Bio-fluid flow analysis based on heat transfer and variable viscosity
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摘要
This study investigates the cilia transport phenomenon from the perspectives of the heat transfer and variable viscosity in a bending channel. The rightward wall is maintained at a temperature of T_0, and the leftward wall has a temperature of T_1. Each wall has a metachronal wave that travels along its wall. The structures of the ciliary assemblies are calculated by the well-known simplifying suppositions of the large wavelength and the small Reynolds number approximation. The flow phenomenon for the Newtonian fluid is described as a function of cilia and a metachronal wave velocity. The pressure rise is calculated with MATHEMATICA. The theme of the cilia beating flow is inspected with scheming plots, and its features are discussed at the end of the article.
This study investigates the cilia transport phenomenon from the perspectives of the heat transfer and variable viscosity in a bending channel. The rightward wall is maintained at a temperature of T_0, and the leftward wall has a temperature of T_1. Each wall has a metachronal wave that travels along its wall. The structures of the ciliary assemblies are calculated by the well-known simplifying suppositions of the large wavelength and the small Reynolds number approximation. The flow phenomenon for the Newtonian fluid is described as a function of cilia and a metachronal wave velocity. The pressure rise is calculated with MATHEMATICA. The theme of the cilia beating flow is inspected with scheming plots, and its features are discussed at the end of the article.
This study investigates the cilia transport phenomenon from the perspectives of the heat transfer and variable viscosity in a bending channel. The rightward wall is maintained at a temperature of T_0, and the leftward wall has a temperature of T_1. Each wall has a metachronal wave that travels along its wall. The structures of the ciliary assemblies are calculated by the well-known simplifying suppositions of the large wavelength and the small Reynolds number approximation. The flow phenomenon for the Newtonian fluid is described as a function of cilia and a metachronal wave velocity. The pressure rise is calculated with MATHEMATICA. The theme of the cilia beating flow is inspected with scheming plots, and its features are discussed at the end of the article.
引文
[1] ELGETI, J. and GOMPPER, G. Emergence of metachronal waves in cilia arrays. Proceedings of the National Academy of Sciences of the United States of America, 110(12), 4470–4475(2013)
[2] SLEIGH, M. A., BLAKE, J. R., and LIRON, N. The propulsion of mucus by cilia. American Review of Respiratory Disease, 137(3), 726–741(1988)
[3] IBANEZ-TALLON, I., HEINTZ, N., and OMRAN, H. To beat or not to beat:roles of cilia in development and disease. Human Molecular Genetics, 12(1), R27–R35(2003)
[4] AGRAWAL, H. L. and ANWARUDDIN. Cilia transport of bio fluid with variable viscosity. Indian Journal of Pure and Applied Mathematics, 15(10), 1128–1139(1984)
[5] BLAKE, J. Flow in tubules due to ciliary activity. Bulletin of Mathematical Biology, 35, 513–523(1973)
[6] MAITI, S. and PANDEY, S. K. Rheological fluid motion in tube by metachronal wave of cilia. Applied Mathematics and Mechanics(English Edition), 38(3), 393–410(2017)https://doi.org/10.1007/s10483-017-2179-8
[7] SHAY, G. and KONSTANTIN, L. G. Computation of the internal forces in cilia:application to ciliary motion, the effects of viscosity, and cilia interactions. Biophysical Journal, 74(4), 1658–1676(1998)
[8] AGARWAL, M. Mucus transport in the lung. Mathematical and Computer Modelling, 11, 797–800(1998)
[9] NADEEM, S. and SADAF, H. Metachronal wave of cilia transport in a curved channel. Zeitschrift f¨ur Naturforschung A, 70, 33–38(2015)
[10] SADAF, H. and NADEEM, S. Influences of slip and Cu-blood nanofluid in a physiological study of cilia. Computer Methods and Programs in Biomedicine, 131, 169–180(2016)
