Heat transfer of ethylene glycol-Fe3O4 nanofluid enclosed by curved porous cavity including electric field

Journal Pre-proof Heat transfer of ethylene glycol-Fe3 O4 nanofluid enclosed by curved porous cavity including electric field Truong Khang Nguyen, Feroz Ahmed Soomro, Jagar A. Ali, Rizwan Ul Haq, M. Sheikholeslami, Ahmad Shafee

PII: DOI: Reference:

S0378-4371(19)32188-0 https://doi.org/10.1016/j.physa.2019.123945 PHYSA 123945

To appear in:

Physica A

Received date : 26 March 2019 Revised date : 25 June 2019 Please cite this article as: T.K. Nguyen, F.A. Soomro, J.A. Ali et al., Heat transfer of ethylene glycol-Fe3 O4 nanofluid enclosed by curved porous cavity including electric field, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123945. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Published by Elsevier B.V.

*Highlights (for review)

Journal Pre-proof Highlights  To gain the best performance of system with nanofluid within a porous space, CVFEM was applied.  Electric field can enhance the convective flow.  Convective mode enhances as consequence of shape factor.

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 Rd has direct relation with Nuave.

*Manuscript Click here to view linked References

Journal Pre-proof Heat transfer of ethylene glycol-Fe3O4 nanofluid enclosed by curved porous cavity including electric field Truong Khang Nguyen a,b, Feroz Ahmed Soomro c, Jagar A. Ali d,e, Rizwan Ul Haq , f, M. Sheikholeslami g,h, Ahmad Shafee i a

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Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam b Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam c Department of Basic Sciences and Related Studies, Quaid-e-Awam University of Engineering, Science and Technology, Larkana Campus 77150, Pakistan d Department of Petroleum Engineering, Faculty of Engineering, Soran University, Soran, Kurdistan Region, Iraq e Department of Petroleum Engineering, College of Engineering, Knowledge University, Erbil, Kurdistan Region, Iraq f Department of Electrical Engineering, Bahria University Islamabad Campus, Islamabad, Pakistan g Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran h Renewable energy systems and nanofluid applications in heat transfer Laboratory, Babol Noshirvani University of Technology, Babol, Iran i Public Authority of Applied Education & Training, College of Technological Studies, Applied Science Department, Shuwaikh, Kuwait

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Abstract

In current model, a complete structured of thermal behavior within a permeable curved domain is discussed in the appearance of Ethylene glycol based Fe3O4 nanofluid. Electrohydrodynamic (EHD), that is an electric force inside a porous space is also simulated. Radiative source term has been introduced and Fe3O4 nanoparticles with different shapes namely: Platelet, bricks, cylinder and spherical are dispersed within the base fluid. The systems of Partial differential equations (PDEs) are solved through CVFEM. It is further described that bottom electrode is movable. Electric field and

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nanoparticles' shape are two factors for changing properties of nanofluid. Impacts of permeability, voltage, radiation parameters and nanoparticles' shape on stream lines, isotherms, Nusselt number

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have been demonstrated. Ranges of defined parameters are retained which are: voltages Darcy number

nanoparticles' shape

and radiative factor

. Outcomes displayed that convection augments with rise of Da. Convective flow becomes stronger as a consequence of adding greater voltage. Keywords: EHD; Radiation; Nanofluid; CVFEM; Porous space; Nanoparticles.

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1. Introduction

It has been proved that the thermal features of working fluid may be improved by dispersing Nano powders (1-100 nm) [1]. Such fluids are generally known as nanofluids and play vital role in present era various applications. Such applications are, drug delivery, electronics, geothermal 

Corresponding author: [email protected] (Rizwan Ul Haq), [email protected] (Truong Khang

Nguyen)

1

Journal Pre-proof science, aerodynamics, and so on [2]. As a specific example, for removing heat from a body the working fluid with enhanced thermal conductivity works better. In this light, many researchers are in quest to develop various working nanofluids to meet the challenges we are facing now a days [3-8]. Convection heat transfer inside enclosures have many practical applications, including, in solar panel, heating/cooling of houses and factories, electronic industry, and so on. Enclosure may be of different geometries, like, triangular, rectangular, trapezoidal and other shaped cavities [9-12]. Due

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to such importance, this research area has remained under the focus of researchers who carried out various studies both mathematically and experimentally. According to scope of current article, we

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shall refrain from focusing on experimental work and only stick to mathematical study of various nanomaterials. For instance, Rizwan et al. [13] scrutinized convection within a rhombus cavity partially heated at the bottom and a differentially heated square obstacle placed in the center. Cavity was considered to be filled with water-based Copper-Oxide nanofluid. Heat transfer study on the cavity was reported by Marina et al. [14] considering lid wall. Enclosure was considered filled with

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alumina. Moreover, two permeable layers of various thermal conditions are places at the bottom of cavity.

