Analysis of entropy generation of ferrofluid flow in the microchannel with twisted porous ribs: The

Powder Technology 380 (2021) 349–357

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Analysis of entropy generation of ferrofluid flow in the microchannel with twisted porous ribs: The two-phase investigation with various porous layers Amirhosein Mosavi a,b, Shahab Naghdi Sedeh c, Davood Toghraie c, Aliakbar Karimipour d,⁎ a

Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam c Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran d Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam b

a r t i c l e

i n f o

Article history: Received 10 July 2020 Received in revised form 8 September 2020 Accepted 26 November 2020 Available online 3 December 2020 Keywords: Entropy generation Twisted porous rib Microchannel Nanofluid flow Two-phase flow

a b s t r a c t Heat sinks are always in the center of electronic cooling researchers' attention. Microchannels, due to their increased surface and better thermal performance than that of normal heat sinks were used in electronic cooling devices. In this numerical investigation, the first and second laws of the thermodynamic impact of twisted porous ribs on the microchannel were studied. The effects of the Reynolds number and volume fraction of nanoparticles were investigated. The range of Reynolds number was 250 to 1000. All types of the microchannel in this study consisted of a clear microchannel, a twisted porous ribbed microchannel with two and three layers of twisted porous ribs. The results show that by inserting porous ribs, the local cross-section decreases, and the local Reynolds number increases. Also, twisted porous ribs are the cause of nanofluid flow circulation and make the heat transfer coefficient greater. Increasing the porous layer from one layer to three layers has an increasing effect on the heat transfer coefficient, and the friction factor and increasing the φ is the reason for increasing the friction factor. Finally, the microchannel with triple layers of twisted porous ribs has better performance in total entropy generation, and by inserting twisted porous ribs, the entropy generation decreases. © 2020 Elsevier B.V. All rights reserved.

1. Introduction In almost all cooling electronic devices, the generated magnetic field due to electricity exists. Electronic cooling devices generate heat, and it is necessary to remove the heat from the devices. At first, the normal heat sink did this task, but in recent years, normal heat sinks have been replaced with microchannels owing to their far better thermal performance. Several approaches, such as the use of nanoparticles and porous medium, contribute to the better thermal performance of microchannels than that heat sinks.

Malvandi et al. [1] studied the impact of nanoparticle immigration on the vertical microchannel considering the thermophysical properties of nanofluid dependent on the temperature. They showed that their results of properties with temperature dependency were almost equal to those of properties with temperature independency. Khodabandeh and Abbassi [2] optimized the thermal and hydrodynamic performance of microchannel coolant contain nanofluid using the Eulerian-Lagrangian method. They indicated that the trapezoidal microchannel with the ⁎ Corresponding authors.

E-mail addresses: amirhosein.mosavi@tdtu.edu.vn (A. Mosavi), aliakbarkarimipour@duytan.edu.vn (A. Karimipour).

https://doi.org/10.1016/j.powtec.2020.11.078 0032-5910/© 2020 Elsevier B.V. All rights reserved.

side angle of 70 degrees had the maximum thermal conductivity.

Hosseini and Sheikholeslami [3] investigated the impact of the magnetic field on the nanofluid and entropy generation in the microchannel.

They demonstrated that by increasing the φ, the friction factor and entropy generation was increased. Hosseini et al. [4] numerically analyzed the magnetohydrodynamic and entropy generation effect on the microchannel contain a porous medium. They illustrated that the optimal value was equal to 6.5 following the Reynolds number and the constant Hartman number for total entropy generation. Yang et al. [5] numerically studied the entropy generation and heat transfer of the microchannel to control flow. Their results indicated that the microchannel with the v groove shape had the minimum entropy generation. Toghraie et al. [6] numerically investigated the performance of the microchannel with L-shaped porous ribs and nanofluid. They inserted porous ribs in the microchannel, which increased thermal performance from 25 to 42% at different Reynolds numbers. For more information about nanoparticles, nanosheets, nanocomposites and membrane, please see Refs. [7–17].

