Numerical investigation of forced convection heat transfer and flow irreversibility in a novel heatsink with helical microchannels working with biologically synthesized water-silver nano-fluid

International Communications in Heat and Mass Transfer 108 (2019) 104324

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Numerical investigation of forced convection heat transfer and flow irreversibility in a novel heatsink with helical microchannels working with biologically synthesized water-silver nano-fluid

T

Amin Shahsavara, Mohammad Mehdi Baseria, Abdullah A.A.A. Al-Rashedb, Masoud Afrandc,d,

⁎

a

Department of Mechanical Engineering, Kermanshah University of Technology, Kermanshah, Iran Department of Automotive and Marine Engineering Technology, College of Technological Studies, The Public Authority for Applied Education and Training, Kuwait c Laboratory of Magnetism and Magnetic Materials, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam d Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam b

ARTICLE INFO

ABSTRACT

Keywords: Biological nano-fluid Electronics cooling Heatsink Irreversibility Silver nanoadditives

This paper aims to evaluate the hydrothermal and irreversibility behaviour of a biological water-Ag nano-fluid in a new heatsink with helical microchannels. Two-phase mixture model is applied to precisely simulate the behavior of nanofluid in the nanoadditive concentration (φ) range of 0–1% and Reynolds number (Re) range of 500–1500. The influences of φ and Re on the convective heat transfer coefficient, CPU surface temperature, pumping power, as well as the irreversibilities due to heat transfer and fluid friction are examined. The findings depict that boosting the Re and φ augments the performance of heatsink by intensifying the convective heat transfer coefficient of the working fluid which favourably declines the CPU surface temperature and the heat transfer irreversibility and importantly results in the temperature uniformity of the CPU surface. However, intensification in Re adversely affects the pumping power, the fluid friction and total irreversibilities in the system. Furthermore, it is revealed that the nano-fluid always has a superior cooling performance as compared with the pure water. Finally, it is found that the best hydrothermal performance of the nano-fluid in the proposed heatsink occurs at Re = 1500 and φ = 1%, while the minimum total irreversibility occurs at Re = 500 and φ = 1%.

1. Introduction

Some scientists working in the field of nanotechnology have concentrated their efforts on boosting the cooling capacity of common cooling fluids such as water and engine oil. To this end, they have utilized nanoadditives of high thermal conductivity in common fluids and then, by employing various physical and chemical schemes, they have attempted to stabilize such nanoadditives in the resulting suspensions. Findings have shown that such suspensions (nano-fluids) enjoy a better thermal conductivity than a base fluid [1–10]. Choi [11] was the first scientist who produced these modern fluids and reported their thermophysical properties. The great potential of nano-fluids has attracted the attention of researchers throughout the world, and numerous experimental [12–16] and numerical [17–21] works have been implemented on the various properties and applications of these nanofluids. As technology advances, electronic devices and systems are becoming ever smaller and more powerful. However, the enhanced performance of these parts is accompanied by a rise in their power consumption and, consequently, an augmentation in the amount of heat

As a branch of applied science and technology, nanotechnology encompasses vast and varied subjects. The main focus of nanotechnology is on the processing of materials or working with equipment that are less than a micrometre in size (usually about 1–100 nm). Nanotechnology actually involves the understanding and use of new material and system properties that emerge at these dimensions. These novel physical effects are primarily due to the quantum properties of such materials overcoming their classical properties. Nanotechnology is an intensely interdisciplinary science and it is associated with fields such as medicine, pharmacology and drug design, veterinary medicine, biology, applied physics, materials engineering, semiconductors, chemistry and even with mechanical, electrical and chemical engineering disciplines. Technology analysts are of the opinion that Nanotechnology, Biotechnology and Information technology (IT) constitute the three major realms of science that form the third industrial revolution. ⁎

Corresponding author at: Ton Duc Thang University, Ho Chi Minh City, Vietnam. E-mail address: [email protected] (M. Afrand).

https://doi.org/10.1016/j.icheatmasstransfer.2019.104324

0735-1933/ © 2019 Published by Elsevier Ltd.

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generated by them. Therefore, it is essential to deal with the issues of cooling and heat management in electronic components and chips. So far, different techniques such as air cooling and ventilation by fans, heatsinks and fluid-based hybrid systems have been exploited to reduce the temperature of electronic chips. Active researchers in the field of nano-fluids have recently investigated, numerically and experimentally, the effectiveness of these novel fluids in cooling electronic parts and systems [22–26]. Al-Rashed et al. [27] performed simulations to evaluate the first-law performane of a non-Newtonian water-CMC/CuO nano-fluid flowing inside an offset strip-fin microchannel heatsink. The outcomes revealed that, in the best case, the use of nano-fluid instead of water results in a 2.29-fold increase in the ratio of heat transfer augmentation to pressure drop augmentation. In an another work, Al-Rashed et al. [28] carried out a numerical investigation to evaluate the hydrothermal aspects of water-Ag nano-fluid inside a micorchannel heatsink with sinsoidal walls. It was found that the performance of heatsink intensifies by boosting the wavelength of sinusoidal walls. In a numerical assessment, Ambreen and Kim [29] examined the first-law performance of a finned heatsink filled with water-TiO2 nano-fluid. The results depicted that the best thermal performance belongs to the heatsink equipped with circular fins. Naphon et al. [30] experimentally analyzed the combined effects of jet impingement and water-TiO2 nanofluid on the first-law performance of a microchannel heatsink. It was found that the performance of heatsink augments with boosting the nanoadditives fraction and nozzle diameter, while it declines with augmenting the nozzle level height. Second-law analysis is an important concept in thermodynamics, which basically investigates energy by its value in terms of its convertibility from one form to another. Literature survey demonstrates that the irreversibility analysis of nano-fluid flow through heatsinks has been rarely examined so far. However, because of the impossibility of converting the whole heat into work, the quality of thermal energy must be assessed. The second-law of thermodynamics can be employed to determine the lost work because of irreversibility of process. Chen et al. [31] numerically determined the optimal constructs of cylindrical pin-fin heatsinks using the irreversibility minimization. They found the optimal geometric parameters and the corresponding number of pin-fin. It was reported that the minimum rate of irreversibility is achieved by using the more fin-material fraction and the lower fluid velocity in the allowed range. Dokken et al. [32] performed simulations to optimize a 3D printed heatsink design using a micro-genetic algorithm with bit array representation. They used the irreversibility minimization as optimization objective. The results revealed that the optimization results in a 26.4% and 21.7% reduction in the irreversibility for the symmetric and nonsymmetric power maps, respectively. Yang et al. [33] utilized constructal and thermo-economic theories to optimize pin-fin heatsinks with inline configuration. They find the optimal value of geometric parameters which minimize the irreversibility-based cost of the heatsinks. It was reported that the optimal designs are various under different considered parameters. In the present research, a new helical heatsink is introduced and the performance of biological water-Ag nano-fluid in it is investigated from the viewpoints of the first and second-laws of thermodynamics. The two-phase mixture model is used to perform the required simulations. Furthermore, the effects of φ and Re on the operating parameters of the heatsink such as temperature uniformity, CPU temperature, pumping power and irreversibilities due to nano-fluid flow and heat are examined.

Fig. 1. Schematic sketch of the (a) heatsink under investigation and (b) insulation cap.

synthesizing the silver nanoadditives involves the reduction of silver ions in the solution or in high temperature in gaseous environments [34]. However, the reducing reagents, such as sodium borohydride, may augment the environmental toxicity or biological hazards [34,35]. Additionally, the capping agents like polyvinyl alcohol (PVA) or gelatin, must be employed to protect the silver nanoadditives from aggregation. Besides, the high temperature may also increase the cost. Therefore, the development of a biological preparation of silver nanoadditives by utilizing environment-friendly solvents and nontoxic reagents is of great interest. In this numerical assessment, the silver nanoadditives were obtained from silver nitrate via the plant extraction technique using green tea leaf extract [36]. The mean size of the particles was 40–50 nm, with spherical morphology and single-phase structure of silver. The synthesized particles were dispersed in pure water as base fluid. The synthesis method of this nano-fluid is presented in Ref. [36] in details. Sun et al. [37] reported that the nano-fluid prepared via this method demonstrates acceptable dispersion stability. The schematic sketch of the studied heatsink is presented in Fig. 1a. The heatsink is made of copper and its length, width and depth are 11.48 mm, 9.6 mm, and 0.4 mm, respectively. It is seen that the heatsink is divided into four symmetrical sections which, each part contains a helical channel with a width of 0.25 mm and a depth of 0.2 mm and the thickness of the walls is 0.1 mm. An insulation cap with a thickness of 0.2 mm is placed at the heatsink top surface (see Fig. 1b) where the inlet and outlet tubes are also placed. For each section, one outlet with a diameter of 0.4 mm is considered in the middle of the section. In addition, the only outlet is located in the center of the insulation cap and its diameter is 0.7 mm. For cooling purpose, the heatsink is placed on the top of a CPU and therefore, the heat flux (q′′ = 80000 W/m2) is applied from the bottom surface of heatsink.

2. Definition of the nano-fluid and microchannel heatsink Among the different metal nanoadditives, silver has received more attraction because it is effective antimicrobial agent, which contain low toxicity. Silver nanoparticles also have the highest thermal and electrical conductivity of all metals. Generally, the technique for

3. Governing equations In order to perform the simulations required in the present study, it 2

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is assumed that the flow is steady and laminar. The fluid flow in the heatsinks is incompressible. In addition, frictional losses and radiant heat transfer are ignored. The governing equations for the problem under consideration are as follows [38]:

.(

m Vm )

.(

m Vm Vm )

=

pm +

p p Vm )

=

. (µm Vm) + f

.(

Vf Cp, f ) T ] =

=

(

p p Vdr , p Vdr , p

(

m

+

f f

T)

p p Vdr , p )

Vdr , f Vdr , f )

n k=1

R=

(5) k k

Vdr , k = Vpf

Vf , k

Vpf =

2

(

m)

p

18µ f fdrag

(g

(Vm ) Vm) = Vp

Vf

p

(7)

Here, Tm = where Tout stands for the leaving fluid temperature. The overall performance of a nano-fluid can be assessed using the Performance Evaluation Criterion (PEC) which gives the relative intensification in heat transfer to pumping power calculated as [28]:

(8)

3.4. Irreversibility The local irreversibility includes the fluid friction and heat transfer terms which are defined as [28]:

SF =

cp, m =

(1

bf

)

bf cp, bf

+

SH =

(9)

p

(11)

km = kbf [0.981 + 0.00114 × T (°C ) + 30.661 × ]

(12)

y

uz 2 + z

+

uy 2 ux + + y x

uz 2 ux + + z x

uy 2 uz + y z

km T2

T x

2

+

T y

2

+

T z

2

(20)

rate of local fluid friction irreversibility and SH is the rate of local heat transfer irreversibility. The global irreversibility within the system is determined by integration with respect to the whole domain. Similarly, the global heat transfer and fluid friction irreversibilities can be calculated as presented in Eq. (21) [28];

(10)

µm = µbf (1 + 2.5 )

uy 2

where ST is the rate of local total irreversibility in the MCHS, SF is the

p cp, p

nf

ux 2 + x

µm 2 T

(19)

The density, specific heat capacity, viscosity, and thermal conductivity of the water-Ag nano-fluid are determined by employing the following equations [36]: m

(18)

ST = SF + SH

3.2. Hydrothermal properties of nano-fluid

+

(17)

where subscript w refers to the water as base fluid.

As mentioned earlier, a constant heat flux (q′′=80,000 W/m2) is imposed on the bottom plate of the heatsink. All the remaining external walls are assumed to be perfectly thermally insulated with no any convective and radiation heat transfer with the surrounding medium. The desired nano-fluid inlet temperature is 300 K. The nano-fluid enters with uniform velocity at the inlet section and other flow boundary conditions are no-slip at the internal walls and atmospheric pressure at the outlet.

)

hm / h w pm / pw

PEC =

3.1. Boundary conditions

= (1

(16)

Tm Tin + Tout 2

1 + 0.15Rep0.687 Re 1000 1 + 0.15ReP Re > 1000

(15)

q TCPU,mean

h=

where g is the gravitational acceleration and dp is the nanoadditive diameter. Additionally, fdrag is the drag coefficient, given as [38]:

fdrag =

(14)

where V is the volumetric flow rate, and ∆p is the pressure loss. The convective heat transfer coefficient is computed by the following equation [28]:

where Vpf is the relative velocity between a particle and fluid, calculated as [38]: p dp

Tin

q

Wpump = V p

(6)

m

k=1

TCPU,mean

where TCPU, mean is the mean temperature of the CPU surface and Tin is the entering temperature of the fluid. A decline in the mean temperature and, consequently, a decline in the thermal resistance means a higher uniformity. The pumping power consumed by the heatsink is computed form the following formula [28]:

k k Vk

n

(13)

(3) (4)

m

TCPU,min q

(2)

where pm is the mixture pressure and T is the temperature. The mass average velocity (Vm), and the drift velocity for nanoadditives (Vdr, k) are as follows [38]:

Vm =

TCPU,max

where TCPU, max and TCPU, min are respectively the highest and lowest CPU surface temperature. A lower θ signifies higher temperature uniformity. Another important parameters to evaluate the performance of a heatsink is thermal resistance which is defined as [28]:

(1)

=0

[( p Vp Cp, p +

(

researchers evaluate the ratio of the difference between the highest and lowest CPU surface temperature to the imposed heat flux [28]:

ST =

where φ is the particle volume fraction, and the subscripts p and bf correspond to particle and base fluid, respectively.

ST dV ; SH =

SH dV ; SF =

SF dV

(21)

3.5. Numerical technique and criteria for performance evaluation

3.3. Evaluation of performance parameters

This study is devoted to the evaluation of the forced convection flow of water-Ag nano-fluid in an innovative heatsink with helical

In order to assess the temperature uniformity of a heatsink, some 3

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Table 1 Findings of mesh study. Grid size

TCPU,

512,904 704,118 998,773 1,222,771 1,442,991

341.61 337.99 334.55 332.41 332.01

max

(K)

Table 2 Details of validation (q′′=6 Kw/m2). Percentage difference −1.06 −1.02 −0.64 −0.12

∆p (kPa) 412.01 405.34 395.77 382.68 380.01

Percentage difference

Mass flow rate (kg/s)

θ (m2K/W) (present)

θ (m2K/W) ([39])

R (m2K/W) (present)

R (m2K/W) ([39])

−1.62 −2.36 −3.31 −0.7

0.000075 0.00015 0.000222 0.0003 0.00373 0.00045

0.00328 0.00234 0.00175 0.00142 0.00123 0.00105

0.00334 0.00239 0.0018 0.00147 0.00128 0.0011

0.00895 0.00446 0.00274 0.00211 0.00166 0.00141

0.00922 0.00461 0.00285 0.00220 0.00174 0.00148

microchannels under laminar regime. The numerical solutions are carried out using the finite volume CFD code Fluent. The second-order upwind scheme was used to solve the momentum and the energy equations. The SIMPLE algorithm was utilized for pressure and velocity coupling. The accuracy of the solution to convergence was monitored at 10−6 for the continuity, x-velocity, y-velocity, z-velocity and the energy equation. Mesh quality has a significant influence on numerical analysis. In this study, five different combinations of node numbers have been examined by comparing the highest CPU temperature and pressure drop in the nano-fluid-cooled heatsink with φ = 1% and Re = 1500. As shown in Table 1, grids with 1,222,771 meshes is taken since there is not any considerable difference between the outcomes by augmenting the number of meshes. The heatsink under investigation is novel and there is no numerical/ experimental data on its performance characteristics in the literature. Therefore, the validation of the numerical method was conducted by comparing the R and θ parameters computed in this assessment with the findings of Ramos-Alvarado et al. [39] for the flow of pure water through a liquid block heatsink with different flow rates. The schematic layout of the considered heatsink is depicted in Fig. 2. The details of the dimensions and working principles of this heatsink can be found in Ref. [39]. The results of this comparison are reported in Table 2. It can be seen that there is a proper agreement between the findings.

improves the convective heat transfer coefficient of nano-fluid by 4.04%. Also, at φ = 1%, the rise of Re from 500 to 1500 improves the convective heat transfer coefficient by 95.99%. The convective heat transfer coefficient is a function of the ratio of thermal conductivity coefficient to thermal boundary layer thickness. The increase of φ at a fixed Re raises the thermal conductivity coefficient and thus improves the convective heat transfer coefficient. Conversely, the elevation of nano-fluid's thermal conductivity lowers the Prandtl number and, since a constant Re leads to a constant velocity layer thickness, it adds to the thermal boundary layer thickness, thereby reducing the convective heat transfer coefficient. According to the results presented in Fig. 4, the impact of the rise of thermal conductivity coefficient overwhelms the influence of the intensification of thermal boundary layer thickness, and therefore the convective heat transfer coefficient goes up as more nanoadditives are added. With the rise of Re at a constant φ, the velocity boundary layer thickness and thus the thermal boundary layer thickness diminish, thereby boosting the convective heat transfer coefficient. The changes of average CPU temperature with φ in terms of Re have been shown in Fig. 5. It is revealed that the mean CPU temperature diminishes with the increase of Re and φ; which is a desired outcome. Figs. 6 and 7 respectively illustrate the influences of φ and Re on the temperature contours of nano-fluid and heatsink wall at the cross section situated in the middle of heatsink channel (z = 0.3 m), and Fig. 8 displays the effects of the same parameters on CPU temperature contour. According to these figures, the increase of φ is accompanied by the rise of nano-fluid temperature and the reduction of heatsink wall temperature. As φ goes up, the thermal conductivity coefficient of nano-fluid increases, thereby augmenting the amount of heat transferred to nano-fluid and thus raising the temperature of nano-fluid and reducing the temperature of heatsink wall. One of the reasons CPUs are damaged and their lifespan is cut short is the formation of hot spots in them. A cooling system for CPUs should be designed so as to prevent their temperature from rising above a certain limit. The influences of φ and Re on maximum CPU temperature have been demonstrated in Fig. 9. One can see that the rise of φ and Re results in the reduction of maximum CPU temperature; which is due to the increase of convective heat transfer coefficient. According to the results, at Re = 1500, as φ goes up from 0 to 1%, the maximum CPU temperature is reduced from 304.01 to 303.54 K. Also, at φ = 1%, the rise of Re from 500 to 1500 lowers the maximum CPU temperature from 308.15 to 303.54 K. So far, the findings show that the rise of φ and Re improves the thermal effectiveness of heatsink. A point that should not be overlooked is the effect of these parameters on pumping power; because as the pumping power increases, the cost of the system goes up; and this is not desirable. Therefore, the influences of φ and Re on nano-fluid pumping power should be examined. The relevant results (displayed in Fig. 10) indicate that, interestingly and desirously, the increase of φ leads to the reduction of pumping power. For example, at Re of 1500, the rise of φ from 0 to 1% lowers the nano-fluid pumping power by 10.31%. As φ rises, nano-fluid density and viscosity go up; but density increases at a greater pace and, consequently, nano-fluid velocity should be lowered in order to keep the Re constant. The reduction of nano-fluid velocity

4. Results and discussion In this section, the results of simulations performed on the flow of biological water-Ag nano-fluid in the proposed heatsink are evaluated. The considered ranges for Re and φ are 500–1500 and 0–1%, respectively. Fig. 3 illustrates the velocity vectors for Re = 1500 and φ = 1%. It is seen that the fluid enters the heatsink, then is divided into 4 helical microchannels. The fluid flowing in each quarter of the heatsink tracks the spiral path and then leaves the heatsink through the outlet. Fig. 4 displays the variations of convective heat transfer coefficient versus φ in terms of Re. It is observed that the increase of both parameters (i.e. φ and Re) leads to the rise of convective heat transfer coefficient. For example, at Re = 1500, the increase of φ from 0 to 1%

Fig. 2. Schematic sketch of the heatsink studied by Ramos-Alvarado et al. [39]. 4

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A. Shahsavar, et al.

Fig. 3. Velocity vectors (in m/s) for flow of nanofluid heatsink at φ = 1% and Re = 1500.

40000 Re=500

Re=750

Re=1000

Re=1500

h (W/m2K)

35000

30000

25000

20000

15000 0

0.2

0.4

0.6

0.8

1

(%) Fig. 4. Influences of Re and φ on the convective heat transfer coefficient.

312 Re=500

Re=750

Re=1000

Re=1500

TCPU,max (K)

310

308

306 Fig. 6. Temperature contours for nanofluid at different φ and Re.

304

lowers the volume flow rate and pressure drop of nano-fluid (according to Darcy’s equation [40]) and thus decreases the pumping power. Moreover, it is observed that the increase of Re at a constant φ augments the pumping power considerably. This is due to the boosting of nano-fluid velocity and thus the rise of the pressure loss and volume flow rate of nano-fluid. Other parameters of importance in the design of a heatsink include the thermal resistance of heatsink and the uniformity of temperature

302 0

0.2

0.4

0.6

0.8

1

(%) Fig. 5. Influences of Re and φ on the mean temperature of the CPU surface.

5

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A. Shahsavar, et al.

Fig. 8. Temperature contours for CPU surface temperature at different φ and Re.

Fig. 7. Temperature contours for body of heatsinks at different φ and Re.

distribution in the heatsink. A designer should be aware that the designed heatsink has a low thermal resistance and that the CPU temperature distribution is uniform as much as possible. The effects of φ and Re on these parameters have been presented in Fig. 11 and Fig. 12, respectively. According to these figures, the increase of Re desirably reduces the thermal resistance of heatsink and improves the consistency of temperature distribution. Conversely, the rise of Re always results in the reduction of thermal resistance and the elevation of parameter θ. For instance, at Re = 1500, as φ goes up from 0 to 1%, the R and θ parameters decrease by 6.06% and 2.81%. Also, at φ = 1%, the rise of Re from 500 to 1500 lowers the R and θ parameters by 60.56% and 38.55%. In order to decide about the best operating conditions of the examined heatsink from the perspective of the first-law of thermodynamics, its PEC parameter should be evaluated. The results of this investigation have been illustrated in Fig. 13. The most important findings extracted from this figure are as follows:

312

•

Re=750

Re=1000

Re=1500

TCPU,max (K)

310

308

306

304

302 0

• In all the explored cases, the PEC value is greater than unity; which •

Re=500

0.2

0.4

0.6

0.8

1

(%)

points to the fact that water-Ag nano-fluid always has a better hydrothermal performance than the pure water. The increase of φ boosts the PEC parameter. This confirms that it is more justified to use water-Ag nano-fluid at higher φ. The rise of φ from 0.1 to 1% at Re = 500 and Re = 1500 improves the PEC value by 1.2 and 6.61%, respectively. The variations of PEC with Re at a constant φ do not follow a regular trend. For example, at 0.5% concentration, the PEC value goes up with the increase of Re from 500 to 1000; but the further rise of Re leads to the decline of PEC. While at φ = 1%, the PEC value surges with the increase of Re from 500 to 1500 and drops as the Re goes up from 1500 to 2000. The highest PEC value in this research (2.04) is obtained at Re of 1500 and φ = 1%.

Fig. 9. Influences of Re and φ on the maximum temperature of the CPU surface.

The amount of irreversibility in a process is a measure of the performance of engineering devices. The irreversibility reduces the thermodynamic efficiency. An irreversibility analysis shows that the energy dissipation is greater in which parts of a physical model or system. Since irreversibility is a criterion for the destruction of the functionality of the devices, its determination is necessary to augment the efficiency of the devices. Fig. 14 displays the influences of φ and Re on the rate of heat transfer irreversibility. It is observed that the rate of heat transfer irreversibility diminishes with the rise of φ and Re. For example, at 6

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A. Shahsavar, et al.

3.2

2.2

Re=500

Re=750

Re=1000

Re=1500

Re=500

2.4 Pumping power (W)

Re=750

Re=1000

Re=1500

2.0 1.8 1.6

1.6

1.4 1.2

0.8

1.0 0.8 0.1

0.5

0

1

(%)

0

0.2

0.4

0.6

0.8

1

Fig. 13. Influences of Re and φ on the PEC.

(%) Fig. 10. Influences of Re and φ on the pumping power.

30000

0.00013 Re=500

Re=750

Re=1000

Re=1500

Re=500

Re=750

Re=1000

Re=1500

25000

(m2K/W)

(m2K/W)

0.00011

0.00009

20000

15000 0.00007

10000 0.00005

5000 0

0.00003 0

0.2

0.4

0.6

0.8

Fig. 11. Influences of Re and φ on the parameter R.

