Effects of magnetic Reynolds number on swimming of gyrotactic microorganisms between rotating circular plates filled with nanofluids

doi:10.1007/s10483-020-2599-7

摘要/Abstract

摘要： The three-dimensional (3D) nanofluid flow among the rotating circular plates filled with nanoparticles and gyrotactic microorganisms is studied. A generalized form of the magnetic Reynolds number is used for the mathematical modeling of the ferro-nanofluid flow. The torque effects on the lower and upper plates are calculated. A differential transform scheme with the Padé approximation is used to solve the coupled highly nonlinear ordinary differential equations. The results show that the squeeze Reynolds number significantly suppresses the temperature, microorganism, and nanoparticle concentration distribution, and agree well with those obtained by the numerical method.

关键词: swimming of microorganism, generalized magnetic Reynolds number, nanofluid, differential transform solution, circular rotating plate

Abstract: The three-dimensional (3D) nanofluid flow among the rotating circular plates filled with nanoparticles and gyrotactic microorganisms is studied. A generalized form of the magnetic Reynolds number is used for the mathematical modeling of the ferro-nanofluid flow. The torque effects on the lower and upper plates are calculated. A differential transform scheme with the Padé approximation is used to solve the coupled highly nonlinear ordinary differential equations. The results show that the squeeze Reynolds number significantly suppresses the temperature, microorganism, and nanoparticle concentration distribution, and agree well with those obtained by the numerical method.

Key words: swimming of microorganism, generalized magnetic Reynolds number, nanofluid, differential transform solution, circular rotating plate

中图分类号:

Lijun ZHANG, M. B. ARAIN, M. M. BHATTI, A. ZEESHAN, H. HAL-SULAMI. Effects of magnetic Reynolds number on swimming of gyrotactic microorganisms between rotating circular plates filled with nanofluids[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(4): 637-654.

