Abstract
In the present study, a single and discrete phase model is employed to obtain analytical solutions of velocity, temperature, and stream function to describe the transport characteristics of a newtonian blood-gold, silver, or copper nanofluid flowing through an inclined multiple stenose artery, under the influence of externally applied heat. The spherical gold nanoparticles are used for discrete phase model to track the nanoparticle in the blood flow within the artery containing multiple stenosis, which is not explored so far. Apart from estimating the velocity, temperature distributions, and stream function, an explicit expression is derived for wall shear stress distribution. The effects of different flow parameters are depicted through graphs for different values of interest. The results reveal that the hemodynamics effects of stenosis reduce with an increase of particle concentration in the blood and also finding that the drug gold nanoparticles are more effective to reduce hemodynamics of stenosis when compared to the drug silver or copper nanoparticle. The normal flow of blood is observed for only 0.03 volume fraction of gold nanoparticle. We also demonstrate that cylindrical-shaped nanoparticle is more effective for drug delivery than spherical shaped as it has less wall shearing stress. The significant effect of Brownian motion is observed on gold nanoparticle in two-phase model. This study would provide valuable information for nanoparticle distribution in a vascular artery in the field of nanoparticle drug delivery.
Similar content being viewed by others
References
Wooton, D.M., & Ku, D.N. (1999). Fluid mechanics of vascular systems, diseases and thrombosis. Annual Review of Biomedical Engineering, 1, 299–329.
Valipour, M., Ebrahim, M.B., & Seyyed Mahmood Reza, B. (2015). Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir. Journal of Hydrology, 476(1), 433–441.
Viero, D.P., & Valipour, M. (2017). Modeling anisotropy in free-surface overland and shallow inundation flows. Advances in Water Resources, 104, 1–14.
Valipour, M., Gholami Sefidkouhi, M.A., & Raeini-Sarjaz, M. (2017). Global experience on irrigation management under different scenarios. Journal of Water and Land Development, 32(1), 95–102.
Valipour, M. (2016). Variations of land use and irrigation for next decades under different scenarios. Irriga: Brazilian Journal of Irrigation and Drainage, 1(1), 262–288.
Valipour, M. (2016). How much meteorological information is necessary to achieve reliable accuracy for rainfall estimations? Agriculture, 6(4), 53, 1–9.
Valipour, M., Gholami Sefidkouhi, M.A., & Raeinisarjaz, M. (2017). Selecting the best model to estimate potential evapotranspiration with respect to climate change and magnitudes of extreme events. Agricultural Water Management, 180(Part A), 50–60.
Changdar, S., & De, S. (2015). Analysis of non-linear pulsatile blood flow in artery through a generalized multiple stenosis. Arabian Journal of Mathematics, 5, 51–61.
Nadeem, S., & Ijaz, S. (2015). Study of radially varying magnetic field on blood flow through catheterized tapered elastic artery with overlapping stenosis. Communications in Theoretical Physics, 64(5), 537–546.
Lee, K.W., & Xu, X.Y. (2002). Modelling of Flowand wall behaviour in a mildly stenosed tube. Medical Engineering and Physics, 24, 575–586.
Stroud, J.S., Berger, S.A., & Saloner, D. (2002). Numerical analysis of flow through a severely stenotic carotid artery bifurcation. Journal of Biomechanical Engineering, 124, 9–20.
Fischer, P.F., Loth, F., Lee, S.E., Lee, S.W., Smith, D., & Bassiouny, H. (2007). Simulation of high Reynolds number vascular flows. Computer Methods in Applied Mechanics and Engineering, 196, 3049–3060.
Chato, J.C. (1980). Heat transfer to blood vessels. Journal of Biomedical Engineering, 102, 110–118.
Arkin, H., Xu, L.X., & Holmes, K.R. (1994). Recent developments in modeling heat transfer in blood perfused tissues. IEEE Transactions on Biomedical Engineering, 41, 97–107.
Nadeem, S., & Ijaz, S. (2015). Influence of metallic nanoparticles on blood flow through arteries having both stenosis and aneurysm. IEEE Transactions on Nanobioscience, 14(6), 668–679.
Nadeem, S., & Ijaz, S. (2015). Theoretical analysis of metallic nanoparticles on blood flow through tapered elastic artery with overlapping stenosis. IEEE Transactions on NanoBioscience, 14(4), 417–428.
Nadeem, S., & Ijaz, S. (2016). Impulsion of nanoparticles as a drug carrier for the theoretical investigation of stenosed arteries with induced magnetic effects. Journal of Magnetism and Magnetic Materials, 410, 230–241.
Ijaz, S., & Nadeem, S. (2016). Slip examination on the wall of tapered stenosed artery with emerging application of nanoparticles. International Journal of Thermal Sciences, 109, 401– 412.
Ijaz, S., & Nadeem, S. (2016). Examination of nanoparticles as a drug carrier on blood flow through catheterized composite stenosed artery with permeable walls. Computer Methods and Programs in Biomedicine, 133, 83–94.
Efstathios, E.M. (2012). Transport properties of nanofluids. A critical review. Journal of Non-Equilibrium Thermodynamics, 38(1), 1– 79.
Taylor, R.A. (2013). Small particles, big impacts: a review of the diverse applications of nanofluids. Journal of Applied Physics, 113(1), 11301–11319.
Fullstone, G., Wood, J., Holcombe, M., & Battaglia, G. (2015). Modelling the transport of nanoparticles under blood flow using an agent-based approach. Nature Scientific reports, 5(10649), 1– 13.
Choi, S.U.S. (1995). Enhancing thermal conductivity of fluids with nanoparticles,developments and applications of non-Newtonian flows. In D. A. Siginer & H. P. Wang (Eds.), Proc. ASME: Fluids Eng. Div. (Vol. 231, pp. 99–105).
Nadeem, S., & Ijaz, S. (2015). Theoretical analysis of metallic nanoparticles on blood flow through tapered elastic artery with overlapping stenosis. IEEE Transactions on NanoBioscience, 14, 417–428.
Akbar, N.S., & Nadeem, S. (2013). Intestinal flow of a couple stress nanofluidin arteries. IEEE Transactions on NanoBioscience, 12, 332–339.
Nadeem, S., & Ijaz, S. (2016). Examination of nanoparticles as a drug carrier on blood flow through catheterized composite stenosed artery with permeable walls. Computer Methods and Programs in Biomedicine, 133, 83–94.
Nadeem, S., & Ijaz, S. (2015). Single wall carbon nanotube (SWCNT) examination on blood flow through a multiple stenosed artery with variable nanofluid viscosity. AIP Advances, 5(10), 107217,1–18.
Changdar, S., & De, S. (2017). Transport of spherical nanoparticles suspended in a blood flowing through stenose artery under the influence of Brownian motion. Journal of Nanofluids, 6(1), 87–96.
Gentile, F., Ferrari, M., & Decuzzi, P. (2007). The transport of nanoparticles in blood vessels, the effect of vessel permeability and blood rheology. Annals of Biomedical Engineering, 36, 254–261.
Ellahi, R., Rahman, S.U., Nadeem, S., & Akbar, N.S. (2014). Blood flow of nano fluid through an artery with composite stenosis and permeable walls. Applied Nanoscience, 4(8), 919–926.
Jain, S., Hirst, D.G., & Sullivan, J. (2012). Gold nanoparticles as novel agents for cancer therapy. The British Journal of Radiology, 85, 101–113.
Wang, X., Xu, X., & Choi, S.U.S. (1999). Thermal conductivity of nanoparticle fluid mixture. Journal of Thermophysics and Heat Transfer, 13, 474–480.
Li, A., & Ahmadi, G. (1992). Dispersion and deposition of spherical particles from point sources in a turbulent channel flow. Aerosol Science and Technology, 16, 209–226.
Dong, S.L., Zheng, L.C., Zhang, X.X., Wu, S.P., & Shen, B.Y. (2014). A new model for Brownian force and the application to simulating nanofluid flow. Microfluidics and Nanofluidics, 16, 131–139.
Acknowledgements
The authors thank to the reviewers for important comments and suggestions to revise and improve the manuscript. The authors grateful to Dr. Samiran Ghosh, Department of Applied Mathematics, University of Calcutta for fruitful discussions. This work is partially supported by CPEPA, UGC, New Delhi.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Changdar, S., De, S. Investigation of Nanoparticle as a Drug Carrier Suspended in a Blood Flowing Through an Inclined Multiple Stenosed Artery. BioNanoSci. 8, 166–178 (2018). https://doi.org/10.1007/s12668-017-0446-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12668-017-0446-7