Effect of nano-particles on MHD flow of tangent hyperbolic fluid in a ciliated tube: an application to fallopian tube

K. Maqbool; S. Shaheen; A. M. Siddiqui; K. Maqbool; S. Shaheen; A. M. Siddiqui

doi:10.3934/mbe.2019144

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 2927-2941. doi: 10.3934/mbe.2019144

Previous Article Next Article

Research article

Effect of nano-particles on MHD flow of tangent hyperbolic fluid in a ciliated tube: an application to fallopian tube

1.
Department of Mathematics & Statistics, International Islamic University, Islamabad 44000, Pakistan
2.
Department of Mathematics, York Campus, Pennsylvania State University, York, Pennsylvania 17403, U. S. A

Received: 28 December 2018 Accepted: 25 February 2019 Published: 10 April 2019

This study shows the effects of magnetic field and copper nanoparticles on the flow of tangent hyperbolic fluid (blood) through a ciliated tube (fallopian tube). The present study will be very helpful for those patients who are facing blood clotting in fallopian tube that may cause for infertility or cancer. The nanoparticles and magnetic field are very helpful to break the clots in blood flowing in fallopian tube. Since blood flows in fallopian tube due to ciliary movement, therefore medicines containing copper nanoparticles and magnetic field with radiation therapy help to improve the patient. Ciliary movement has a particular pattern of motion i.e., metachronal wavy motion which helps to fluid flow. For the forced convective MHD flow of tangent hyperbolic nano-fluid, momentum and energy equations are solved by the small Reynolds' number approximation and Adomian decomposition method by constructing the recursive relation of ADM and solved by software "MATHEMATICA". The effects of parameters such as nanoparticle volume fraction, Hartmann number, entropy generation and Bejan's number have been discussed through graphs plotted in software "MATHEMATICA". It is found that blood flow is accelerated and heat transfer enhancement is maximum in the presence of nano particles, also magnetic effects accelerates the blood flow and help to enhance the heat transfer whereas the presence of porous medium increases the fluid's velocity and reduce the transfer of heat through fluid flow.
- nano particles,
- MHD,
- tangent hyperbolic fluid,
- ciliated axisymmetric tube,
- porous medium
Citation: K. Maqbool, S. Shaheen, A. M. Siddiqui. Effect of nano-particles on MHD flow of tangent hyperbolic fluid in a ciliated tube: an application to fallopian tube[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2927-2941. doi: 10.3934/mbe.2019144

Related Papers:

Abstract

This study shows the effects of magnetic field and copper nanoparticles on the flow of tangent hyperbolic fluid (blood) through a ciliated tube (fallopian tube). The present study will be very helpful for those patients who are facing blood clotting in fallopian tube that may cause for infertility or cancer. The nanoparticles and magnetic field are very helpful to break the clots in blood flowing in fallopian tube. Since blood flows in fallopian tube due to ciliary movement, therefore medicines containing copper nanoparticles and magnetic field with radiation therapy help to improve the patient. Ciliary movement has a particular pattern of motion i.e., metachronal wavy motion which helps to fluid flow. For the forced convective MHD flow of tangent hyperbolic nano-fluid, momentum and energy equations are solved by the small Reynolds' number approximation and Adomian decomposition method by constructing the recursive relation of ADM and solved by software "MATHEMATICA". The effects of parameters such as nanoparticle volume fraction, Hartmann number, entropy generation and Bejan's number have been discussed through graphs plotted in software "MATHEMATICA". It is found that blood flow is accelerated and heat transfer enhancement is maximum in the presence of nano particles, also magnetic effects accelerates the blood flow and help to enhance the heat transfer whereas the presence of porous medium increases the fluid's velocity and reduce the transfer of heat through fluid flow.