[11] NADEEM, S. and SADAF, H. Theoretical analysis of Cu-blood nanofluid for metachronal wave of cilia motion in a curved channel. IEEE Transactions On Nanobioscience, 14(4), 447–454(2015)
[12] SLEIGH, M. A. Patterns of Ciliary Beating, Academic Press, New York(1968)
[13] MILLS, Z. G., AZIZ, B., and ALEXEEV, A. Beating synthetic cilia enhance heat transport in microfluidic channels. Soft Matter, 45, 11508–11513(2012)
[14] AKBAR, N. S., KHAN, Z. H., and NADEEM, S. Metachronal beating of cilia under influence of Hartmann layer and heat transfer. The European Physical Journal Plus, 129, 176(2014)
[15] MEKHEIMER, K. S. and ABD-ELMABOUD, Y. The influence of heat transfer and magnatic field on peristaltic transport of a Newtonian fluid in a vertical annulus:application of an endoscope.Physics Letter A, 372(3), 1657–1665(2008)
[16] AKRAM, S., NADEEM, S., and HUSSAIN, A. Effects of heat and mass transfer on peristaltic flow of a Bingham fluid in the presence of inclined magnetic field and channel with different wave forms. Journal of Magnetism and Magnetic Materials, 362, 184–192(2014)
[17] ELLAHI, R., BHATTI, M. M., and VAFAI, K. Effects of heat and mass transfer on peristaltic flow in a non-uniform rectangular duct. International Journal of Heat and Mass Transfer, 71,706–719(2014)
[18] KHAN, A. A., ELLAHI, R., and VAFAI, K. Peristaltic transport of a Jeffery fluid with variable viscosity through a porous medium in an asymmetric channel. Advances in Mathematical Physics,2012, 169642(2012)
[19] EBAID, A. A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method. Physics Letters A,372, 5321–5328(2008)
[20] NADEEM, S. and AKBAR, N. S. Influence of temperature dependent viscosity on peristaltic transport of a Newtonian fluid:application of an endoscope. Applied Mathematics and Computation, 216, 3606–3619(2010)
[21] HAKEEM, A. E., NABY, A. E., MISIERY, M. E., and SHAMY, E. Hydromagnetic flow of fluid with variable viscosity in a uniform tube with peristalsis. Journal of Physics A:Mathematical and General, 36, 8535–8547(2003)
[22] AKBAR, N. S., MARAJ, E. N., and BUTT, A. W. Copper nanoparticles impinging on a curved channel with compliant walls and peristalsis. The European Physical Journal Plus, 129, 183(2014)
[23] RAMANAMURTHY, J. V., PRASAD, K. M., and NARLA, V. K. Unsteady peristaltic transport in curved channels. Physics of Fluids, 25, 091903(2013)
[24] ELLAHI, R., ARSHAD, R., NADEEM, S., and ALI, M. Peristaltic flow of Carreau fluid in a rectangular duct through a porous medium. Mathematical Problems in Engineering, 2012, 329639(2012)
[25] ELLAHI, R., RAZAB, M., and VAFAIA, K. Series solutions of non-Newtonian nanofluids with Reynolds’ model and Vogel’s model by means of the homotopy analysis method. Mathematical and Computer Modelling, 55, 1876–1891(2012)
[26] NADEEM, S. and AKBAR, N. S. Peristaltic flow of a Jeffrey fluid with variable viscosity in an asymmetric channel. Zeitschrift f¨ur Naturforschung A, 64, 713–722(2009)
[27] ELGHNAM, R. I. Experimental and numerical investigation of heat transfer from a heated horizontal cylinder rotating in still air around its axis. Ain Shams Engineering Journal, 5(1), 177–185(2014)
[28] MUTHURAJ, R. and SRINIVAS, S. A note on heat transfer to MHD oscillatory flow in an asymmetric wavy channel. International Communications in Heat and Mass Transfer, 37, 1255–1260(2010)
[2] SLEIGH, M. A., BLAKE, J. R., and LIRON, N. The propulsion of mucus by cilia. American Review of Respiratory Disease, 137(3), 726–741(1988)
[3] IBANEZ-TALLON, I., HEINTZ, N., and OMRAN, H. To beat or not to beat:roles of cilia in development and disease. Human Molecular Genetics, 12(1), R27–R35(2003)
[4] AGRAWAL, H. L. and ANWARUDDIN. Cilia transport of bio fluid with variable viscosity. Indian Journal of Pure and Applied Mathematics, 15(10), 1128–1139(1984)
[5] BLAKE, J. Flow in tubules due to ciliary activity. Bulletin of Mathematical Biology, 35, 513–523(1973)
[6] MAITI, S. and PANDEY, S. K. Rheological fluid motion in tube by metachronal wave of cilia. Applied Mathematics and Mechanics(English Edition), 38(3), 393–410(2017)https://doi.org/10.1007/s10483-017-2179-8
