Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T16:00:15.710Z Has data issue: false hasContentIssue false
  • English
  • Français

Temperature-Dependent Electrical Conductivity and Thermal Radiation Effects on MHD Peristaltic Motion of Williamson Nanofluids in a Tapered Asymmetric Channel

Published online by Cambridge University Press:  11 October 2019

W. M. Hasona Open the ORCID record for W. M. Hasona [Opens in a new window]
W. M. Hasona*
Affiliation:
Mathematics Department, Faculty of Science, Zagazig University, ZagazigEgypt.
*
*Corresponding author ([email protected])
Get access

Abstract

This paper is intended for dealing with the peristaltic flow of an electrically conducting Williamson nanofluid in a tapered asymmetric channel through a porous medium with heat and mass transfer. In the current paper, temperature-dependent electrical conductivity formulation was introduced for the first time in peristaltic literature. The flow is pervaded by an oblique uniform magnetic field. The present investigation includes the influences of thermal radiation, Joule heat, viscous dissipation, Hall Current, 1st order chemical reaction, and Dofour and Soret numbers. Current problem is reformulated under the molds of low Reynolds number and long wavelength approximation. Afterwards, semi analytical solutions have been evaluated for the distributions of velocity, temperature, nanoparticle concentrations as well as longitudinal pressure gradient. Solutions can be obtained by using multi-step differential transform method (MS-DTM), a reliable and powerful technique that improve accuracy and overcome drawbacks raised in using the standard differential transform method (DTM). Detailed comparisons have been made at different values of 𝑥 through graphs by Ms-DTM. The graphically results were prepared to visualize the effects of various physical parameters of interest. The semi-analytical results had shown that, as the thermal radiation increases, the nanoparticles diameter and concentration of fluid increase (thermal radiation is a decreasing function in temperature when the temperature decreases the diameter of the nanoparticles increases i.e. the volume of nanoparticle and its concentration increases and become more effective near to tumor tissues). Consequently, it can be used as agents for radiation therapy, generate localized raises in radiation doses and selectively target tumor cells for localized damage (Radiotherapy of oncology).