References

[1]	S. M. Mousazadeh, M. M. Shahmardan, T. Tavang, et al., Numerical investigation on convective heat transfer over two heated wall-mounted cubes in tandem and staggered arrangement, Theor. Appl., 8 (2018), 171–183.
[2]	S. S. Ghadikolaei, S. S. Hosseinzadeh, K. Ganji, et al., Fe₃O₄-(CH₂OH)₂ nano-fluid analysis in a porous medium under MHD radiative boundary layer and dusty fluid, J. Mol. Liq., 258 (2018), 172–185.
[3]	A. Karampatzakis and T. Samaras, Numerical model of heat transfer in the human eye with consideration of fluid dynamics of the aqueous humour, Phys. Med. Bio., 55 (2010), 5653.
[4]	Tripathi, S. K. Pandey and O. A. Bég, Mathematical modelling of heat transfer effects on swallowing dynamics of viscoelastic food bolus through the human oesophagus, Int. J. Therm. Sci., 70 (2013), 41–53.
[5]	A. Zaman, N. Ali, O.A. Bég, et al., Heat and mass transfer to blood flowing through a tapered overlapping stenosed artery, Int. J. Heat. Mass. Tran., 95 (2016), 1084–1095.
[6]	S. U. S. Choi and J. A. Estman, Enhancing thermal conductivity of fluids with nanoparticles, ASME-Publications-Fed, 231 (1995), 99–106.
[7]	W. Dongsheng and Y. Ding, Experimental investigation into convective heat transfer of nano-fluids at the entrance region under laminar flow conditions, Int. J. Heat. Mass. Tran., 47 (2004), 5181–5188.
[8]	S. Maïga, T. Nguyen, N. Galanis, et al., Heat transfer enhancement in turbulent tube flow using Al₂O₃ nanoparticle suspension, Int. J. Numer. Method. H., 16 (2006), 275–292.
[9]	S. Ibsen, A. Sonnenberg, C. Schutt, et al., Recovery of drug delivery nanoparticles from human plasma using an electrokinetic platform technology, Small, 11 (2015), 5088–5096.
[10]	M. A. Sleigh, J. R. Blake and N. Liron, The propulsion of mucus by cilia, Amer. Rev. Resp. Dis., 137 (1988), 726–741.
[11]	C. Brennen and H. Winet, Fluid mechanics of propulsion by cilia and flagella, Annu. Rev. Fluid. Mech., 9 (1977), 339–398.
[12]	M. J. Sanderson and M. A. Sleigh, Ciliary activity of cultured rabbit tracheal epithelium: beat pattern and metachrony, J. Cell. Sci., 47 (1981), 331–347.
[13]	A. Murakami and K. Takahashi, Correlation of electrical and mechanical responses in nervous control of cilia, Nature, 257 (1975), 48.
[14]	J. Blake, A model for the micro-structure in ciliated organisms, J. Fluid. Mech., 55 (1972), 1–23.
[15]	R. A. Lyons, E. Saridogan and O. Djahanbakhch, The reproductive significance of human Fallopian tube cilia, Hum. Reprod. Update, 12 (2006), 363–372.
[16]	M. B. Carlson, Human Embryology and Developmental Biology, Elsevier Health Sciences, 2012.
[17]	R. A. Lyons, E. Saridogan and O. Djahanbakhch, The effect of ovarian follicular fluid and peritoneal fluid on Fallopian tube ciliary beat frequency, Hum. Reprod., 21 (2005), 52–56.
[18]	K. Maqbool, S. Shaheen and A. B. Mann, Exact solution of cilia induced flow of a Jeffrey fluid in an inclined tube, Springerplus, 5 (2016), 1379.
[19]	K. Maqbool, A. B. Mann and A. M. Siddiqui, et al., Fractional generalized Burgers' fluid flow due to metachronal waves of cilia in an inclined tube, Adv. Mech. Eng., 9 (2017), 1687814017715565.
[20]	A. M. Siddiqui, A. Sohail and K. Maqbool, Analysis of a channel and tube flow induced by cilia, Appl. Math. Comp., 309 (2017), 133–141.
[21]	A. A. Khan, F. Zaib and A. Zaman, Effects of entropy generation on Powell Eyring fluid in a porous channel, J. Braz. Soc. Mech. Sci. Eng., 39 (2017), 5027–5036.
[22]	M. S. Alam, M. A. Alim and M. A. Hakim, Entropy generation analysis for variable thermal conductivity MHD radiative nano-fluid flow through channel, J. Appl. Fluid. Mech., 9 (2016).
[23]	N. S. Akbar, Z. H. Khan and S. Nadeem, Influence of magnetic field and slip on Jeffrey fluid in a ciliated symmetric channel with metachronal wave pattern, J. Appl. Fluid. Mech., 9 (2016), 565–572.