Thermal improvement within a heated square cavity incorporating heater of varying size and position was carried out by Mahalakshmi et al. [15] and silver powder was utilized. In another study [16], annulus was taken under consideration to encounter the thermal management utilizing the water-based hybrid fluid combing two types of nanoparticles ( MWCNT and Fe3O 4 ). In recent years,

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scientists present various techniques for improving the performance [17-23]. Besides the fact that the thermal features of working fluid may be improved by dispersing nanoparticles in it, another factor which affects its thermophysical properties is the shape of nanoparticles. Various shaped

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nanoparticles were applied to scrutinize its effect on thermal efficiency. For example, Sheikholeslami and Shehzad [24] performed the laminar flow of nanofluid ( Fe3O4 -H 2O ) through irregular shaped cavity using four shaped nanoparticles (sphere, platelet, cylinder, and brick). Close investigation revealed that the heat transfer using platelet shaped nanoparticles were greater than those of other

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shapes. The lowest conductivity among the considered nanoparticles is due to spherical nanoparticles. In another study, Sheihkholeslami and Rokni [25] used Ethylene glycol based nanofluid combing with Fe3O 4 nanoparticles to report the characteristics of nanomaterial within the angular cavity. It was revealed that a platelet nanoparticle is a good choice for maximum heat transfer rate. Study of the CuO nanoparticles shape effects on the heat transfer inside irregular shaped cavity suggests augment in shape factor augment convective rate [26]. To address the difficulty of open cavities various mathematical methods have been proposed to seek the 2

Journal Pre-proof approximate numerical solutions. For example, FDM was employed by Alsabery et al. [27] to investigate free convection within an inclined enclosure filled with various kinds of nanofluids. Heat transfer augmentation has been reported by Khan et al. [28] as a consequence of dispersing copper nanomaterial. Lattice Boltzmann Method was proposed by Sheikholeslami et al. [28] to scrutinize 3D nanomaterial flow within a cavity. Different ways exist for simulation of problems to reach the best efficiency [29-35]. Porous media simulation with implementation of new method was

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scrutinized by Sheikholeslami [36] and he indicated that using alumina powders can help the performance. To find the optimal input to gain best performance, Mohyud-Din et al. [37] scrutinized

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nanomaterial flow within a porous duct and they involved the impact of thermal radiation. Minimization of irreversibility was performed by Sheikholeslami [38] and simulations were done via CVFEM inside a permeable cavity. Finite Volume Method was developed by Liao [39] to study the hybrid nanofluid thermal features. Finite element analysis of fluid behavior within a permeable rectangular cavity was done by Haq et al. [40]. The upper and lower wall was considered as

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corrugated.

Keeping the above reported literature, the present article deals with the Ethylene glycol based nanomaterial flow involving electric force. Radiation and various shape factors have also been incorporated in the model. Present study is new and has not been reported before. The solution of governing partially differential equations is sought by the help of CVFEM. Moreover, FORTRAN is used for simulations purpose. The rest of article is divided as follows: physical problem and

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numerical approach; mathematical formulation and numerical procedure of the considered physical problem is done in section 2; validation of code used for present simulation; detailed discussion over the obtained results is pondered in section 3; the precise conclusion of present study is presented in

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section 4. The last section of references enlists all the cited reference.

2. Problem Statement and CVFEM modeling Consider the porous cavity filled with Ethylene glycol based ferrofluid (Fe3O4 – C2H6O2).

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Moreover, the cavity is under the impact of electric field. See Fig. 1 for geometrical representation and imposed boundary conditions. Uniform triangular elements are used to discretize the space domain. Contour plots of electric density are demonstrated in the Fig. 2. It is revealed that contour behavior becomes more complex due to higher Darcy number. To improve the performance of ethylene glycol, iron oxide nanoparticle was dispersed in it and properties were mentioned in Ref. [41]. Furthermore, the coefficients for viscosity and shape factor values are as same as [41]. The following equations [25] are utilized to incorporate Coulomb force:

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Journal Pre-proof J  D q   E  qV ,

(1)

q  . E ,

(2)



   E ,

(3)

q  .J , t

(4)

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  .V  0,       p  nf  2 V   V  q E  1   V V V .   ,   nf nf    t  nf K    nf      1 q  k nf J .E T    r   2T    V . T   C p nf y  C p   C p nf    t  nf     q  . E  0, . J   q ,   E ,  t

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Then the full forms of governing equations for current problem are [42]:

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T 4  1   4 3 4 , T  4 T T  3 T , q   3  4    c c r R e ,   y   

(5)

To improve the performance of ethylene glycol, iron oxide nanoparticle was dispersed in it and properties were mentioned in Ref. [41]. Furthermore, the coefficients for viscosity and shape factor values are as same as [41].

