for a better understanding of a VWC DL-MCHS system.

Qloss = Q − Qtotal

2.2. Data reduction

The combined effect on the thermal and hydraulic performance of a VWC DL-MCHS is realized in terms of Coefficient of Performance (COP). It is the ratio of total heat dissipated from the MCHS (Qtotal )and total pumping power (W˙ )and is inversely proportional to the temperature non-uniformity in the substrate (Ts )[31]. It is defined as per Eq. (11).

The performance of a VWC DL-MCHS was analysed and discussed in terms of major thermal performance parameters such as thermal resistance, pressure drop and temperature non-uniformity. The thermal resistance, Rth,total was calculated by Eq. (8).

Rth,total =

COP =



Qupper = m˙ upperC p T f,U,out − T f,U,in



(8)

Q

(9)

(10)

Qtotal

(11)

(Ts )W˙

Here, W˙ is the total pumping power to drive the flow in a MCHS, which is calculated using Eq. (12).







W˙ = PLowerV˙ lower + PU pperV˙ lower

Here, Q is the total heat input and Ab is the base area of the substrate of a VWC DL-MCHS. Total heat dissipated by the coolant in the lower and upper layers of a VWC DL-MCHS was estimated by Eqs. (3) and (4) respectively [26].





Ptotal = PLower + PU pper

(2)



T f,L,in +T f,U,in 2

The pressure drops of the upper layer (PU pper )and lower layer (PLower )were measured using DPT. The total pressure drops (Ptotal )of a VWC DL-MCHS was calculated based on Eq. (10).

Here, Qis the total heat input provided, which is calculated based the measured current (I) voltage (V) from the control panel. The heat flux (q) given at the base of the substrate is determined using Eq. (2).

Qlower = m˙ lowerC p T f,L,out − T f,L,in



Ts = TS,max − TS,min

(1)

Q q= Ab

Ts,max −

Here, Ts,max is the maximum temperature measured among the six thermocouples attached in the substrate of a VWC DL-MCHS. T f,L,in and T f,U,in are the inlet fluid temperatures measured in the lower and upper layer respectively and were set to 20 °C. The difference between the maximum and minimum substrate temperature measured at the substrate of a VWC DL-MCHS, which shows the thermal imbalance of a cooling system, is defined as temperature non-uniformity (Ts ). It was calculated using Eq. (9)[31].

Total heat supplied from a control panel unit to AC power sourced cartridge heaters was calculated by Eq. (1) [26].

Q = I ×V

(7)



(12)

Though COP does not hold a physical significance, it is used here for the sake of comparison and overall evaluation of thermohydraulic parameters of a MCHS. The wall temperature at the lower channel is determined from the measured substrate temperature using Fourier’s law, as shown in Eq. (13) [26].

(3)

Tc,z,lower = Ts,z −

(4)

Qlower × tsc Ab × ks

(13)

Here, Tc,z,lower is the lower channel temperature, Ts,z is the local substrate temperature measured by thermocouples, Qlower is the heat dissipated by the lower layer, tsc the distance between the substrate and the base of the lower channel, Ab is the base area and ks is the thermal conductivity of the substrate material. The local heat transfer coefficient in the lower layer is determined from the Eq. (14) [26],

Here, m˙ lower = ρV˙ lower is the mass flow rate given at the lower layer. C p is the specific heat of DI water. T f,L,in and T f,L,out are the fluid temperatures at the inlet and outlet of the lower layer, respectively, which were measured from the thermocouples placed at the inlet and outlet plenums and the time-averaged after the steady-state was reached. Similarly, m˙ upper is the mass flow rate given at the upper layer i.e. m˙ upper = ρV˙ upper . The total volumetric flow rate is determined by the summation of the volumetric flow rate given in each layer. i.e. V˙ total = V˙ lower + V˙ upper .

hz = 8



Qlower

As Tc,z,lower − T f,z



(14)

N. Patel and H.B. Mehta

International Journal of Heat and Mass Transfer 165 (2021) 120633

Fig. 7. Boundary conditions applied to the computational domain.

Here, hz is the local heat transfer coefficient in the lower layer and As is the total convective surface area in lower layer. T f,z is the local fluid temperature in the lower layer that is determined from the numerical analysis. Based on the local heat transfer coefficient, the local Nusselt number is calculated using Eq. (15).

