### Study of Water and Ethylene Glycol Based Cu Nanoparticles inside Parallel Disks with VMHD

#### Abstract

In this article, we have developed a mathematical model for water and ethylene glycol based copper nanoparticles between two parallel Disks under the influence of variable magnetic field. