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Entropy Analysis for boundary layer Micropolar fluid flow

  • Received: 28 September 2019 Accepted: 09 February 2020 Published: 21 February 2020
  • MSC : 74A15, 76D10, 76S05

  • This paper reports entropy generation analysis of radiative micropolar fluid flow in porous medium. The mathematical model depicting convective boundary layer flow due to a vertically moving infinite plate bounding the porous medium on one side is solved numerically. An implicit finite difference method together with Gauss elimination method is used. The numerically computed velocity and temperature fields are employed to analyze entropy. The plots for entropy generation number for various sets of parameters are drawn. It is found that entropy generation number Ns decreases with increasing values of heat sink parameter Q and radiation parameter N whereas it increases with increasing values of Grashoff number Gr, Brinkman number Br. The Bejan number shows pronounced variations for the parameters entering into the problem.

    Citation: Paresh Vyas, Rajesh Kumar Kasana, Sahanawaz Khan. Entropy Analysis for boundary layer Micropolar fluid flow[J]. AIMS Mathematics, 2020, 5(3): 2009-2026. doi: 10.3934/math.2020133

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  • This paper reports entropy generation analysis of radiative micropolar fluid flow in porous medium. The mathematical model depicting convective boundary layer flow due to a vertically moving infinite plate bounding the porous medium on one side is solved numerically. An implicit finite difference method together with Gauss elimination method is used. The numerically computed velocity and temperature fields are employed to analyze entropy. The plots for entropy generation number for various sets of parameters are drawn. It is found that entropy generation number Ns decreases with increasing values of heat sink parameter Q and radiation parameter N whereas it increases with increasing values of Grashoff number Gr, Brinkman number Br. The Bejan number shows pronounced variations for the parameters entering into the problem.


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    [1] A. C. Eringen, Theory of micropolar fluids, J. Math. Mech., 16 (1966), 1-18.
    [2] A. C. Eringen, Theory of thermomicrofluids, J. Math. Anal. Appl., 38 (1966), 480-496.
    [3] M. M. Khonsari, On the self-excited whirl orbits of a journal in a sleeve, bearing lubricated with micropolar fluids, Acta Mech., 81 (1990), 235-244.
    [4] M. M. Khonsari, D. Brewe, On the performance of finite journal bearing lubricated with micropolar fluids, STLE Tribol. Transm., 32 (1989), 155-160. doi: 10.1080/10402008908981874
    [5] B. Hadimoto, T. Tokioka, Two-dimensional shear flows of linear micropolar fluids, Int. J. Eng. Sci., 7 (1969), 515-522. doi: 10.1016/0020-7225(69)90036-6
    [6] F. Lockwood, M. Benchaita, S. Friberg, Study of polyotropic liquid crystals in viscometric flow and elasto hydrodynamic contact, ASLE Tribol. Transm., 30 (1987), 539-548.
    [7] J. D. Lee, A. C. Eringen, Boundary effects of orientation of nematic liquid crystals, J. Chem. Phys., 55 (1971), 509-512.
    [8] V. Kolpashchikov, N. P. Migun, P. P. Prokhorenko, Experimental determinations of material micropolar coefficients, Int. J. Eng. Sci., 21 (1983), 405-411. doi: 10.1016/0020-7225(83)90123-4
    [9] T. Ariman, M. A. Turk, N. D. Sylvester, Micro continuum fluid mechanics: A review, Int. J. Eng. Sci., 11 (1973), 905-930. doi: 10.1016/0020-7225(73)90038-4
    [10] T. Ariman, M. A. Turk, N. D. Sylvester, Application of micro continuum fluid mechanics, Int. J. Eng. Sci., 12 (1974), 273-293. doi: 10.1016/0020-7225(74)90059-7
    [11] G. Ahmedi, Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate, Int. J. Eng. Sci., 14 (1976), 639-646. doi: 10.1016/0020-7225(76)90006-9
    [12] S. K. Jena, M. N. Mathur, Free convection in the laminar boundary layer flow of thermomicropolar fluid past a non-isothermal vertical flat plate with suction/injection, Acta Mech., 42 (1982), 227-238. doi: 10.1007/BF01177194
    [13] E. M. Abo-Eldahab, M. A. El-Aziz, Flow and heat transfer in a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium with uniform free stream, Appl. Math. Comput., 162 (2005), 881-899.