N uz =

hz Dh kf

The boundary conditions applied for solid and fluid region for the present investigations are shown in Fig. 7 (a) and (b) respectively and the conditions are written as below: Velocity Inlet boundary condition at the inlet of a channel in each layer: w = v; T f,in =293.15 K Pressure outlet at the exit of a channel in each layer; P = Pout = 1.01325 kPa Constant heat flux at the Bottom wall of substrate: q = −ks ∂∂Tns = Constant Solid-fluid interface boundary condition: u = 0, v = 0, w = 0 and ks ∂∂Tns = k f ∂∂Tns

(15)

Here, hz is the local heat transfer coefficient in the lower layer, Dh is the hydraulic diameter and k f is the thermal conductivity of a coolant. The performance characteristics of different MCHS configurations are compared based on the normalization technique. The performance parameters of a VWC DL-MCHS are normalized based on the respective performance parameters of a conventional DLMCHS. The normalized parameters are shown in Eqs. (16)–(18). It involves Normalised pressure drop (NP as Eq. 16), Normalised temperature non-uniformity in the substrate (NTs as Eq. 17) and Normalised Coefficient of Performance (NCOP as Eq. 18).

N P =

P of VWC DL − MCHS P of Conventional DL − MCHS

(16)

NTS =

TS of VWC DL − MCHS TS of Conventional DL − MCHS

(17)

NCOP =

COP of VWC DL − MCHS COP of Conventional DL − MCHS

(18)

Solid-thermal paste interface boundary condition, ks ∂∂Tns = kT P ∂∂Tns

The side boundaries are considered as symmetry and upper and the end wall of the substrate is given as no-slip adiabatic boundary conditions. Ansys fluent software is used for numerical analysis. The Finite Volume Method (FVM) is used for the simulation of solid and fluid domains of a VWC DL-MCHS. As the flow remains to be in laminar condition throughout, the simulations are performed using a viscous laminar model. The second-order upwind scheme is used for the discretization of advection and diffusion terms. The pressure and velocity of flow fields are coupled and solved using SIMPLEC algorithm. The permissible residual error for the convergence of the momentum and energy equations are set as 10−6 and 10−8 respectively. Moreover, the code was developed to incorporate the temperature-dependent thermophysical properties of coolant to the numerical model. Based on the numerical analysis and results obtained, the major performance parameters of VWC DL-MCHS are investigated [29].

2.3. Numerical methodology The numerical model and methodology to be used for the present investigations were reported by the authors [28,29] and is summarized here. The fluid flow is assumed to be single phase, laminar and continuous. Flow mal-distribution in channels of a MCHS is neglected. This, in turn, reduces the numerical modeling and analysis limited to a single channel analysis. A 3-D solidfluid conjugated heat transfer model is used for the analysis. Single solid domain for the lower layer and upper layer is used for a VWC DL-MCHS. In experiments, the upper layer is placed over the lower layer, separated with the help of 0.5 mm Aluminum sheet. The upper and lower planum are tightly joined with the help of Allen screw fasteners, which ensures that there is no air gap remains. However, the numerical investigations for a VWC DL-MCHS are performed by considering the effect of thermal paste at the bottom of the substrate.

3. Results and discussion As mentioned earlier, VWC DL-MCHS with zero overlap geometry was observed efficient based on the authors’ numerical study [28,29]. In which a 3-D structured hexahedral mesh was applied for the discretization of solid and fluid computational domains. The number of elements in x, y and z directions was varied from 10 × 17 × 50 (9350 elements) to 40 × 170 × 200 (13,60,000 elements). A negligible deviation was observed in thermal resistance after 1,70,0 0 0 elements, which relate the grid size of 20 × 85 × 100. Hence, this grid size was used for the simulations. In a lack of experiments for such a VWC DL-MCHS geometry, the numerical procedure adopted was validated in two folds. Firstly, numerical investigations were performed for a conventional 9