[7] SHAY, G. and KONSTANTIN, L. G. Computation of the internal forces in cilia:application to ciliary motion, the effects of viscosity, and cilia interactions. Biophysical Journal, 74(4), 1658–1676(1998)
[8] AGARWAL, M. Mucus transport in the lung. Mathematical and Computer Modelling, 11, 797–800(1998)
[9] NADEEM, S. and SADAF, H. Metachronal wave of cilia transport in a curved channel. Zeitschrift f¨ur Naturforschung A, 70, 33–38(2015)
[10] SADAF, H. and NADEEM, S. Influences of slip and Cu-blood nanofluid in a physiological study of cilia. Computer Methods and Programs in Biomedicine, 131, 169–180(2016)
[11] NADEEM, S. and SADAF, H. Theoretical analysis of Cu-blood nanofluid for metachronal wave of cilia motion in a curved channel. IEEE Transactions On Nanobioscience, 14(4), 447–454(2015)
[12] SLEIGH, M. A. Patterns of Ciliary Beating, Academic Press, New York(1968)
[13] MILLS, Z. G., AZIZ, B., and ALEXEEV, A. Beating synthetic cilia enhance heat transport in microfluidic channels. Soft Matter, 45, 11508–11513(2012)
[14] AKBAR, N. S., KHAN, Z. H., and NADEEM, S. Metachronal beating of cilia under influence of Hartmann layer and heat transfer. The European Physical Journal Plus, 129, 176(2014)
[15] MEKHEIMER, K. S. and ABD-ELMABOUD, Y. The influence of heat transfer and magnatic field on peristaltic transport of a Newtonian fluid in a vertical annulus:application of an endoscope.Physics Letter A, 372(3), 1657–1665(2008)
[16] AKRAM, S., NADEEM, S., and HUSSAIN, A. Effects of heat and mass transfer on peristaltic flow of a Bingham fluid in the presence of inclined magnetic field and channel with different wave forms. Journal of Magnetism and Magnetic Materials, 362, 184–192(2014)
[17] ELLAHI, R., BHATTI, M. M., and VAFAI, K. Effects of heat and mass transfer on peristaltic flow in a non-uniform rectangular duct. International Journal of Heat and Mass Transfer, 71,706–719(2014)
[18] KHAN, A. A., ELLAHI, R., and VAFAI, K. Peristaltic transport of a Jeffery fluid with variable viscosity through a porous medium in an asymmetric channel. Advances in Mathematical Physics,2012, 169642(2012)
[19] EBAID, A. A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method. Physics Letters A,372, 5321–5328(2008)
[20] NADEEM, S. and AKBAR, N. S. Influence of temperature dependent viscosity on peristaltic transport of a Newtonian fluid:application of an endoscope. Applied Mathematics and Computation, 216, 3606–3619(2010)
[21] HAKEEM, A. E., NABY, A. E., MISIERY, M. E., and SHAMY, E. Hydromagnetic flow of fluid with variable viscosity in a uniform tube with peristalsis. Journal of Physics A:Mathematical and General, 36, 8535–8547(2003)
[22] AKBAR, N. S., MARAJ, E. N., and BUTT, A. W. Copper nanoparticles impinging on a curved channel with compliant walls and peristalsis. The European Physical Journal Plus, 129, 183(2014)
[23] RAMANAMURTHY, J. V., PRASAD, K. M., and NARLA, V. K. Unsteady peristaltic transport in curved channels. Physics of Fluids, 25, 091903(2013)
[24] ELLAHI, R., ARSHAD, R., NADEEM, S., and ALI, M. Peristaltic flow of Carreau fluid in a rectangular duct through a porous medium. Mathematical Problems in Engineering, 2012, 329639(2012)
[25] ELLAHI, R., RAZAB, M., and VAFAIA, K. Series solutions of non-Newtonian nanofluids with Reynolds’ model and Vogel’s model by means of the homotopy analysis method. Mathematical and Computer Modelling, 55, 1876–1891(2012)
[26] NADEEM, S. and AKBAR, N. S. Peristaltic flow of a Jeffrey fluid with variable viscosity in an asymmetric channel. Zeitschrift f¨ur Naturforschung A, 64, 713–722(2009)
[27] ELGHNAM, R. I. Experimental and numerical investigation of heat transfer from a heated horizontal cylinder rotating in still air around its axis. Ain Shams Engineering Journal, 5(1), 177–185(2014)
[28] MUTHURAJ, R. and SRINIVAS, S. A note on heat transfer to MHD oscillatory flow in an asymmetric wavy channel. International Communications in Heat and Mass Transfer, 37, 1255–1260(2010)