  A1  A 2     A3     A 4    , 2

3

(7)

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m  k f  k p     k p  k f    mk f  k p  k f k nf  kf mk f   k f  k p    k f  k p

(6)

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After incorporating equations (6) and (7), the last forms are:

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  .V  0,  1     S E q E  1  /  1  2 V  p  1 nf   nf  V   V  V . V   nf f       /   t  Re Re Da f  f   f  nf   1   2 (8)   C  V .         Pr Re 1  2  Ec  E . J  S  p f  4  k nf  Rd         E   2   t  3 kf  Y     C p  nf   q   k nf / k f  0, q  . E ,   E    0, . J  t  C p nf /  C p f 

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u ,v   U

u ,v 

  0 T T 0 ,  ,  T Lid tU q E   1  0 , t  Lid , q  , E  , L q0 E0 , 

 T  T 1 T 0 , p 

(9)

y ,x  P , y ,x  , 2 L U Lid





LU Lid   ,v  

v u  , U Lid L1   x y

(10)

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

  , u, x y

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The P can be omitted by utilizing the bellow equations:

To better description of convective mode the following functions were defined: 1  k  4  k    Nu loc   nf  1  Rd  nf    k f   3  k f   X

1 Nu loc dY L 0

(12)

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L

Nu ave 

(11)

The technique, which gathered the profits of Finite Element Method (FEM) and Finite Volume Method, called Control Volume Finite Element Method (CVFEM) [43] is applied for modeling. The method has been tested by solving heat transfer problems. Uniform triangular elements mesh is used to discretize the space domain. Validation of the code is an important aspect of the applicability of

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obtained results. For such reason, the outputs obtained by present FORTRAN code are compared with already published outcomes [44]. Fig. 2 depicts the applicability of the present solutions.

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Moreover, the results are considered reliable if they do not depend upon the mesh size. Table 1 illustrated of certain case corresponding to various mesh sizes.

3. Results and discussion

Outputs of hydrothermal behavior of ferrofluid (Fe3O4 – C2H6O2 nanofluid) were classified in

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current section. Effects of shape factor ( m  3 to 5.7 ), supplied voltage (   0 to 10 kV ), Radiation ( Rd  0 to 0.8 ), permeability ( Da  10 2 to 10 5 ) were illustrated. Fig. 2 presents the comparison of

current solutions with the ones already presented in the literature. Strong agreement between the profiles shows the validity of the present numerical solution. Fig.

3

shows

the

impact

of

porosity

on

the

electric

density

function

at

  10kV ,   0.05, Rd  0.8, Re  3000 . The trend of Fig. 3 shows that the electric density distribution is enhanced due to augment in the Darcy parameter. Figs. 4 and 5 illustrate the impact of 5

Journal Pre-proof Porosity parameter on the flow and temperature fields under zero supplied voltage when

  0.05, Rd  0.8, Re  3000 . It can be seen from streamlines trend that the cavity produces the two bullous near to the heated lengths of cavity. The flow distribution gets stronger by increasing the porosity parameter, which can be seen from the increased size of both bullous. Moreover, temperature distribution is also greatly influenced by the augment of Darcy number. The Fig. 4 shows that the heat is distributed along the hot portions of the cavity, which tends to increase, and

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more heat is distributed within the cavity. This is contribute to the fact that augment in porosity augments the effect of convection heat transfer, which results in more heat is distributed inside

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cavity. Now, in comparison to the zero-supplied voltage, the temperature and velocity fields were further enhanced due to the impact of supplied voltage. Figs. 6 and 7 shows the effects of porosity parameter under the effect of supplied voltage   10kV when   0.05, Rd  0.8, Re  3000 . It is very clear from the profile trends that velocity and temperature were enhanced due to augment in porosity parameter and supplied voltage. Moreover, due to increase in supplied voltage the size of

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bullous formed inside the cavity is increased.

The effect of emerging physical factors on Nuave is demonstrated in Fig. 8 and below correlation:

Nuave  2.15  0.055m  0.28  0.44log Da  0.73Rd 0.17  log Da   0.18  log Da  Rd  0.001m2

(13)

It can be observed that augmentation in Rd decreases Nuave . There is insignificant effect of

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increase in m on Nuave . Increase in  and log( Da) augments Nuave which is due to greater

4. Conclusion

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convective mode.