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flux of 11.44 W/cm2 , 15.56 W/cm2 , 148.8 W/cm2 , 188.1 W/cm2 and Re = 46, 92 and 138. The Reynolds number and volumetric flow rate was kept the same in each layer of a VWC DLMCHS, i.e V˙ = V˙ lower = V˙ upper . The maximum substrate temperature of Ts, max < 85 °C was maintained. The experimental analysis is discussed in terms of thermal resistance (Rth ), temperature nonuniformity in the substrate (Ts ) and total pressure drop (P). The overall thermo-hydraulic performance was estimated using the Coefficient of Performance (COP). In order to compare the present geometry of VWC DL-MCHS with zero overlap, numerical investigations were also performed for a conventional DL-MCHS with the same set of thermo-hydraulic conditions. The results in the subsequent sections were discussed first with numerical and experimental validation of a VWC DL-MCHS with zero overlap and then compared with the numerical study of a conventional DL-MCHS. The error analysis was carried out in terms of Mean Absolute Relative Deviation (MARD). 3.1. In situ analysis The present experiments were conducted first for in-situ analysis under no flow heating conditions to ensure proper mounting of thermocouples and uniform heating conditions. Total of six thermocouples was installed beneath the MCHS substrate to measure the substrate temperature. As shown in Fig. 9(a), the constant value of temperature at q = 0 W/cm2 confirms the functioning and proper installation of all the six thermocouples. Moreover, an increase in heat flux increases the temperature of the substrate, which is seen from Fig. 9(a). This verifies the uniform heating condition at the bottom of the substrate. All the thermocouples show the measurement error of ±0.5 °C at each heat flux.

Fig. 8. Validation of Present numerical model with the experimental study of Wei et al. [25].

SL-MCHS and then compared with the experimental data reported by Tuckerman and Pease [3]. The results were found in agreement with the error of ±0.37% for thermal resistance and ±0.46% for pressure drop. Afterward, the numerical investigations were performed for a conventional DL-MCHS and compared with the experimental data of Wei et al. [25]. The axial substrate temperatures for all the flow rates were obtained and shown in Fig. 8. The results were found in agreement with the Mean Absolute Relative Deviation (MARD) in the range of 0.05% to 0.27% at various flow rates. This two-fold validation study confirms the adopted numerical methodology for a VWC DL-MCHS. The numerical study in ref [28] was performed only for a single flow rate of 1.5LPM. Hence, a set of numerical studies were performed for the present research work with various Re and heat fluxes. The numerical results obtained so were validated by conducting experiments. The experiments were performed for heat

3.2. Repeatability study In order to ensure the repeatability of the experiments, the experiments were performed three times using the same set of parameters. The maximum surface temperature observed for each run at different heat flux and Re is shown in Fig. 9(b). The repeatability of the experiments was found in the error range of MARD = ±1.08%.

Fig. 9. Surface temperature plot for in-situ analysis and repeatability. 10

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Table 3 Uncertainty in Measured and Calculated parameters. Measured parameter

Relative uncertainty

Calculated parameter

Relative uncertainty Minimum

Maximum

±2.8%

Voltage (V), Current (I) Temperature (T) Volumetric Flow rate (V˙ )

±1%

Heat Input (Qinput )

±0.5% ±2%

Pressure Drop (P)

±0.1%

Thermal Resistance (Rth ) Total Heat Dissipated (Qtotal ) COP

±2.83% ±1.82

±2.86% ±6.7

±1.5

±6.5

Fig. 10. Total Thermal resistance as a function of various heat flux and Re.

3.3. Calibration of DPT

3.4. Uncertainty analysis

The calibration of DPT was carried out for pressure drop measurement. The calibration study was performed with tube experiments since the standard theoretical data are available for validation. Stainless Steel Tube (Diameter: 4 mm, Length: 58 cm, 0.015 mm roughness) was considered. The flow rates were set in the range of 100 ml/min to 10 0 0 ml/min. The pressure drop data were found in agreement with the theoretical data in the error range of MARD = ±1.75% to ±3.95.

The uncertainty analysis was carried out using Kline and McClintock method [32]. It is determined using the uncertainties of measured variables (W1 , W2 , W3 . . .Wn ), the uncertainties (W) of dependent variables are calculated based on the Kline & McClintock equation as shown in Eq. 19.



W = 11

∂R W ∂ X1 1

2



∂R + W ∂ X2 2

2



∂R + .. . . . . W ∂ Xn n

2 12

(19)

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International Journal of Heat and Mass Transfer 165 (2021) 120633

Fig. 11. Substrate temperature non-uniformity as a function of heat flux and Re.

Fig. 12. Substrate Temperature in the axial direction at various heat flux.

Where, R is a function of independent variables (X1, X2. . ., Xn). Each term of the basic equation presents the partial derivative of R with respect to Xi multiplied by the uncertainty of those independent measurements. Each term represents the contribution of inaccuracy associated with individual measurement in the final derived results. In the present experiments, the measured parameters considered were voltage, current, temperature, volumetric flow rate and pressure drop. The accuracy associated with each parameter is shown in Table 1. The uncertainty for heat input, thermal resistance, total dissipated heat and COP were estimated using Eqs. (20)–(23) respectively. Engineering Equation Solver (EES) is used to carry out uncertainty analysis.

 COP =

∂ COP Qtotal ∂ Qtotal

2

The uncertainty associated with all the measured and calculated parameters is tabulated in Table 3.



Qinput =

 Rth =

∂ Rth T ∂T

 Qtotal =

 +

∂ COP (P ) ∂ P

12

∂ Qinput V ∂V 2

 +

 +

 +

∂ Qtotal ˙ V ∂ V˙

2

2

∂ Qinput I ∂I

∂ Rth

∂ Qinput

2

 +

2 (20)

2 Qinput

∂ Qtotal T ∂T

(21)

2

   ∂ COP ˙ ∂ COP V + T ∂T ∂ V˙

(22)

(23)

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International Journal of Heat and Mass Transfer 165 (2021) 120633

Fig. 13. Fluid temperature at the outlet as a function of heat flux and Re.

Fig. 14. Local heat transfer coefficient in the axial direction for the lower layer of a VWC DL-MCHS. 13

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Fig. 15. Local Nu in the axial direction for the lower layer of a VWC DL-MCHS.

3.5. Effect on thermal resistance

which increases the convective heat transfer in a VWC DL-MCHS. Along with that, in channels with higher aspect ratio, the flow speed increases with the increment in Re and therefore, the heat transfer coefficient of fluid along the channel rises. The higher flow rate assists in minimizing the fluid temperature across the channel, which in turn delays the development of the thermal boundary layer. Therefore, the increase in the flow speed along the channel results in diminishing of the boundary layer effects and thus reduces the thermal resistance, making temperature distribution more uniform, which ultimately improves the performance of the heat sink. Moreover, at any specific Re, Ts is observed to increase with the increment in heat flux due to the increment in thermal load. The experimental data of Ts is observed in agreed comparison with the numerical data for all the considered experimental conditions. Moreover, the experimental Ts of a VWC DL- MCHS is compared with the conventional DL-MCHS and shown in Fig. 11(b). It is observed that VWC DL-MCHS outperformed the conventional DL-MCHS in terms of Ts for all the considered experimental conditions. The overall decrement in Ts for a VWC DL-MCHS is in the range of 16.08% to 34.59%. This decrement in Ts for a VWC DL-MCHS as compared to conventional DL-MCHS is attributed to

Thermal resistance as a function of heat flux and Re is shown in Fig. 10. Thermal resistance is observed to decrease with an increase in the Re at a particular heat input. This is due to the effective dissipation of heat with an increase in Re, which in turn decreases the convective thermal resistance. Moreover, a marginal increment in thermal resistance is observed with an increase in heat flux at a particular Re. This is due to the fact that with an increase in heat flux, the maximum surface temperature increases and more heat is sprightly dissipated into the environment by the convective way. The experimental observations are found in agreement with the numerical study in the error range of MARD=1.23% to 3.12%. 3.6. Effect on temperature non-uniformity The experimental temperature non-uniformity in the substrate of a VWC DL-MCHS as a function of Re and heat flux is shown in Fig. 11(a). At a specific heat flux (e.g., q = 30.09 W/cm2 ), Ts is observed to decrease (6.01°C to 3.26°C) with an increase in Re (46 to 138). It is due to the proper mixing of fluid flow at a high Re, 14

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International Journal of Heat and Mass Transfer 165 (2021) 120633

Fig. 16. Flow vortices and flow reversal phenomenon at the stepped location.