Re=500

Re=750

Re=1000

Re=1500

θ (m2K/W)

0.000035

0.00003

0.000025

0.00002

0.000015 0.4

0.6

0.8

1

nano-fluid temperature and thus the intensification of heat transfer irreversibility. On the other hand, with the fall of average nano-fluid temperature, thermal conductivity diminishes, thereby reducing the rate of heat transfer irreversibility. Moreover, the decline of thermal conductivity leads to the growth of temperature gradient and, hence, the escalation of heat transfer irreversibility. The results displayed in Fig. 14 indicate that the influence of thermal conductivity reduction dominates the influences of the reduction of mean nano-fluid temperature and rise of temperature gradient, and that the rate of heat transfer irreversibility declines with the increase of Re. As was previously stated, with the rise of φ at a fixed Re, the average velocity of nano-fluid goes up, thereby reducing the mean nano-fluid temperature and, thus, lowering the thermal conductivity and raising the temperature gradient. Conversely, the increase of φ directly results in the boosting of thermal conductivity. Fig. 14 reveals that the effects of decreasing parameters overcome those of increasing parameters, and that the rate of heat transfer irreversibility diminishes with the rise of φ at a fixed Re. The influences of φ on the rate of fluid friction irreversibility at various Re have been depicted in Fig. 15. According to this figure, the rate of fluid friction irreversibility diminishes with the escalation of φ and severely increases with the rise of Re. For example, at Re = 1500, the rate of fluid friction irreversibility declines by 10.4% as φ goes up from 0 to 1%. Also, at φ = 1%, the rate of fluid friction irreversibility augments by 1056.16% as Re rises from 500 to 1500. The elevation of φ

0.00004

0.2

0.4

Fig. 14. Influences of Re and φ on the heat transfer irreversibility.

(%)

0

0.2

φ (%)

1

0.6

0.8

1

φ (%) Fig. 12. Influences of Re and φ on the parameter θ.

φ = 1%, the increase of Re from 500 to 1500 results in 55.65% reduction in the rate of heat transfer irreversibility. Also, at Re = 1500, the heat transfer irreversibility falls by 12.53% as φ goes up from 0 to 1%. The increase of Re at a constant φ leads to the reduction of average 7

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and Re on the operating parameters of the considered heatsink were evaluated. The most important outcomes of the numerical work are as follows:

• The convection heat transfer coefficient is raised by boosting the φ and Re. • The boosting of φ and Re reduces the likelihood of hot spots formation in the examined heatsink. • Thermal resistance goes down with the intensification of φ and Re. • The rise of φ and Re improves the temperature uniformity of CPU surface. • Pumping power diminishes with the rise of φ and goes up significantly with the augmentation of Re. • PEC augments with intensification of φ. • The nano-fluid's highest PEC is 2.04 which occurs at Re = 1500 and φ = 1%. • The thermal, frictional and total irreversibilities go down with the rise of φ. • The fluid friction and total irreversibilities augments and the heat

Fig. 15. Impacts of Re and φ on the fluid friction irreversibility.

transfer irreversibility declines with the rise of Re.

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Fig. 16. Impacts of Re and φ on the total irreversibility.

leads to the upsurge of rate of fluid friction irreversibility (through the rise of nano-fluid viscosity and fall of average nano-fluid temperature) and decline of fluid friction irreversibility (through the reduction of velocity gradient). Fig. 15 shows that the velocity gradient has a greater influence, and that the rate of fluid friction irreversibility diminishes with the rise of φ. Furthermore, by raising the Re, nano-fluid temperature diminishes and velocity gradient goes up, thereby escalating the rate of fluid friction irreversibility. Fig. 16 demonstrates the impact of φ on total irreversibility in terms of Re. It is clear that the total irreversibility declines and augments by boosting the φ and Re, respectively. Consequently, it can be said that. The data presented in this section indicate that, form the first law point of view, the merit of using water-Ag nano-fluid in the studied heatsink is greater at higher φ and Re. On the other hand, from the second law point of view, the results reveal that the benefits of using such a biological nano-fluid is greater at higher φ and lower Re. Hence, the decision about the suitable Re is made by the designer on the basis of relative importance of the hydrothermal and irreversibility aspects. 5. Conclusion The two-phase mixture method was employed in the present research to evaluate the hydrothermal and irreversibility aspects of biological water-Ag nano-fluid flow in a novel heatsink. The impacts of φ 8

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