Influence of Hall current and Joule heating on entropy generation during electrokinetically induced thermoradiative transport of nanofluids in a porous microchannel

doi:10.1007/s10483-019-2528-7

摘要/Abstract

摘要： A comprehensive theoretical study of entropy generation during electrokinetically driven transport of a nanofluid is of prime concern in the paper. The flow is considered to take place on a wavy channel under the action of an external transverse magnetic field and an external pressure gradient. Navier slips at the walls of the channel and thermal radiation have been taken into account in the study. The theoretical study has been carried out by developing a mathematical model by taking into account the effects of Joule heating, viscous dissipation, and the transverse magnetic field on heat transfer during the electrokinetic transport of the fluid. The derived analytical expressions have been computed numerically by considering the nanofluid as a mixture of blood and ferromagnetic nanoparticles. Variations in velocity, streaming potential, temperature distribution, Nusselt number, and Bejan number associated with the electrokinetic flow in capillaries have been investigated by the parametric variation method. The results have been presented graphically. The present investigation reveals that streaming potential decreases due to the Hall effect, while for the cooling capacity of the microsystem, we find an opposite behavior due to the Hall effect. The study further reveals that the fluidic temperature is reduced due to increase in the Hall current, and thereby thermal irreversibility of the system is reduced significantly. The results presented here can be considered as the approximate estimates of blood flow dynamics in capillaries during chemotherapy in cancer treatment.

关键词: electrokinetic induction, Hall current, nanofluid, porous media, thermal transport, entropy generation

Abstract: A comprehensive theoretical study of entropy generation during electrokinetically driven transport of a nanofluid is of prime concern in the paper. The flow is considered to take place on a wavy channel under the action of an external transverse magnetic field and an external pressure gradient. Navier slips at the walls of the channel and thermal radiation have been taken into account in the study. The theoretical study has been carried out by developing a mathematical model by taking into account the effects of Joule heating, viscous dissipation, and the transverse magnetic field on heat transfer during the electrokinetic transport of the fluid. The derived analytical expressions have been computed numerically by considering the nanofluid as a mixture of blood and ferromagnetic nanoparticles. Variations in velocity, streaming potential, temperature distribution, Nusselt number, and Bejan number associated with the electrokinetic flow in capillaries have been investigated by the parametric variation method. The results have been presented graphically. The present investigation reveals that streaming potential decreases due to the Hall effect, while for the cooling capacity of the microsystem, we find an opposite behavior due to the Hall effect. The study further reveals that the fluidic temperature is reduced due to increase in the Hall current, and thereby thermal irreversibility of the system is reduced significantly. The results presented here can be considered as the approximate estimates of blood flow dynamics in capillaries during chemotherapy in cancer treatment.

Key words: electrokinetic induction, Hall current, nanofluid, porous media, thermal transport, entropy generation

中图分类号:

B. MALLICK, J. C. MISRA, A. R. CHOWDHURY. Influence of Hall current and Joule heating on entropy generation during electrokinetically induced thermoradiative transport of nanofluids in a porous microchannel[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(10): 1509-1530.