the distinct flow phenomenon befalls in a VWC DL-MCHS, which is discussed in the subsequent section. To portray the actual axial distribution of temperature in the substrate of a VWC DL-MCHS, the experimentally measured surface temperature (Ts ) along the streamwise direction (z) at various heat flux and Re is shown in Fig. 12. At a specific axial location, the surface temperature is observed to increase with an increase in heat flux due to the increment in the conductive thermal resistance. Contrary, the local surface temperature at a specific heat flux is observed to decrease with an increase in Re. This is due to the proper mixing of fluid at a high Re, which increases the local heat transfer in a VWC DL-MCHS. The surface temperatures measured at the different axial location is found in agreement with the numerical data in the error range of MARD=0.32% to 1.72%. In addition to this, rise in surface temperature along the streamwise direction is not observed continuous rather, it decreases at z=6.5 mm at any experimental conditions. This is attributed to the distinct flow and thermal phenomenon formed near the stepped location at z=5 mm in a VWC DL-MCHS. To get the insight, the local heat transfer coefficient at various Re and heat flux was estimated using (Eq. 14) and plotted in Fig. 14. The local channel wall surface temperatures were first estimated based on the local surface temperature measured at the bottom of the substrate using a 1-D thermal conduction approach (Eq. 13). The local fluid temperatures were not measured experimentally and hence it was estimated based on the numerical study. In order to ensure the correctness of the numerically obtained local fluid temperatures, the experimentally measured outlet fluid temperatures (Tf, Out ) were compared with the numerically obtained outlet fluid temperatures for both the layers. The comparison of experimental and numerical fluid temperatures at the outlet for the lower and upper layer of a VWC DL-MCHS is shown in Fig. 13 (a) and (b), respectively. It is observed that, for the lower

layer, experimental data of Tf, Out is in accordance with the numerical data having MARD of 1.32%. Therefore, the determination of the fluid temperature at different axial locations from the numerical study is vindicated for the lower layer. However, slightly higher deviations between experimental and numerical data of Tf, Out are observed for the upper layer having MARD of 6.89% due to heat spreading loss between two layers. Therefore, the heat transfer mechanism based on the local heat transfer coefficient is explained and discussed only for the lower layer of a VWC DL-MCHS in the subsequent section. 3.7. Heat transfer mechanism in a VWC DL-MCHS The variation in local heat transfer coefficient (hz ) at different heat flux and Re in the lower layer of a VWC DL-MCHS is shown in Fig. 14 (a-d). Along with that, the local Nu in the axial direction is also shown in Fig. 15. At a specific heat flux, the local heat transfer coefficient is observed to increase with the increment in Re due to the decrement in convective thermal resistance. In general, the local heat transfer coefficient is significantly influenced by the geometrical aspects of a channel. A channel of a VWC DLMCHS consisting three regions namely upstream region (before the stepped location), at the stepped location, downstream region (after the stepped location). Therefore, the diverse flow phenomenon and heat transfer mechanism associated with different region of a channel of a VWC DL-MCHS is discussed individually. Before the stepped location The upstream region between z= 0 to z = 5 mm contains the coarser fin region. It is observed from Fig. 13(a) to (d) that the heat transfer coefficient decreases continuously in the upstream region (before the stepped location). It is due to the combined effect of the emergence of growth of the boundary layer near the entrance 15

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Fig. 17. Fluid temperature contours at various axial locations in the lower layer of a VWC DL-MCHS.

region and availability of coarser fins that offers less effective heat transfer surface area. Therefore, the heat transfer coefficient in the upstream region is also observed lower than the other regions of a channel. At the stepped location The stepped location is at 5 mm from the inlet of a channel. It is observed that the heat transfer coefficient increases instantaneously at the stepped location. It is due to the fact that the availability of stepped fin causes the disruption of the boundary layer and entails the heat transfer at the stepped location. Along with that, the presence of a stepped fin altogether impacts the flow stream field and temperature dispersal inside a channel. To get the insight into the flow phenomenon occurs at the stepped location, the numerical model of a VWC DL-MCHS at 30.09 W/cm2 heat input and Re = 138 is used. The post-processing of the numerical model and data captures the distinctive flow phenomenon and temperature contours inside a channel and it is shown in Figs. 16–18. It is observed from Fig. 16 that the partial flow reversal appears at the stepped location in both the upper and lower layer near the vicinity of the stepped fin. The upcoming flow stream encroaches on the frontal wall of a stepped fin and a partial flow stream gets diverted the opposite (reverse) way. At the point when the liquid encroaches on the frontal surface, it disseminates the heat from the frontal wall of the stepped fin and gets warmed. This warm flow stream reversed around and blended in with the upcoming cold flow stream. This upstream cold liquid somewhat chill off the warm liquid at the stepped location. This partial flow reversal phenomenon causes a minor decrement in fluid temperature at the stepped location (Fig. 17),