[24]	N. S. Akbar, M. Shoaib and D. Tripathi, et al., Analytical approach to entropy generation and heat transfer in CNT-nano-fluid dynamics through a ciliated porous medium, J. Hydrodyn., 30 (2018), 296–306.
[25]	U. Mercke, The influence of varying air humidity on mucociliary activity, Acta. Oto-Laryngol., 79 (1975), 133–139.
[26]	S. N. Khaderi, C. B. Craus, J. Hussong, et al., Magnetically-actuated artificial cilia for microfluidic propulsion, Lab. Chip., 11 (2011), 2002–2010.
[27]	N. S. Akbar, D. Tripathi, Z. H. Khan, et al., Mathematical model for ciliary-induced transport in MHD flow of Cu-H₂O nano-fluids with magnetic induction, Chinese. J. Phys., 55 (2017), 947–962.
[28]	M. Hassan, A. Zeeshan, A. Majeed, et al., Particle shape effects on ferrofuids flow and heat transfer under influence of low oscillating magnetic field, J. Magn. Mater., 443 (2017), 36–44.
[29]	S. Rashidi, S. Akbar, M. Bovand, et al,. Volume of fluid model to simulate the nano-fluid flow and entropy generation in a single slope solar still, Renew. Energ., 115 (2018): 400–410.
[30]	M. Hassan, M. Marin, R. Ellahi, et al., Exploration of convective heat transfer and flow characteristics synthesis by Cu--Ag/water hybrid-nano-fluids, Heat. Transf. Res., 49 (2018).
[31]	A. Majeed, A. Zeeshan, A. Z. Sultan, et al., Heat transfer analysis in ferromagnetic viscoelastic fluid flow over a stretching sheet with suction, Neural. Comput. Appl., 30 (2018): 1947–1955.
[32]	A. Zeeshan, N. Ijaz, T. Abbas, et al., The sustainable characteristic of bio-bi-phase flow of peristaltic transport of MHD Jeffrey fluid in the human body, Sustainability-Basel., 10 (2018), 2671.
[33]	M. Akbarzadeh, S. Rashidi, N. Karimi, et al., Convection of heat and thermodynamic irreversibilities in two-phase, turbulent nano-fluid flows in solar heaters by corrugated absorber plates, Adv. Powder. Technol., 29 (2018), 2243–2254.
[34]	S. Z, Alamri, R. Ellahi, N. Shehzad, et al., Convective radiative plane Poiseuille flow of nano-fluid through porous medium with slip: An application of Stefan blowing, J. Mol. Liq., 273 (2019), 292–304.
[35]	N. Shehzad, A. Zeeshan, R. Ellahi, et al., Modelling study on internal energy loss due to entropy generation for non-darcy poiseuille flow of silver-water nano-fluid: An application of purification, Entropy, 20 (2018), 851.
[36]	M. M. Bhatti, A. Zeeshan, R. Ellahi, et al., Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy-Brinkman-Forchheimer porous medium, Adv. Powder. Technol., 29 (2018), 1189–1197.
[37]	R. Ellahi, S. Z. Alamri, A. Basit, et al., Effects of MHD and slip on heat transfer boundary layer flow over a moving plate based on specific entropy generation, J. Taibah. Uni. Sci., (2018), 1–7.
[38]	C. Fetecau, R. Ellahi, M. Khan, et al., Combined porous and magnetic effects on some fundamental motions of Newtonian fluids over an infinite plate, J. Porous. Media., 21 (2018).
[39]	S. Z. Alamri, A. A. Khan, M. Azeez, et al., Effects of mass transfer on MHD second grade fluid towards stretching cylinder: A novel perspective of Cattaneo--Christov heat flux model, Phys. Lett. A., 383 (2019), 276–281.
[40]	S. Z. Alamri, R. Ellahi, N. Shehzad, et al., Convective radiative plane Poiseuille flow of nano-fluid through porous medium with slip: An application of Stefan blowing, J. Mol. Liq., 273 (2019), 292–304.
[41]	T. Hayat, M. Shafique, A. Tanveer, et al., Magnetohydrodynamic effects on peristaltic flow of hyperbolic tangent nano-fluid with slip conditions and Joule heating in an inclined channel, Int. J. Heat. Mass. Tran., 102 (2016), 54–63.
[42]	A. M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, Beijing and Springer, Verlag Berlin Heidelberg, 2009.
[43]	A. M. Siddiqui, A. A. Farooq and M. A. Rana, Study of MHD effects on the cilia-induced flow of a Newtonian fluid through a cylindrical tube, Magnetohydrodynamics, 50 (2014), 249–261.

Reader Comments

Your name:*

Email:*
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)