    [14] M. M. Rashidi, N. Kavyani, S. Abelman, Investigation of entropy generation in MHD and slip flowover a rotating porous disk with variable properties, Int. J. Heat Mass Tran., 70 (2014), 892-917. doi: 10.1016/j.ijheatmasstransfer.2013.11.058
    [15] D. Gupta, L. Kumar, O. A. Bég, et al. Finite element simulation of mixed convection flow of micropolar fluid over a shrinking sheet with thermal radiation, P. I. Mech. Eng. E, 228 (2014), 61-72.
    [16] N. Ali, A. Zaman, O. A. Bég, Numerical simulation of unsteady micropolar hemodynamics in a tapered catheterized artery with a combination of stenosis and aneurysm, Med. Biol. Eng. Comput., 54 (2015), 1423-1436.
    [17] M. J. Uddin, M. N. Kabir, Y. M. Alginahi, Lie group analysis and numerical solution of magnetohydrodynamic free convective slip flow of micropolar fluid over a moving plate with heat transfer, Comput. Math. Appl., 70 (2015), 846-856. doi: 10.1016/j.camwa.2015.06.002
    [18] I. Dražić, N. Črnjarić-Žic, L. Simčić, A shear flow problem for compressible viscous micropolar fluid: Derivation of the model and numerical solution, Math. Comput. Simulat., 162 (2019), 249-267. doi: 10.1016/j.matcom.2019.01.013
    [19] A. A. Farooq, D. Tripathib, T. Elnaqeeb, On the propulsion of micropolar fluid inside a channel due to ciliary induced metachronal wave, Appl. Math. Comput., 347 (2019), 225-235.
    [20] H. H. Sherief, M. S. Faltas, S. El-Sapa, Interaction between two rigid spheres moving in a micropolar fluid with slip surfaces, J. Mol. Liq., 290 (2019), 111165.
    [21] M. S. Uddin, K. Bhattacharyya, S. Shafie, Micropolar fluid flow and heat transfer over an exponentially permeable shrinking sheet, Popul. Power Res., 5 (2016), 310-317.
    [22] R. D. Cess, The Interaction of thermal radiation with free convection heat transfer, Int. J. Heat Mass Tran., 9 (1966), 1269-1277. doi: 10.1016/0017-9310(66)90119-0
    [23] A. A. Hayday, D. A. Bowlus, R. A. McGraw, Free convection from a vertical flat plate with step discontinuities in surface temperature, ASME J. Heat Tran., 89 (1967), 244-250. doi: 10.1115/1.3614371
    [24] T. T. Kao, Laminar free convective heat transfer response along a vertical plat plate with step jump in surface temperature, Heat Mass Transfer, 2 (1975), 419-428.
    [25] P. Cheng, W. J. Minkowycz, Flow about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike, J. Geophys. Res., 82 (1977), 2040-2044. doi: 10.1029/JB082i014p02040
    [26] A. Raptis, N. Kafousias, Heat transfer in flow through a porous medium bounded by an infinite vertical plate under the action of a magnetic field, Energy Res., 6 (1982), 241-245. doi: 10.1002/er.4440060305
    [27] M. V. A. Bianchi, R. Viskanta, Momentum and heat transfer on a continuous flat surface moving in a parallel counterflow free stream, Warme-und Stoffubertrangung, 29 (1993), 89-94. doi: 10.1007/BF01560077
    [28] H. S. Thakhar, R. S. R. Gorla, V. M. Soundalgekar, Radiation effect on MHD free convection flow of a radiating gas past a semi-infinite vertical plate, Int. J. Numer. Method Heat, 6 (1996), 77-83.
    [29] A. J. Chamkha, Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption, Int. J. Eng. Sci., 24 (2004), 217-230.