which in turn increases the heat transfer coefficient at the stepped location. After the stepped location The downstream region contains the denser fin region between z= 5 mm to z=25 mm. Therefore, the downstream region offers a more effective surface area for heat transfer. Moreover, it is observed from the velocity contours (shown in Fig. 18) that the fluid velocity increases in the downstream region due to decreased hydraulic diameter. Along with that, the effect of horseshoe vortices still persists in the downstream region and provides better fluid mixing. In a nutshell, the combined effect of the higher effective surface area increased coolant acceleration and low coolant temperature is responsible for the higher heat transfer coefficient observed in the downstream region in comparison to the upstream region. Moreover, the boundary layer redevelopment emerges in the downstream region, which eventually lowers down the heat transfer coefficient in the downstream region as the axial distance increases. Therefore, the heat transfer coefficient is observed slightly lower near the outlet of a channel.

3.8. Heat dissipation in a VWC DL-MCHS Heat dissipation analysis of a VWC DL-MCHS is carried out by energy balance equations Eqs. (2)–((4)) and the results are shown in Fig. 19. It involves heat dissipation in the lower layer (QLower ), the upper layer (QUpper ), total heat dissipation (QTotal ) and heat loss (QLoss ) estimated at various flow rates and heat inputs (Q). As shown in Fig. 19 (a-b) when the Re is increased from 46 to 138 for 16

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International Journal of Heat and Mass Transfer 165 (2021) 120633

Fig. 18. Velocity contours at various axial locations in the lower layer of a VWC DL-MCHS.

the heat input of 71.5 W, QLower is increased from 71.55% to 85.35%, QUpper is decreased from 21.07% to 11.42%, QLoss is decreased from 7.36% to 3.22% and QTotal is increased from 92.62% to 96.77%. A similar trend is observed at other heat inputs. Higher heat dissipation by the lower layer is due to the availability of denser fin region (80% dense and 20% coarse (of Lhs )) as compared to the upper layer (20% dense and 80% coarse (of Lhs )). For a particular heat input, total heat dissipation (QTotal ) is observed to increase with an increase in Re. The increment in total heat transfer with Re is due to an increase in the momentum of the coolant, which increases the heat carrying capacity of the coolant. For a particular Re and heat input, the lower layer dissipates more amount of heat as compared to the upper layer. At low heat input (Q=71.5 W) and high Re (138), the majority of the heat is observed to dissipate by the lower layer (85.35%) and less amount of heat is reached to the upper layer (11.42%). Therefore, at low heat input, the lower layer shows significant dominance for heat dissipation over the upper layer. This is due to the geometrical parameters of channels. As reported by Xie et al. [33] that the upper-branch channel can accept more heat than the lower-branch channel when the height of lower-branch channel is almost less than 0.4 mm. The lower-branch channel can accept more heat when the flow distribution is uniform. However, the lower layer channel can accept more and more heat with the increasing height of the lower channel. In the present geometry of a VWC DL-MCHS, the channel height is 2.5 mm. Therefore, a higher channel flow area dissipates more heat. Along with that, the length of the denser fin region in the lower and upper layer is 20 mm and 5 mm, respectively. Therefore, higher heat transfer surface area of the lower layer dissipates more heat as compared to the upper layer. Therefore, the lower layer is dominant over the upper layer in terms of overall heat dissipation. However, the dominance of the lower layer is observed to decline marginally (71.55% to 69.79%)

and more heat reaches the upper layer (11.42% to 14.97%) at high heat input of Q= 188.1 W. Total heat transfer by the coolant (QTotal ) is observed less as compared to heat input (Q), as shown in Fig. 19 (a-h). This shows that heat is not fully dissipated by the coolants of both layers. Some amount of undissipated heat persists experimentally. VWC DL-MCHS is fully insulated from all the sides and there is no way out for heat loss to the surrounding atmosphere. This was also verified by measuring the temperature through one thermocouple placed above the insulation box and the other was kept open to the atmosphere. Faintly any temperature difference between the insulation box and atmospheric temperature was observed. Therefore, the possible reason here for heat loss is that this heat was distributed and remained in the aluminum sheet that separated both the layers. This undissipated heat by both the layers is represented as heat spreading loss. The maximum heat spreading loss was observed in the experiments as 9.56% at high input and low flow rate (Fig. 19h), while minimum heat loss as 3.22% at low heat input and high flow rate (Fig. 19b). Lower heat loss at higher flow rates shows that the efficiency of both the layers increases with an increase in flow rate irrespective of heat input.