In this study, the thermal performance of twisted porous ribs compared to the clear microchannel was analyzed. The effects of porosity percentage, the φ, and dimensionless numbers, including Reynolds and Hartman numbers on nanofluid flow and entropy generation,

A. Mosavi, S.N. Sedeh, D. Toghraie et al.

Powder Technology 380 (2021) 349–357

The energy equation for fluid part [21,22]:

Nomenclature CM MSLPR MDLPR MTLPR DHTC S''' T S''' F Be h Re Dh k K CP f

n

!k

μf ∇ ∑ ρk cp,k ϕk εV T ¼ ∇:km ΔT þ þhsf asf T s −T f þ V 2f κ k¼1

Clear microchannel Microchannel with Single Layer Porous Rib Microchannel with Double Layers of Porous Rib Microchannel with Triple Layers of Porous Rib Dimensionless Heat Transfer Coefficient Entropy generation due to heat transfer [W. m−3. K−1] Entropy generation due to Friction [W. m−3. K−1] Bejan number Average heat transfer coefficient [W. m−2. K−1] Reynolds number The hydraulic diameter of the channel [m] Thermal conductivity [W. m−1. K−1] Permeability [m−1] Specific heat capacity [J. kg−1. K−1] Friction factor

The energy equation for solid part [21,22]:

ks ∇2 T ¼ hsf asf T s −T f

n

V dr,k ¼ V pf − ∑

k¼1

ϕ k ρk V f ,k ρm

ð6Þ

n

∑ ϕk μ k V k

V m ¼ k¼1

ð7Þ

ρm

n

ρm ¼ ∑ ϕk ρk

ð8Þ

k¼1 n

μ m ¼ ∑ ϕk μ k

ð9Þ

k¼1

The relative velocity [24] and Shiller-Neumann's drag coefficient [25] represent as follows:

Super- and sub-scripts p Particle P Porous medium m Mixture dr Drift bf Base fluid f Fluid in Inlet h Hydraulic

V pf ¼ V p −V f

V bf ¼

2 ρp dp ρp −ρm 18μ f f drag ρp (

f drag ¼

Re ¼ were investigated. The range of variables in this study was φ=0 to 2%, Re = 250 to 1000, and 0 to 80% for the porosity percentage. In this investigation, despite the clear microchannel, all other types of microchannel were abbreviated to clarify its situation. Microchannels with twisted porous ribs have various layers from one layer to three layers. The foundation of this study is based on the constant volume of the porous medium and the microchannel.

ð10Þ

½g−ðV m :∇ÞV m

1 þ 0:15 Re p0:687 Re p ≤1000

Re p >1000 0:0183 Re p

ð11Þ

ð12Þ

ρf V p −V f dp μf

ð13Þ

q00 ðxÞ ðT w ðxÞ−T b Þ

ð14Þ

hðxÞ ¼

T w ðxÞ ¼

1 A

Z TdA

!

Tρ VdA T b ðxÞ ¼ R !

ρ VdA

ð15Þ

R

2. Mathematical formulation Continuity equation [18]: ð1Þ

h¼

Momentum equation [19]:

1 L

Z

L 0

hðxÞdx

ð16Þ

ð17Þ

The friction factor [26]:

n

! ! ! !T ! ! ∇: ρm V m V m ¼ −∇P þ ∇: μ m ∇V m þ ∇V m þ ∇: ∑ ϕk ρk V dr,k V dr,k k¼1 ! εμ f ρf ε2 C F ! ! þ pffiffiffiffiffi V V − ks kp ð2Þ

f ¼

ΔpDh 2LρV 2in

Nu ¼

f ¼

ð3Þ 350

ð18Þ

The local and average Nusselt numbers [27]: NuðxÞ ¼

In Eq. (4), CF is the quadratic drag coefficient. This coefficient defined as follows [20]:

d C F ¼ 0:55 1−5:5 Dh

ð5Þ

where [23]:

Greek letters ρ Density [kg/m3] μ Viscosity [kg/m. s] φ The volume fraction of nanoparticles ε Porosity θ Dimensionless temperature

∇:ðρm V m Þ ¼ 0

ð4Þ

hðxÞDh knf

hDh knf

ΔpDh 2LρV 2in

ð19Þ

ð20Þ

ð21Þ

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Powder Technology 380 (2021) 349–357

Fig. 1. Schematic of the investigation.