参考文献

[1] OHNO, K., TACHIKAWA, K., and MANZ, A. Microfluidics:applications for analytical purposes in chemistry and biochemistry. Electrophoresis, 29(22), 4443-4453(2008)
[2] SHOJI, S., NAKAGAWA, S., and ESASHI, M. Micropump and sample injector for integrated chemical analysis systems. Sensors and Actuators A, 21, 189-192(1990)
[3] BECKER, H. and GARTNER, C. Polymer microfabrication methods for microfluidic analytical applications. Electrophoresis, 21(1), 12-26(2000)
[4] CHAKRABORTY, R., DEY, R., and CHAKRABORTY, S. Thermal characteristics of electromagnetohydrodynamic flows in narrow channels with viscous dissipation and Joule heating under constant wall heat flux. International Journal of Heat and Mass Transfer, 67, 1151-1162(2013)
[5] SI, D. Q. and JIAN, Y. J. Electromagnetohydrodynamic (EMHD) micropump of Jeffrey fluids through two paralle microchannels with corrugated walls. Journal of Physics D:Applied Physics, 48, 085501(2015)
[6] BUREN, M., JIAN, Y. J., and CHANG, L. Electromagnetohydrodynamic flow through a microparallel channel with corrugated walls. Journal of Physics D:Applied Physics, 47, 425501(2014)
[7] ARIFIN, D. R., YEO, L. Y., and FRIEND, J. R. Microfluidic blood plasma separation via bulk electrohydrodynamic flows. Biomicrofluidics, 1(1), 014103(2007)
[8] ABHIMANYU, P., KAUSHIK, P., MONDAL, P. K., and CHAKRABORTY, S. Transiences in rotational electro-hydrodynamics microflows of a viscoelastic fluid under electrical double layer phenomena. Journal of Non-Newtonian Fluid Mechanics, 231, 56-67(2016)
[9] CHANDRA, S. and MISRA, J. C. Influence of Hall current and microroation on the boundary layer flow of an electrically conducting fluid:application to hemodynamics. Journal of Molecular Liquids, 224, 818-824(2016)
[10] MISRA, J. C., CHANDRA, S., and HERWIG, H. Flow of a micropolar fluid in a micro-channel under the action of an alternating electric field:estimates of flow in bio-fluidic devices. Journal of Hydrodynamics, 27, 350-358(2015)
[11] MISRA, J. C. and SINHA, A. Electro-osmotic flow and heat transfer of a non-Newtonian fluid in a hydrophobic microchannel with Navier slip. Journal of Hydrodynamics, 27, 647-657(2015)
[12] MISRA, J. C., CHANDRA, S., SHIT, G. C., and KUNDU, P. K. Electroosmotic oscillatroy flow of micropolar fluid in microchannels:application to dynamics of blood flow in microfluidic devices. Applied Mathematics and Mechanics (English Edition), 35(6), 749-766(2014) https://doi.org/10.1007/s10483-014-1827-6
[13] MISRA, J. C. and CHANDRA, S. Electro-osmotically actuated oscillatory flow of a physiological fluid on a porous microchannel subject to an external AC electric field having dissimilar frequencies. Central European Journal of Physics, 12(4), 274-285(2014)
[14] MISRA, J. C. and CHANDRA, S. Electro-osmotic flow of a second-grade fluid in a porous microchannel subject to an AC electric field. Journal of Hydrodynamics, 25, 309-316(2013)
[15] MISRA, J. C., SHIT, G. C., CHANDRA, S., and KUNDU, P. K. Electro-osmotic flow of a viscoelastic fluid in a channel:applications to physiological fluid mechanics. Applied Mathematics and Computation, 217, 7932-7939(2011)
[16] JIAN, Y. J. Transient MHD heat transfer and entropy generation in a microparallel channel combined with pressure and electroosmotic effects. International Journal of Heat and Mass Transfer, 89, 193-205(2015)
[17] SINHA, A. and SHIT, G. C. Electromagnetohydrodynamic flow of blood and heat transfer in a capillary with thermal radiation. Journal of Magnetism and Magnetic Materials, 378, 143-151(2015)
[18] ZHAO, G., JIAN, Y., and LI, F. Streaming potential and heat transfer of nanofluids in microchannels in the presence of magnetic field. Journal of Magnetism and Magnetic Materials, 407, 75-82(2016)
[19] ZHAO, G., JIAN, Y., and LI, F. Streaming potential and heat transfer of nanofluids in parallel plate microchannels. Colloids and Surfaces A:Physicochemical and Engineering Aspects, 498, 239-247(2016)
[20] MISRA, J. C. and ADHIKARY, S. D. Flow of a Bingham fluid in a porous bed under the action of a magnetic field:application to magneto-hemorheology. Engineering Science and Technology, an International Journal, 20, 973-981(2017)
[21] SCHENCK, J. F. Safety of strong, static magnetic fields. Journal of Magnetic Resonance Imaging, 12(1), 2-19(2000)
[22] COWLING, T. G. Magnetohydrodynamics, InterScience, New York (1975)
[23] BEJAN, A. Second law analysis in heat transfer. Energy, 5, 720-732(1980)
[24] SINGH, P. K., ANOOP, K. B., SUNDARARAJAN, T., and DAS, S. K. Entropy generation due to flow and heat transfer in nanofluids. International Journal of Heat and Mass Transfer, 53, 4757-4767(2010)
[25] MAHMOUDI, A. H., POP, I., SHAHI, M., and TALEBI, F. MHD naturnal convection and entropy generation in a trapezoidal enclosure using Cu-water nanofluid. Computer and Fluids, 72, 46-62(2013)
[26] MATIN, M. H. and KHAN, W. A. Entropy generation analysis of heat and mass transfer in mixed electrokinetically and pressure driven flow thorugh a slit microchannel. Energy, 56, 207-217(2013)
[27] ABDALLA, S., AL-AMEER, S. S., and AL-MAGAISHI, S. H. Electrical properties with relaxation through human blood. Biomicrofluidics, 4, 034101(2010)
[28] SIMA, W., SHI, J., YANG, Q., HUANG, S., and CAO, X. Effects of conductivity and permittivity of nanoparticle on transformer oil insulation performance:experiment and theory. IEEE Transactions on Dielectrics and Electrical Insulation, 22(1), 380-390(2015)
[29] XUAN, Y. and LI, Q. Investigation on convective heat transfer and flow features of nanofluids. ASME Journal of Heat Transfer, 125, 151-155(2003)
[30] YU, W. and CHIO, S. U. S. The role of interfacial layers in the enhanced thermal conductivity of nanofluids:a renovated Maxwell model. Journal of Nanoparticle Research, 5, 167-171(2003)
[31] SUTTON, G. W. and SHERMAN, A. Engineering Magnetohydrodynamics, Mc Graw-Hill, New York (1965)
[32] MOHAMED, R. A. and ABO-DAHAB, S. M. Influence of chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium with heat generation. International Journal of Thermal Sciences, 48, 1800-1813(2009)
[33] HUNTER, R. J. Zeta Potential in Colloid Science, Academic Press, London/New York (1981)
[34] MASLIYAH, J. H. and BHATTACHARJEE, S. Electrokinetic and Colloid Transport Phenomena, Wiley, Hoboken/New Jersey (2006)
[35] CHAKRABORTY, S. and ROY, S. Thermally developing electroosmotic transport of nanofluids in microchannels. Microfluidics and Nanofluidics, 4, 501-511(2008)
[36] QIAN, S. and BAU, H. H. Magneto-hydrodynamic based microfluidics. Mechanics Research Communications, 36, 10-21(2009)
[37] THOMPSON, P. A. and TROIAN, S. M. A general boundary condition for liquid flow at solid surface. nature, 389, 360-362(1997)
[38] MISRA, J. C., MALLICK, B., SINHA, A., and ROYCHOWDHURY, A. Impact of CattaneoChristov heat flux on electroosmotic transport of third-order fluids in a magnetic environment. The European Physical Journal Plus, 133(5), 195(2018)
[39] BEJAN, A. A study of entropy generation in fundamental convective heat transfer. Journal of Heat Transfer, 101(1), 718-725(1979)
[40] HIGASHI, T., YAMAGISHI, A., TAKEUCHI, N., KAWAGUCHI, N., SAGAWA, S., ONISHI, S., and DATE, M. Orientation of erythrocytes in a strong static magnetic field. Blood, 82, 1328-1334(1993)