3.9. Effect on total pressure drop Experimental pressure drop in the upper layer (Pupper ) and lower layer (Plower ) of a VWC DL-MCHS along with the total pressure drop (PUpper + PLower ) as a function of various Re is shown in Fig. 20(a). The pressure drop in each layer was measured through a calibrated DPT. It is observed from Fig. 20(a) that the pressure drop increases continuously with an increase in Re. For a particular Re, the pressure drop in the upper layer is observed 17

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International Journal of Heat and Mass Transfer 165 (2021) 120633

much less as compared to the lower layer. It is due to the fact that, in zero overlap condition of a VWC DL-MCHS, the dense fin region in the upper layer is much less as compared to the lower layer that offers less frictional resistance to flow and induces less pressure drop. The numerical simulations for a VWC DL-MCHS were also performed considering inlet-outlet plenums to portray the actual experimental condition. The expansion and contraction pressure losses and pressure losses that occur in plenums were found much less as compared to the pressure loss observed across the channels. This shows that the variable width channels contribute majorly to the overall pressure drop induced in a VWC DL-MCHS test section. The numerical and experimental pressure drop is found in agreement with MARD of ±1.04%. The total experimental pressure drop of a VWC DL-MCHS is compared with the conventional DL-MCHS in terms of normalized pressure drop (NP = PVWC DL-MCHS / PDL-MCHS ) and is shown in Fig. 20(b). The value of NP is observed much lesser than unity, which means that P observed for a VWC DL-MCHS is significantly reduced as compared to a conventional DL-MCHS. This decrement in total pressure drop is observed 1.89 times at Re = 46 to 1.67 times at Re = 138. This shows that the VWC DL-MCHS geometry outperformed the conventional DL-MCHS in terms of total pressure drop. This is due to the fact that the removal of denser fins from

the upstream of the VWC DL-MCHS decreases the frictional resistance as compared to a conventional DL-MCHS having continuous dense fins throughout the axial length. This decrement in pressure drop penalty leads to less pumping power and ultimately reduces the overall operational cost of the electronic cooling system. 3.10. Effect on overall thermo-hydraulic performance The overall thermo-hydraulic performance of a VWC DL-MCHS is determined using Eq. (11) and shown in Fig. 21 as a function of various Re and heat flux. At a specific heat flux, COP is observed to decrease with an increase in Re due to increment in pumping power. The experimental data of COP are observed to be in agreement with the numerical data having MARD of 3.47% to 9.73%. Moreover, at a specific Re, the trend and value of numerical COP at various heat flux are observed nearly the same. However, variations in the trend of experimental COP at different heat flux is observed, which marginally deviates the experimental trend from the numerical. The major cause of this deviation is the variations in experimental total heat dissipation (QTotal ), as the difference between the experimental and numerical value of Ts , as well as P, is marginal. At low flow rate-high heat flux experimental condition, undissipated heat is more, which decreases the amount of

Fig. 19. Distribution of Total heat dissipation and spreading loss in a VWC DL-MCHS. 18

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Fig. 19. Continued

Fig. 20. Pressure drop as a function of various Re in a VWC DL-MCHS.

19

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International Journal of Heat and Mass Transfer 165 (2021) 120633

Fig. 21. Actual COP as a function of heat flux and Re in a VWC DL-MCHS.

