Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H2O nanofluid on a flat surface in a porous medium: A stability analysis

doi:10.1088/1674-1056/ac229b

中国物理B ›› 2022, Vol. 31 ›› Issue (4): 44701-044701.doi: 10.1088/1674-1056/ac229b

Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium: A stability analysis

Astick Banerjee¹, Krishnendu Bhattacharyya^2,†, Sanat Kumar Mahato¹, and Ali J. Chamkha³

1 Department of Mathematics, Sidho-Kanho-Birsha University, Purulia 723104, India;
2 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India;
3 Faculty of Engineering, Kuwait College of Science and Technology, Doha District, Kuwait

收稿日期:2021-05-13 修回日期:2021-07-15 接受日期:2021-09-01 出版日期:2022-03-16 发布日期:2022-03-25
通讯作者: Krishnendu Bhattacharyya E-mail:krish.math@yahoo.com,krishmath@bhu.ac.in

Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium: A stability analysis

Astick Banerjee¹, Krishnendu Bhattacharyya^2,†, Sanat Kumar Mahato¹, and Ali J. Chamkha³

1 Department of Mathematics, Sidho-Kanho-Birsha University, Purulia 723104, India;
2 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India;
3 Faculty of Engineering, Kuwait College of Science and Technology, Doha District, Kuwait

Received:2021-05-13 Revised:2021-07-15 Accepted:2021-09-01 Online:2022-03-16 Published:2022-03-25
Contact: Krishnendu Bhattacharyya E-mail:krish.math@yahoo.com,krishmath@bhu.ac.in

摘要/Abstract

摘要： The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems. So, here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium is examined. Moreover, the thermal radiation and viscous dissipation effects are considered. The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method. The computed results can reveal many vital findings of practical importance. Firstly, dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows, the solution is unique. The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium. But different shapes of nanoparticles are not disturbing the dual solution existence range, though it has a considerable impact on thermal conductivity of the mixture. Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid, i.e., the water here. On the other hand, the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium. Regarding the cooling rate of the heated surface, it rises with the permeability parameter, shape factor (related to various shapes of Cu-nanoparticles), and radiation parameter. The surface drag force becomes stronger with the permeability parameter. Also, with growing values of nanoparticle volume fraction, the boundary layer thickness (BLT) increases and the thermal BLT becomes thicker with larger values of shape factor. For decelerating unsteady flow, the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed. The thermal BLT is thicker with radiation parameter. Due to the existence of dual solutions, a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.

关键词: Cu-H₂O nanofluid, various shapes of nanoparticles, unsteady stagnation-point flow, dual solutions, stability analysis

Abstract: The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems. So, here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium is examined. Moreover, the thermal radiation and viscous dissipation effects are considered. The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method. The computed results can reveal many vital findings of practical importance. Firstly, dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows, the solution is unique. The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium. But different shapes of nanoparticles are not disturbing the dual solution existence range, though it has a considerable impact on thermal conductivity of the mixture. Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid, i.e., the water here. On the other hand, the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium. Regarding the cooling rate of the heated surface, it rises with the permeability parameter, shape factor (related to various shapes of Cu-nanoparticles), and radiation parameter. The surface drag force becomes stronger with the permeability parameter. Also, with growing values of nanoparticle volume fraction, the boundary layer thickness (BLT) increases and the thermal BLT becomes thicker with larger values of shape factor. For decelerating unsteady flow, the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed. The thermal BLT is thicker with radiation parameter. Due to the existence of dual solutions, a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.

Key words: Cu-H₂O nanofluid, various shapes of nanoparticles, unsteady stagnation-point flow, dual solutions, stability analysis

中图分类号: (Laminar boundary layers)

47.15.Cb

47.15.Fe (Stability of laminar flows) 44.30.+v (Heat flow in porous media)

Astick Banerjee, Krishnendu Bhattacharyya, Sanat Kumar Mahato, and Ali J. Chamkha. Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium: A stability analysis[J]. 中国物理B, 2022, 31(4): 44701-044701.

参考文献

[1] Choi S U S 1995 In:D.A. Siginer and H.P. Wang, Eds., Developments and Applications of Non-Newtonian Flows, ASME, New York 66 99
[2] Buongiorno J 2006 ASME J. Heat Transf. 128 240
[3] Tiwari R K and Das M K 2007 Int. J. Heat Mass Transf. 50 2002
[4] Maxwell J C 1881 A Treatise on Electricity and Magnetism (2nd edn.) (Oxford:Clarendon Press)
[5] Hamilton R L and Crosser O K 1962 Ind. Eng. Chem. Fundam. 1 187
[6] Yu W and Choi S U S 2003 J. Nanoparticle Res. 5 167
[7] Jang S P and Choi S U S 2004 Appl. Phys. Lett. 84 4316
[8] Beck M P, Sun T F and Teja A S 2007 Fluid Phase Equilibr. 260 275
[9] Timofeeva E V, Routbort J L and Singh D 2009 J. Appl. Phys. 106 014304
[10] Ellahi R, Hassan M and Zeeshan A 2015 Int. J. Heat Mass Transf. 81 449
[11] Hamid M, Usman M, Zubair T, Ul Haq R and Wang W 2018 Int. J. Heat Mass Transf. 124 706
[12] Akbar N S, Butt A W and Tripathi D 2017 Res. Phys. 7 2477
[13] Dogonchi A S, Waqas M, Seyyedi S M, Tilehnoee M H and Ganji D D 2019 Int. J. Heat Mass Transf. 132 473
[14] Dogonchi A S, Tilehnoee M H, Waqas M, Seyyedi S M, Animasaun I L and Ganji D D 2020 Physica A 540 123034
[15] Hosseinzadeh K, Roghani S, Asadi A, Mogharrebi A and Ganji D D 2021 Int. J. Numer. Methods Heat Fluid Flow 31 402
[16] Tlili I, Samrat S P, Sandeep N and Nabwey H A 2021 Ain Shams Eng. J. 12 935
[17] Iftikhar N, Rehman A and Sadaf H 2021 Int. Commun. Heat Mass Transf. 120 105012
[18] Nield D A and Kuznetsov A V 2009 Int. J. Heat Mass Transf. 52 5796
[19] Kuznetsov A V and Nield D A 2010 Transp. Porous Media 81 409
[20] Ahmad S and Pop I 2010 Int. Commun. Heat Mass Transf. 37 987
[21] Gorla R S R, Chamkha A J and Rashad A M 2011 Nanoscale Res. Lett. 6 207
[22] Hatami M and Ganji D D 2013 J. Mol. Liq. 188 155
[23] Xu H, Gong L, Huang S and Xu M 2015 Int. J. Heat Mass Transf. 83 399
[24] Xu H and Xing Z 2017 Int. Commun. Heat Mass Transf. 89 73
[25] Xu H, Xing Z and Vafai K 2019 Int. J. Heat Fluid Flow 77 242
[26] Xu H, Xing Z B and Ghahremannezhad A 2019 J. Porous Media 22 1553
[27] Xu H J, Xing Z B, Wang F Q and Cheng Z M 2019 Chem. Eng. Sci. 195 462
[28] Mehryan S A M, Sheremet M A, Soltani M and Izadi M 2019 J. Mol. Liq. 277 959
[29] Rosca A V, Rosca N C and Pop I 2021 Int. J. Numer. Methods Heat Fluid Flow 31 75
[30] Oztop H F and Abu-Nada E 2008 Int. J. Heat Fluid Flow 29 1326
[31] El-Aziz M A 2014 J. Egypt. Math. Soc. 22 529
[32] Seddeek M A and Abdelmeguid M S 2006 Phys. Lett. A 348 172
[33] Seth G S, Singha A K, Mandal M S, Banerjee A and Bhattacharyya K 2017 Int. J. Mech. Sci. 134 98
[34] Mukhopadhyay S and Mandal I C 2014 Chin. Phys. B 23 044702
[35] Bhattacharyya K and Pop I 2014 Chin. Phys. B 23 024701
[36] Mukhopadhyay S 2014 Chin. Phys. B 23 014702
[37] Bhattacharyya K, Hayat T and Alsaedi A 2014 Chin. Phys. B 23 124701
[38] Bhattacharyya K 2011 Chin. Phys. Lett. 28 084702
[39] Pandey A K, Rajput S, Bhattacharyya K and Sibanda P 2021 Pramana-J. Phys. 95 5
[40] Bachok N, Ishak A and Pop I 2012 Int. J. Heat Mass Transf. 55 6499
[41] Salem A M, Ismai G and Fathy R 2015 Eur. Phys. J. Plus 130 113
[42] Weidman P D, Kubitschek D G and Davis A M J 2006 Int. J. Eng. Sci. 44 730
[43] Bakar A, Arifin N M, Ali M F, Bachok N, Nazar R and Pop I 2018 Appl. Sci. 8 483

Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium: A stability analysis

Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium: A stability analysis

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