    [30] M. M. Abdelkhalek, Heat and Mass transfer in MHD free convection from a moving permeable vertical surface by a perturbation technique, Commun. Nonlinear Sci., 14 (2009), 2091-2102. doi: 10.1016/j.cnsns.2008.06.001
    [31] O. D. Makinde, Similarity solution for natural convection from a moving vertical plate with internal heat generation and a convective boundary condition, Therm. Sci., 15 (2011), 5137-5143.
    [32] D. Srinivasacharya, O. Surender, Non-similar solution for natural convective boundary layer flow of ananofluid past a vertical plate embedded in a doubly stratified porous medium, Int. J. Heat Mass Tran., 71 (2014), 431-438. doi: 10.1016/j.ijheatmasstransfer.2013.12.001
    [33] A. Khalid, I. Khan, S. Shafie, Heat transfer in ferrofluid with cylindrical shape nanoparticles past a vertical plate with ramped wall temperature embedded in a porous medium, J. Mol. Liq., 221 (2016), 1175-1183. doi: 10.1016/j.molliq.2016.06.105
    [34] S. R. Mishra, I. Khanb, Q. M. Al-mdallalc, et al. Free convective micropolar fluid flow and heat transfer over a shrinking sheet with heat source, Case Stud. Therm. Eng., 11 (2018), 113-119. doi: 10.1016/j.csite.2018.01.005
    [35] H. Chen, J. Ma, H. Liu, Least square spectral collocation method for nonlinear heat transfer in moving porous plate with convective and radiative boundary conditions, Int. J. Therm. Sci., 132 (2018), 335-343. doi: 10.1016/j.ijthermalsci.2018.06.020
    [36] A. Bejan, A study of entropy generation in fundamental convective heat transfer, J. Heat Trans., 101 (1979), 718-725. doi: 10.1115/1.3451063
    [37] A. Bejan, Second law analysis in heat transfer, Energy, 5 (1980), 721-732.
    [38] P. Vyas, S. Soni, Entropy analysis for MHD casson fluid flow in a channel subjected to weakly temperature dependent convection coefficient and hyderodynamic slip, J. Rajasthan Acad. Phys. Sci., 15 (2016), 1-18.
    [39] P. Vyas, N. Srivastava, Entropy analysis of generalized MHD Couette flow inside a composite duct with asymmetric convective cooling, Arab. J. Sci. Eng., 40 (2015), 603-614. doi: 10.1007/s13369-014-1562-0
    [40] N. Srivastava, P. Vyas, S. Soni, Entropy generation analysis for oscillatory flow in a vertical channel filled with Porous Medium, IEEE International Conference on Recent Advances and Innovations in Engineering (ICRAIE-2016), December 23-25, Jaipur, India.
    [41] M. F. Modest, Heat Transfer, 2 Eds., Academic press, 2003.
    [42] D. Srinivasacharya, K. H. Bindu, Entropy generation due to micropolar fluid flow between concentric cylinders with slip and convective boundary conditions, Ain Shams Eng. J., 9 (2018), 245-255. doi: 10.1016/j.asej.2015.10.016
    [43] D. Srinivasacharya, K. H. Bindu, Entropy generation of micropolar fluid flow in an inclined porous pipe with convective boundary conditions, Sadhna, 42 (2017), 729-740. doi: 10.1007/s12046-017-0639-3
    [44] S. K. Asha, C. K. Deepa, Entropy generation for peristaltic blood flow of a magneto-micropolar fluid with thermal radiation in a tapered asymmetric channel, Results Eng., 3 (2019), 100024.
    [45] A. Z. Sahin, Second law analysis of laminar viscous flow through a duct subjected to constant wall temperature, J. Heat Trans., 120 (1998), 76-83. doi: 10.1115/1.2830068
    [46] J. V. R. Murthy, J. Srinivas, Second law analysis for Poiseuille flow of immiscible micropolar fluids in a channel, Int. J. Heat Mass Tran., 65 (2013), 254-264. doi: 10.1016/j.ijheatmasstransfer.2013.05.048
    [47] C. K. Chen, Y. T. Yang, K. H. Chang, The effect of thermal radiation on entropy generation due to micro-polar fluid flow along a wavy surface, Entropy, 13 (2011),1595-1610. doi: 10.3390/e13091595
    [48] A. Shahsavar, P. T. Sardari, D. Toghraie, Free convection heat transfer and entropy generation analysis of water-Fe3O4/CNT hybridnanofluid in a concentric annulus, Int. J. Numer. Meth. Heat Fluid Flow, 424 (2018), 0961-5539.