参考文献

[1] EASTMAN, J. A. and CHOI, S. U. S. Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress and Exposition, San Fransisco, 99-105(1995)
[2] Pak, B. C. and CHO, Y. I. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Experimental Heat Transfer:An International Journal, 11, 151-170(1998)
[3] LIN, J. Z. and YANG, H. L. A review on the flow instability of nanofluids. Applied Mathematics and Mechanics (English Edition), 40(9), 1227-1238(2019) https://doi.org/10.1007/s10483-019-2521-9
[4] DAS, S. K., PUTRA, N., THIESEN, P., and ROETZEL, W. Temperature dependence of thermal conductivity enhancement for nanofluids. Journal of Heat Transfer, 125, 567-574(2003)
[5] XUAN, Y. and ROETZEL, W. Conceptions for heat transfer correlation of nanofluids. International Journal of Heat and Mass Transfer, 43, 3701-3707(2000)
[6] GHERASIM, I., ROY, G., NGUYEN, C. T., and VO-NGOC, D. Experimental investigation of nanofluids in confined laminar radial flows. International Journal of Thermal Sciences, 48, 1486-1493(2009)
[7] ZHANG, X., GU, H., and FUJII, M. Effective thermal conductivity and thermal diffusivity of nanofluids containing spherical and cylindrical nanoparticles. Experimental Thermal and Fluid Science, 31, 593-599(2007)
[8] HAMILTON, R. L. and CROSSER, O. K. Thermal conductivity of heterogeneous two-component systems. Industrial and Engineering Chemistry Fundamentals, 1, 187-191(1962)
[9] SHEIKHOLESLAMI, M., HAYAT, T., and ALSAEDI, A. MHD free convection of Al₂O₃-water nanofluid considering thermal radiation:a numerical study. International Journal of Heat and Mass Transfer, 96, 513-524(2016)
[10] FAKOUR, M., VAHABZADEH, A., and GANJI, D. D. Study of heat transfer and flow of nanofluid in permeable channel in the presence of magnetic field. Propulsion and Power Research, 4, 50-62(2015)
[11] ELLAHI, R., ZEESHAN, A., HUSSAIN, F., and ABBAS, T. Thermally charged MHD bi-phase flow coatings with non-Newtonian nanofluid and hafnium particles along slippery walls. Coatings, 9, 300(2019)
[12] ZHU, J., WANG, S., ZHENG, L., and ZHANG, X. Heat transfer of nanofluids considering nanoparticle migration and second-order slip velocity. Applied Mathematics and Mechanics (English Edition), 38(1), 125-136(2017) https://doi.org/10.1007/s10483-017-2155-6
[13] BASKAYA, E., KOMURGOZ, G., and OZKOL, I. Investigation of oriented magnetic field effects on entropy generation in an inclined channel filled with ferrofluids. Entropy, 19, 377(2017)
[14] HAMID, M., USMAN, M., HAQ, R. U., KHAN, Z. H., and WANG, W. Wavelet analysis of stagnation point flow of non-Newtonian nanofluid. Applied Mathematics and Mechanics (English Edition), 40(8), 1211-1226(2019) https://doi.org/10.1007/s10483-019-2508-6
[15] ZEESHAN, A., SHEHZAD, N., ABBAS, T., and ELLAHI, R. Effects of radiative electromagnetohydrodynamics diminishing internal energy of pressure-driven flow of titanium dioxidewater nanofluid due to entropy generation. Entropy, 21, 236(2019)
[16] IMTIAZ, M., SHAHID, F., HAYAT, T., and ALSAEDI, A. Melting heat transfer in Cu-water and Ag-water nanofluids flow with homogeneous-heterogeneous reactions. Applied Mathematics and Mechanics (English Edition), 40(4), 465-480(2019) https://doi.org/10.1007/s10483-019-2462-8
[17] HUSSAIN, F., ELLAHI, R., ZEESHAN, A., and VAFAI, K. Modelling study on heated couple stress fluid peristaltically conveying gold nanoparticles through coaxial tubes:a remedy for gland tumors and arthritis. Journal of Molecular Liquids, 268, 149-155(2018)
[18] ELLAHI, R., HASSAN, M., and ZEESHAN, A. Shape effects of nanosize particles in Cu-H₂O nanofluid on entropy generation. International Journal of Heat and Mass Transfer, 81, 449-456(2015)
[19] HEIDARY, H., HOSSEINI, R., PIRMOHAMMADI, M., and KERMANI, M. J. Numerical study of magnetic field effect on nano-fluid forced convection in a channel. Journal of Magnetism and Magnetic Materials, 374, 11-17(2015)
[20] LIN, J., XIA, Y., and KU, X. K. Friction factor and heat transfer of nanofluids containing cylindrical nanoparticles in laminar pipe flow. Journal of Applied Physics, 116, 133513(2014)
[21] LIN, J. Z., XIA, Y., and KU, X. K. Pressure drop and heat transfer of nanofluid in turbulent pipe flow considering particle coagulation and breakage. Journal of Heat Transfer, 136, 111701(2014)
[22] LIN, J. Z., XIA, Y., and KU, X. K. Flow and heat transfer characteristics of nanofluids containing rod-like particles in a turbulent pipe flow. International Journal of Heat and Mass Transfer, 93, 57-66(2016)
[23] SOBAMOWO, M. G., JAYESIMI, L. O., and WAHEED, M. A. Magnetohydrodynamic squeezing flow analysis of nanofluid under the effect of slip boundary conditions using variation of parameter method. Karbala International Journal of Modern Science, 4, 107-118(2018)