QTotal and results to decrement of COP. However, the amount of undissipated heat is decreased at a high Re. Therefore, the deviation of the experimental COP from the numerical trend is observed to decrease at a high Re. i.e. for q = 30.09 W/cm2 , MARD in COP is observed about 10.08% at Re = 46 which reduces to 6.29% at Re = 138. The comparison of the overall thermal performance of a VWC DL-MCHS and conventional DL-MCHS is obtained based on the normalized coefficient of performance (NCOP) and shown in Fig. 22. It is observed that NCOP of the VWC DL-MCHS for all the experimental conditions is higher than a conventional DL-MCHS. The improvement in the overall thermal performance of a VWC DLMCHS is about 1.53 to 2.35 times the conventional DL-MCHS for the considered experimental conditions. This is due to the combined effect of the decrement in temperature non-uniformity in the substrate with the reduced overall pressure drop across the channel in a VWC DL-MCHS. Moreover, it is observed that at any specific heat flux, NCOP is increased with an increase in Re. It is because of the fact that the difference between the Ts of a VWC DL-MCHS and a conventional DL-MCHS is increased with an increase in Re (reiterate to Fig. 11 (b)). It shows that a VWC DL-MCHS compensates the increase in pressure drop penalty at a high Re with the decrement in the temperature non-uniformity. Therefore,

Fig. 22. Normalised COP as a function of heat flux and Re.

20

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International Journal of Heat and Mass Transfer 165 (2021) 120633

a VWC DL-MCHS should be preferred over conventional DL-MCHS for any heat flux and Re.

Government of India under the Core Research Grant Sanction No. SERB/EMR/2017/0 0 0429.

4. Conclusions References The experimental investigations on a VWC DL-MCHS were carried out in the present research. The influence of various heat flux and Re on the thermal performance of a VWC DL-MCHS was investigated. The experimental and numerical thermal performance of a VWC DL-MCHS was compared in terms of thermal resistance, temperature non-uniformity in the substrate and total pressure drop and COP. Moreover, the thermal performance of a VWC DL-MCHS was compared with the conventional DL-MCHS in terms of normalised parameters. The conclusions drawn from the present investigations are as follows:

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1 The experimental results of a VWC DL-MCHS are in accordance with the numerical results having identical thermo-hydraulic conditions. The maximum deviations between the experimental and numerical data of thermal resistance, temperature nonuniformity in the substrate, total pressure drop and COP of a VWC DL-MCHS are found about 3.12%, 1.72%, 1.04% and 9.73%, respectively. Therefore, the hypothesis of the present study that was to measure the real-life applicability of a VWC DL-MCHS geometry and to experimentally validate the thermal performance of a VWC DL-MCHS geometry is fulfilled. 2 The decrement in temperature non-uniformity in the substrate of a VWC DL-MCHS in comparison of a conventional DL-MCHS is about 16.08% to 34.59%. It shows that the present geometry of VWC DL-MCHS is obliging to dampen the thermal stresses generated in the substrate as well as microelectronic chips, which in-turn beneficial to improve the lifespan of electronic components. 3 The experimental distribution of heat dissipation in both the layers of a VWC DL-MCHS suggests that the lower layer is dominant over the upper layer in terms of overall heat dissipation. For high heat flux-low Re experimental conditions, the lower layer dissipates about 69.78% to 78.75% of the total dissipate heat, which increases to 71.55% to 85.35% for the low heat fluxhigh Re experimental condition. 4 Total pressure drop penalty of a VWC DL-MCHS is found 1.67 to 1.89 times lower than the conventional DL-MCHS. Therefore, the lower pumping power requirement of the VWC DL-MCHS would be worthwhile to decrease the overall operational cost of the MCHS based cooling system. 5 A VWC DL-MCHS outperformed the conventional DL-MCHS in terms of overall thermo-hydraulic performance for all the considered experimental conditions. The improvement in the thermo-hydraulic performance of a VWC DL-MCHS over conventional DL-MCHS is about 1.53 to 2.35 times in terms of COP. Looking to the potential in the proposed novel geometry of DLMCHS from the numerical and experimental investigations, the ongoing research work is planned to extend in future for various nanofluids. Moreover, flow boiling with this novel geometry will also be performed experimentally. Declaration of Competing Interest The authors would like to certify that we have no conflict of interest for the submitted manuscript of our research paper entitled “Experimental Investigations on a Variable Channel Width Double Layered Minichannel Heat Sink”. Acknowledgments This work is financially supported by the Science and Engineering Research Board (SERB), Department of Science and Technology, 21

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International Journal of Heat and Mass Transfer 165 (2021) 120633

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