In the present study, transportation of iron oxide nanoparticles was presented. The physical model was modeled in the form of PDEs which numerical solution was obtained using CVFEM. The effects of several parameters, including voltage, radiation parameter, nanoparticles shape factor, and

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permeability, on the nanofluid behavior were investigated. The study revealed that Darcy number and supplied voltage augment the convection. Thermal performance improves as consequence of employing electric field and involving radiation.

Acknowledgment: Authors would like to thank the National Elites Foundation of Iran and Babol Noshirvani University of Technology (Grant program No. BNUT/390051/98) for their moral and financial support throughout this project 6

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Journal Pre-proof [40] R.U. Haq, F.A. Soomro, T. Mekkaoui, Q.M. Al-Mdallal, MHD natural convection flow enclosure in a corrugated cavity filled with a porous medium, International Journal of Heat and Mass Transfer, 121 (2018) 1168-1178 [41] Mohsen Sheikholeslami, Ali J. Chamkha, Flow and convective heat transfer of a ferro-nanofluid in a double-sided lid-driven cavity with a wavy wall in the presence of a variable magnetic field,

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Numerical Heat Transfer, Part A, 2016, VOL. 69, NO. 10, 1186–1200, https://doi.org/10.1080/10407782.2015.1125709

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[42] M. Sheikholeslami, Mikhail A. Sheremet, Ahmad Shafee, Zhixiong Li, CVFEM approach for EHD flow of nanofluid through porous medium within a wavy chamber under the impacts of radiation

and

moving

walls,

Journal

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Thermal

https://doi.org/10.1007/s10973-019-08235-3

Analysis

and

Calorimetry,

2019,

[43] Mohsen Sheikholeslami, Application of Control Volume based Finite Element Method

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(CVFEM) for Nanofluid Flow and Heat Transfer, (2019), ISBN: 9780128141526 [44] Khanafer K, Vafai K, Lightstone M. Buoyancy-driven heat transfer enhancement in a two-

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dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transf. 2003; 446: 3639–3653

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Fig. 1. Enclosure under the electric field with two lid walls

Gr  10 4 ,   0.1

Fig. 2. Comparing temperature distribution with previous work [44]

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Da  105

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Da  102

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05

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0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

-1.8E-05 -5E-05 -0.0001 -0.00015 -0.0002 -0.00025 -0.0003 -0.00035 -0.0004

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Fig. 3. Distribution of electric density at   0.05,   10kV , Re  3000, Rd  0.8 .

Streamline isotherm 2 Fig. 4. Ferrofluid behavior when   0kV , Da  10 , Rd  0.8, Re  3000,   0.05 .

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0.98 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

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-3E-05 -8E-05 -0.0005 -0.001 -0.0015 -0.002 -0.0025 -0.003

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

-5E-05 -0.0001 -0.00015 -0.0002 -0.00025 -0.0003 -0.00035 -0.0004 -0.00045 -0.0005

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Streamline isotherm 5 Fig. 5. Ferrofluid behavior when   0kV , Da  10 , Rd  0.8, Re  3000,   0.05

Streamline isotherm 2 Fig. 6. Ferrofluid behavior when   10kV , Da  10 , Rd  0.8, Re  3000,   0.05

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-0.0008 -0.0012 -0.002 -0.004 -0.006 -0.008 -0.01 -0.012

Streamline

isotherm

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Fig. 7. Ferrofluid behavior when   10kV , Da  105 , Rd  0.8, Re  3000,   0.05

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0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

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log  Da   3.5 ,Rd  0.4 ,  0.05

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Rd  0.4 ,m  4.35 ,  0.05

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log  Da   3.5 ,   5 ,  0.05

Rd  0.4 ,   5 ,  0.05

log  Da   3.5 ,m  4.35 ,  0.05

m  4.35 ,   5 ,  0.05

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log  Da   3.5 ,Rd  0.4 ,  0.05

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Rd  0.4 ,m  4.35 ,  0.05

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log  Da   3.5 ,   5 ,  0.05

Rd  0.4 ,   5 ,  0.05

log  Da   3.5 ,m  4.35 ,  0.05

m  4.35 ,   5 ,  0.05

Fig. 8. Roles of Rd ,m ,Da,  on Nu ave

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different grids at Re  3000 ,Rd  0.8 ,  10 ,  0.05 ,Da 10 5 51  151

4.0369

71  211

4.0403

61 181

4.0417

4.0422 101  301

4.0472

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4.0377

81  241

91  271

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Table1. Changing of

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