    [49] E. Manay, E. F. Akyürek, B. Sahin, Entropy generation of nanofluid flow in a microchannel heat sink, Results Phys., 9 (2018), 615-624. doi: 10.1016/j.rinp.2018.03.013
    [50] P. Barnoon, D. Toghrai, R. B. Dehkordi, et al. MHD mixed convection and entropy generation in a lid-driven cavity with rotating cylinders filled by a nanofluid using two phase mixture model, J. Magn. Magn. Mater., 483 (2019), 224-248. doi: 10.1016/j.jmmm.2019.03.108
    [51] P. Barnoon, D. Toghraie, F. Eslami, et al. Entropy generation analysis of different nanofluid flows in the space between two concentric horizontal pipes in the presence of magnetic field: Single-phase and two-phase approaches, Comput. Math. Appl., 73 (2019), 662-692.
    [52] A. A. A. A. Abdullah, O. A. Akbari, A. Heydari, et al. The numerical modeling of water/FMWCNT nanofluid flow and heat transfer in a backward-facing contracting channel, Physica B, 537 (2018), 176-183. doi: 10.1016/j.physb.2018.02.022
    [53] S. M. Seyyedi, A. S. Hashemi-Tilehnoee, M. Waqas, et al. Entropy generation and economic analyses in a nanofluid filled L-shaped enclosure subjected to an oriented magnetic field, Appl. Therm. Eng., 168 (2019), 114789.
    [54] M. Maskaniyan, M. Nazari, S. Rashidi, et al. Natural convection and entropy generation analysis inside a channel with a porous plate mounted as a cooling system, Therm. Sci. Eng. Prog., 6 (2018),186-193. doi: 10.1016/j.tsep.2018.04.003
    [55] P. Gholamalipour, M. Siavashi, M. H. Doranehgard, Eccentricity effects of heat source inside a porous annulus on the natural convection heat transfer and entropy generation of Cu-water nanofluid, Int. Commun. Heat Mass Tran., 109 (2019), 104367.
    [56] P. Vyas, S. Khan, Entropy analysis for MHD dissipative Casson fluid flow in porous medium due to stretching cylinder, Acta Tech., 61 (2016), 299-315.
    [57] P. Vyas, N. Srivastava, Entropy analysis for magnetohyrodynamic fluid flow in porous medium due to a non-isothermal stretching sheet, J. Rajasthan Acad. Phys. Sci.,14 (2015), 323-336.
    [58] Y. J. Kim, Heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium, Transport in Porous Med., 56 (2004), 17-37. doi: 10.1023/B:TIPM.0000018420.72016.9d
    [59] A. A. Raptis, V. M. Soundalgekar, MHD flow past a steadily moving infinite vertical porous plate with constant heat flux, Nucl. Eng. Des., 72 (1982), 373-379. doi: 10.1016/0029-5493(82)90050-4
    [60] P. Vyas, A. Rai, K. S. Shekhawat, Dissipative heat and mass transfer in porous medium due to continuously moving plate, Appl. Math. Sci., 6 (2012), 4319-4330.
    [61] A. A. Raptis, Flow of a micropolar fluid past a continuously moving plate by the presence of rotation, Int. J. Heat Mass Tran., 41 (1998), 2865-2866. doi: 10.1016/S0017-9310(98)00006-4
    [62] F. Atlan, M. E. A. El-Mikkawy, A new symbolic algorithm for solving general opposite-bordered tridiagonal linear systems, Am. J. Comput. Math., 5 (2015), 258-266. doi: 10.4236/ajcm.2015.53023
    [63] J. Jia, S. Li, New algorithms for numerically solving a class of bordered tridiagonal systems of linear equations, Comput. Math. Appl., 78 (2019), 144-151.< doi: 10.1016/j.camwa.2019.02.028
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