[24] VAJRAVELU, K., PRASAD, K. V., NG, C. O., and VAIDYA, H. MHD squeeze flow and heat transfer of a nanofluid between parallel disks with variable fluid properties and transpiration. International Journal of Mechanical and Materials Engineering, 12, 9(2017)
[25] HOSSEINZADEH, K., ALIZADEH, M., and GANJI, D. D. Hydrothermal analysis on MHD squeezing nanofluid flow in parallel plates by analytical method. International Journal of Mechanical and Materials Engineering, 13, 4(2018)
[26] HASHMI, M. M., HAYAT, T., and ALSAEDI, A. On the analytic solutions for squeezing flow of nanofluid between parallel disks. Nonlinear Analysis:Modelling and Control, 17, 418-430(2012)
[27] SINGH, K., RAWAT, S. K., and KUMAR, M. Heat and mass transfer on squeezing unsteady MHD nanofluid flow between parallel plates with slip velocity effect. Journal of Nanoscience, 1-11(2016)
[28] BHATTA, D. P., MISHRA, S. R., and DASH, J. K. Unsteady squeezing flow of water-based nanofluid between two parallel disks with slip effects:analytical approach. Heat Transfer-Asian Research, 48, 1-20(2019)
[29] MADAKI, A. G., ROSLAN, R., MOHAMED, M., and KAMARDAN, M. G. Analytical solutions of squeezing unsteady nanofluid flow in the presence of thermal radiation. Journal of Computer Science and Computational Mathematics, 6, 451-463(2016)
[30] VIMALA, P. and MANIMEGALAI, K. Natural convection flow of nanofluids in squeeze film with an exponential curvature. Journal of Informatics and Mathematical Sciences, 10, 371-381(2010)
[31] ACHARYA, N., DAS, K., and KUNDU, P. K. The squeezing flow of Cu-water and Cu-kerosene nanofluids between two parallel plates. Alexandria Engineering Journal, 55, 1177-1186(2016)
[32] THONGMOON, M. and PUSJUSO, S. The numerical solutions of differential transform method and the Laplace transform method for a system of differential equations. Nonlinear Analysis:Hybrid Systems, 4, 425-431(2010)
[33] FATOOREHCHI, H. and ABOLGHASEMI, H. Differential transform method to investigate mass transfer phenomenon to a falling liquid film system. Australian Journal of Basic and Applied Sciences, 5, 337-345(2011)
[34] YOUSIF, M. A., HATAMI, M., and ISMAEL, H. F. Heat transfer analysis of MHD three dimensional Casson fluid flow over a porous stretching sheet by DTM-Padé. International Journal of Applied and Computational Mathematics, 3, 813-828(2017)
[35] ÇILINGIR, S., İNCI, A. A., BULUT, H., HAMMOUCH, Z., BASKONUS, H. M., MEKKAOUI, T., MUHAMMAD, B., and BIN, F. Numerical investigation on MHD flow and heat transfer over an exponentially stretching sheet with viscous dissipation and radiation effects, ITM Web of Conferences, 13, 01025(2017)
[36] KHAN, W. A., RASHAD, A. M., ABDOU, M. M. M., and TLILI, I. Natural bioconvection flow of a nanofluid containing gyrotactic microorganisms about a truncated cone. European Journal of Mechanics-B/Fluids, 75, 133-142(2019)
[37] SALEEM, S., RAFIQ, H., AL-QAHTANI, A., EL-AZIZ, M. A., MALIK, M. Y., and ANIMASAUN, I. L. Magneto Jeffrey nanofluid bioconvection over a rotating vertical cone due to gyrotactic microorganism. Mathematical Problems in Engineering, 2019, 3478037(2019)
[38] KHAN, W. A., MAKINDE, O. D., and KHAN, Z. H. MHD boundary layer flow of a nanofluid containing gyrotactic microorganisms past a vertical plate with Navier slip. International Journal of Heat and Mass Transfer, 74, 285-291(2014)
[39] FAROOQ, S., HAYAT, T., ALSAEDI, A., and AHMAD, B. Numerically framing the features of second order velocity slip in mixed convective flow of Sisko nanomaterial considering gyrotactic microorganisms. International Journal of Heat and Mass Transfer, 112, 521-532(2017)
[40] WAQAS, H., KHAN, S. U., HASSAN, M., BHATTI, M. M., and IMRAN, M. Analysis on the bioconvection flow of modified second-grade nanofluid containing gyrotactic microorganisms and nanoparticles. Journal of Molecular Liquids, 291, 111231(2019)
[41] WAQAS, H., KHAN, S. U., IMRAN, M., and BHATTI, M. M. Thermally developed Falkner-Skan bioconvection flow of a magnetized nanofluid in the presence of a motile gyrotactic microorganism:Buongiorno's nanofluid model. Physica Scripta, 94, 115304(2019)
[42] AZIZ, A., KHAN, W. A., and POP, I. Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms. International Journal of Thermal Sciences, 56, 48-57(2012)
[43] RAEES, A., XU, H., SUN, Q., and POP, I. Mixed convection in gravity-driven nano-liquid film containing both nanoparticles and gyrotactic microorganisms. Applied Mathematics and Mechanics (English Edition), 36(2), 163-178(2015) https://doi.org/10.1007/s10483-015-1901-7
[44] MEADE, D. B., HARAN, B. S., and WHITE, R. E. The shooting technique for the solution of two-point boundary value problems. Maple Technical Newsletter, 3, 1-8(1996)