Table 1 Properties of nanoparticles and base fluid [32].

Water Fe3O4

Table 2 Grid study for Nu.

Density

kg:m−3

Heat capacity h i −1 J:kg :K−1

Thermal conductivity h i W:m−1 :K−1

Viscosity

kg:m−1 :s−1

997.1 5200

4179 670

0.613 6

0.001003 –

No. of cells [CM] No. of cells [MSLPR] No. of cells [MDLPR] No. of cells [MTLPR] Error (%) [CM] Error (%) [MSLPR] Error (%) [MDLPR] Error (%) [MTLPR]

4,00,000 5,35,736 5,60,000 7,52,000 – – – –

6,25,000 6,96,800 8,06,400 9,02,500 6.018 7.235 6.184 5.216

9,37,500 10,35,000 12,06,000 13,42,000 3.321 4.224 4.484 3.463

11,70,000 13,80,300 14,47,200 15,32,400 0.2045 0.5613 1.0021 1.2105

The entropy generation caused by heat transfer and friction [28]: S000 gen,T ¼ S000 gen,F ¼

knf T2

ð∇T Þ2

ð22Þ

μ nf ϕ T

ð23Þ

By integrating from Eqs. (22), (23) [29]: Z Sgen,T ¼ S000 gen,T dV Z

S000 gen,F dV

Sgen,F ¼ Z Sgen,Tot ¼

S000 gen,T dV þ

ð24Þ ð25Þ

Z

S000 gen,F dV

ð26Þ

Bejan number [30].

Be ¼

Fig. 2. Validation with experimental data [31].

351

Sgen,T Sgen,T þ Sgen,F

ð27Þ

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Powder Technology 380 (2021) 349–357

Fig. 3. Average pressure drop in various Reynolds number for clear microchannel and twisted porous ribbed microchannels for different φ at porosity percentage of 40%.

Boundary conditions 8 > < V r ðz, r Þ ¼ 0 No‐slip on the wall Vz ðz, r Þ ¼ 0 > : Vθ ðz, r Þ ¼ 0 8 > < V r ð0, r Þ ¼ 0 Vz ð0, r Þ ¼ Vin > : Vθ ðz, r Þ ¼ 0 8 > < T ð0, r Þ ¼ T in T ðz, r Þ ¼ T w > : 00 q ðz, r Þ ¼ q00 ðxÞ 8 > < Tjw ¼ Tjf

∂T ∂T > k ¼ k m : m ∂r w ∂r f

Inlet velocity

Inlet temperature

3. Numerical simulation In this numerical analysis, the hydrodynamic, first and second laws of thermodynamics were investigated. The microchannel in this study contained one to three different layers of porous twisted ribs (Fig. 1), Fe3O4 nanoparticles, and water as base-fluid. To a couple of pressure and velocity, the finite volume method and the SIMPLE scheme were applied. For the accuracy of solving mass, momentum, and energy and equations, the double-precision and the second-order upwind on conservation equations variables were used. Local thermal nonequilibrium (LTNE) and Brinkman model approaches were applied to porous ribs. A comparison was performed for the constant volume of the microchannels and porous ribs of all study cases.

ð28Þ

ð29Þ

ð30Þ

4. Grid independency and validation Table 1 shows the grid independency of seven different shapes of the cases. As the table indicates, by increasing the number of cells, the difference error between the numbers of cells decreases. In this numerical

ð31Þ

352

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Fig. 4. Average friction factor versus Reynolds number for clear and twisted porous ribbed microchannels in various φ at porosity percentage of 10%.

two parameters and owing to the direct relationship between the Reynolds number and the average pressure drop, the average pressure drop increases.

Fig. 4 shows the average friction factor for various Reynolds numbers in clear and three types of the twisted porous ribbed microchannel.

In this figure, by increasing the Reynolds number in all parts, the average friction factor increases. As Fig. 4 shows, by increasing the layers of twisted porous ribs from one (A. 1) to three (A. 3), the difference amount of the fraction factor between clear and twisted porous ribbed microchannels increases. It is due to the instant decrease of local cross-section and an increase in the velocity gradient near the microchannel wall. Another reason for increasing velocity gradient in this figure is the increasing density of nanofluid flow by adding certain amounts of the nanoparticle to the base fluid. Overall, the microchannel with three layers of twisted porous ribs has the highest amount of the average fraction factor in all Reynolds numbers.

Fig. 5 shows the local dimensionless heat transfer coefficient, along with the length of the microchannel for clear and different types of twisted porous ribbed microchannels in all ranges of the Reynolds number. As this figure shows, by inserting porous ribs from one layer to three layers, the trend of the local dimensionless heat transfer coefficient goes up and down. This behavior can be explained in two parts. In part one (when the line goes up), the parameter value increases due to velocity increase, along with instant

investigation, the adequate number of cells was considered when the percentage of error became less than 2%, and normalized residual became less than 10−7 for every reported parameter in the results part.

To save time and incur a lower cost of calculation, the structured 3D grids for every seven shapes of microchannel were generated. As Fig. 2 shows, this figure represents an excellent overlapping between the experimental study by Wen and Ding [31] and this experimental study. To validate the present investigation results, the local heat transfer coefficient at Reynolds number equal to 1000, φ = 0%, and clear microchannel (CM) are considered. The convergence criterion 10−8 is considered (Table 2).

5. Results and discussion Fig. 3 presents the average pressure drop in different Reynolds numbers and φ in the clear microchannel as well as different types of the twisted porous ribbed microchannel. As the figure shows, the average pressure drop increases by increasing the Reynolds number and φ.

The reasons for this behavior are increasing velocity and density of the nanofluid flow. The density of the nanofluid flow increases by adding nanoparticle to the base fluid, and the inlet velocity increases due to the Reynolds number. Reynolds number is a function of density and velocity in this numerical investigation. Both velocity and density are directly related to the Reynolds number. Therefore, by increasing these 353

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Powder Technology 380 (2021) 349–357

Fig. 5. Local dimensionless heat transfer coefficient along the microchannel for different Reynolds number and all types of microchannels at the porosity percentage of 40%.

cross-section decrease. In part two (when the line goes down), the parameter value decreases due to the velocity increase, along with instant cross-section increase. These ups and downs expand the lower thermal boundary layer in the nanofluid flow and are the cause of increasing the dimensionless local thermal boundary layer. Also, the figure presents a comparison between the impacts of several twisted porous layers on microchannels. As indicated, by increasing the number of twisted porous layers from one layer to three layers, the change in the cross-section and local dimensionless heat transfer coefficient increases. It should be noted that by increasing the inlet Reynolds number, the local hea t transfer increases.

Fig. 6 illustrates the local dimensionless temperature along the microchannel for clear and twisted porous ribbed microchannels. This figure is a comparison between all types of microchannels in the present numerical investigation. As demonstrated by increasing the number of twisted porous layers, the local dimensionless temperature increases.

In the line trend of microchannels with twisted porous rib compared to clear microchannels, there are ups and downs. This change in the line trend is because of the instant change in the cross-section on the microchannel due to porous ribs. By increasing the number of twisted porous rib layers, the local dimensionless heat transfer coefficient increases. Nanofluid flow circulation and local increase in the velocity are the reason of this behavior. As the lines in Fig. 6 shows, the

Fig. 6. comparison of local dimensionless temperature in the length of microchannel for all types of microchannels at porosity percentage of 80%.

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gradient near the microchannel wall goes up. When this reason disappears, the line significantly goes down. Furthermore, by increasing the density of nanofluid by adding nanoparticle, the inlet Reynolds number and the velocity gradient near the microchannel wall increase, and the entropy generation increases due to the friction factor. Eventually, in the comparison between different types of the microchannel, the microchannel with triple layers of twisted porous ribs has the highest entropy generation due to the friction factor.

Fig. 9 depicts the average Bejan number in φ = 0.5% in all types of the microchannel. The Bejan number is a fraction of entropy generation due to heat transfer over total entropy generation and expresses thermodynamic irreversibility. In this figure, by increasing the Reynolds number, the Bejan number decreases. The cause of this behavior is the velocity increase and lower expansion of the thermal boundary layer.

Owing to the dominancy of entropy generation due to heat transfer and negligibility of frictional entropy generation, the line trend of the Bejan number is like generated entropy by heat transfer. By increasing the velocity due to the instant decrease of local cross-section, nanofluid flow circulation, and insertion of more twisted porous ribs, the Bejan decreases. As Fig. 9 shows, the microchannel with triple layers twisted porous ribs shows the least amount of the Bejan number.

microchannel with three layers of twisted porous ribs has the highest local dimensionless temperature.

Fig. 7 indicates the average entropy generation due to heat transfer in all ranges of the Reynolds number for various φ. By increasing the Reynolds number at the inlet, the entropy generation due to heat transfer decreases. The reason for this behavior is that velocity is reversely related to expanding and thermodynamic irreversibility; therefore, the entropy generation due to heat transfer decreases. Furthermore, the Reynolds number directly increases by increasing velocity and density, and density increases by adding nanoparticle. In the comparison between each part of this figure, due to the increasing number of twisted porous rib layers, the microchannel with triple layers, porous rib has the lowest entropy generation due to heat transfer.

Fig. 8 shows the local entropy generation due to friction factor along the microchannel length for clear and twisted porous ribbed microchannels in different φ. As the figure illustrates, the line trend of local entropy generation due to the friction factor decreases by moving forward alongside the clear microchannel. Still, in the twisted ribbed microchannel, the line trend goes up and down. Owing to the increase in the local Reynolds number due to local velocity, nanofluid flow circulation, and an instant decrease in local cross-section, the velocity

Fig. 7. Average entropy generation due to heat transfer versus Reynolds number in various microchannels at porosity percentage of 20%.

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Fig. 8. Entropy generation due to fraction factor alongside of microchannel length for different φ and all types of microchannel at porosity percentage of 10%.

6. Conclusion This numerical analysis investigated the impact of twisted porous ribs with different porous layers from one layer to three layers. Various ranges of the Reynolds number, porosity percentage, and φ were also studied. Local thermal non-equilibrium and the Brinkman model were the approaches to study the porous medium. The main conclusions drawn from the results are expressed as follows: • By inserting porous ribs, the local cross-section decreases, and the local Reynolds number increases.

• Twisted porous ribs are the cause of nanofluid flow circulation and make the heat transfer coefficient greater.

• Increasing the porous layer from one layer to three layers has an increasing effect on the heat transfer coefficient and the friction factor.

• Increasing the φ is the reason for increasing the friction factor.

• The microchannel with triple layers of twisted porous ribs has better performance in total entropy generation.

• By inserting twisted porous ribs, the entropy generation decreases.

Credit authorship contribution statement Amirhosein Mosavi: Methodology, Software, Validation, Writing review & editing, Writing - original draft. Shahab Naghdi Sedeh: Methodology, Software, Validation, Writing - original draft, Investigation.

Fig. 9. Average Bejan number in various Reynolds number in all types of microchannels at porosity percentage of to 40%.

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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