Keywords

PeristalsisThermal radiationTemperature dependent electrical conductivityWilliamson nanofluidMulti-step differential transform method (MS-DTM)
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 1 , February 2020 , pp. 103 - 118
Copyright
Copyright © 2019 The Society of Theoretical and Applied Mechanics 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Latham, T.W., Fluid Motions in a Peristaltic Pump(M.S. Thesis) MIT, Cambridge, MA, (1966).Google Scholar
Shapiro, A.H., Jaffrin, M.Y., Weinberg, S.L., “Peristaltic pumping with long wavelengths at low Reynolds number”, Journal of Fluid Mechanics, 37, pp. 799–825, (1969).CrossRefGoogle Scholar
Hariharan, V. S., Banerjee, R. K., “Peristaltic transport of non-Newtonian fluid in a diverging tube with different wave forms”, Mathematical and Computer Modeling, 48, pp. 998–1017, (2008).CrossRefGoogle Scholar
Ali, N. and Tasawar, H., “Peristaltic flow of a micro polar fluid in an asymmetric channel”, Computers and Mathematics with Applications, 55, pp. 589–608, (2008).CrossRefGoogle Scholar
Muthu, P., Rathish, B.V. and Peeyush, C., “Peristaltic motion of micro polar fluid in circular cylindrical tubes: Effect of wall properties”, Applied Mathematical Modeling, 32, pp. 2019–2033, (2008).CrossRefGoogle Scholar
Pozrikidis, C., “A study of peristaltic flow”, Journal of Fluid Mechanics, 180, pp. 515–527, (1986).CrossRefGoogle Scholar
Nagarani, P., “Peristaltic transport of a Casson fluid in an inclined channel”, Korea-Australia Rheology Journal, 22, pp.105–111, (2010).Google Scholar
Manton, M. J., “Long-wavelength peristaltic pumping at low Reynolds number”, Journal of Fluid Mechanics, 68, pp. 467–476, (1975).CrossRefGoogle Scholar
Williamson, R.V, The flow of pseudoplastic materials, Industrial & Engineering Chemistry, 21 (1929) 1108–1111.CrossRefGoogle Scholar
Malik, M. Y., Bilal, S., Salahuddin, T. and Rehman, K., Three-Dimensional Williamson Fluid Flow over a Linear Stretching Surface, Mathematical Sciences Letters, (2017) 53–61.CrossRefGoogle Scholar
MalikI, Z., Yousaf, M. and Nadeem, S., Numerical solutions of Williamson fluid with pressure dependent viscosity, Results in Physics , 5, (2015) 20–25.Google Scholar
Malik, M. Y., Bibi, M., Khan, F., and Salahuddin, T., Numerical solution of Williamson fluid flow past a stretching cylinder and heat transfer with variable thermal conductivity and heat generation/absorption, AIP Advances 6, 035101 (2016).CrossRefGoogle Scholar
Kothandapani, M. and Prakash, J., “Effects of thermal radiation parameter and magnetic field on the peristaltic motion of Williamson nanofluids in a tapered asymmetric channel”, International Journal of Heat and Mass Transfer, 81 pp. 234–245, (2015).CrossRefGoogle Scholar
Khanafer, K., Vafai, K. and Lightstone, M., “Buoyancy-driven heat transfer enhancement in a two dimensional enclosure utilizing nanofluids”, International Journal of Heat and Mass Transfer, 46, pp. 3639–3653, (2003).CrossRefGoogle Scholar
Dong, S., Zheng, L., Zhang, X. and Lin, P., “Improved drag force model and its application in simulating nanofluid flow”, Microfluidics and Nanofluidics, 17, pp. 253–261, (2014).CrossRefGoogle Scholar
Hayat, T., Shafique, M., Tanveer, A. and Alsaedi, A., “Magnetohydrodynamic effects on peristaltic flow of hyperbolic tangent nanofluid with slip conditions and Joule heating in an inclined channel”, International Journal of Heat and Mass Transfer, 102 pp. 54–63, (2016).CrossRefGoogle Scholar
Mustafa, M., Hina, S., Hayat, T. and Alsaedi, A., “Influence of wall properties on the peristaltic flow of a nanofluid: Analytic and numerical solutions”, International Journal of Heat and Mass Transfer 55, pp. 4871–4877, (2012).CrossRefGoogle Scholar
Hayat, T., Abbasi, F.M., Al-Yami, M. and Monaquel, S., “Slip and Joule heating effects in mixed convection peristaltic transport of nanofluid with Soret and Dufour effects”, Journal of Molecular Liquids, 194, pp. 93–99, (2014).CrossRefGoogle Scholar
Akbar, N. S., Raza, M. and Ellahi, R., “Peristaltic flow with thermal conductivity of H2O + Cu nanofluid and entropy generation”, Results in Physics, 5, pp. 115–124, (2015).CrossRefGoogle Scholar
Prakash, J., Sharma, A. and Tripathi, D., Thermal radiation effects on electroosmosis modulated peristaltic transport of ionic nanoliquids in biomicrofluidics channel, Journal of Molecular Liquids, 249 (2018) 843–855.CrossRefGoogle Scholar
Bhatti, M.M., Zeeshan, A., Ijaz, N., Anwar Beg, O. and Kadir, A., Mathematical modelling of nonlinear thermal radiation effects on EMHD peristaltic pumping of viscoelastic dusty fluid through a porous medium duct, Engineering Science and Technology, 20 (2017) 1129–1139.Google Scholar
Hayat, T., Rafiq, M. and Ahmad, B., Combined effects of rotation and thermal radiation on peristaltic transport of Jeffrey fluid, International Journal of Biomathematics, 8 (2015) 1550061–21.CrossRefGoogle Scholar
Sadia Ayub, T. Hayat, Asghar, S. and Ahmad, B., Thermal radiation impact in mixed convective peristaltic flow of third grade nanofluid, Results in Physics, 7 (2017) 3687–3695.CrossRefGoogle Scholar
Kothandapani, M. and Prakash, J., Influence of heat source, thermal radiation and inclined magnetic field on peristaltic flow of a hyperbolic tangent nanofluid in a tapered asymmetric channel, IEEE Transactions on NanoBioscience, (2013) 1536–1241.Google Scholar
Ramesh, K. and Devakar, M., “Effects of heat and mass transfer on the peristaltic transport of MHD couples stress fluid through porous medium in a vertical asymmetric channel”, Journal of Fluids, ID 163832, pp. 1–19, (2015).CrossRefGoogle Scholar
Shaaban, A. A. and Abouzeid, M. Y., “Effects of heat and mass transfer on MHD peristaltic flow of a Non-Newtonian fluid through a porous medium between two coaxial cylinders”, mathematical problems in Engineering, ID 819683, pp. 1–11, (2013).CrossRefGoogle Scholar
Eldabe, N.T., Elshaboury, S.M., Alfaisal, A. H. and Elogail, M.A., “MHD Peristaltic Flow of a Couple Stress Fluids with Heat and Mass Transfer through a Porous Medium”, Innovative Systems Design and Engineering, 3, pp. 51–67, (2012).Google Scholar
Zhou, J. K., Differential transformation and its applications for electrical circuits, Huazhong University Press, Wuhan, China, (1986).Google Scholar
Nourifar, M., Sani, and Keyhani, A., “Efficient multistep differential transform method: Theory and its application to nonlinear oscillators”, Communications in Nonlinear Science and Numerical Simulation, 17, pp. 1–64, (2016).Google Scholar
Zait, R.A., El-Shekhipy, A.A. and Abdo, N.M., “Statistical measures approximations for the Gaussian part of the stochastic nonlinear damped Duffing oscillator solution process under the application of Wiener Hermit expansion linked by the multi-step differential trans-formed method”, Journal of the Egyptian Mathematical Society, 1, (2016), 1–12.CrossRefGoogle Scholar
Odibat, Z. M., Bertelle, C., Aziz-Alaouic, M. A., Duchamp, G. H. E., “A multi-step differential transform method and application to non-chaotic or chaotic systems”, Computers and Mathematics with Applications, 59, (2010), 1462–1472.CrossRefGoogle Scholar
Hayashi, M., “temperature electrical conductivity relation of water for environmental monitoring and geophysical data inversion”, Environmental Monitoring and Assessment, 96, pp. 119–128, (2004).CrossRefGoogle ScholarPubMed
Sorensen, J. A. and Glass, G. E., “Ion and temperature dependence of electrical conductance for natural waters”, Analytical Chemical, 59, pp. 1594−159, (1987).CrossRefGoogle Scholar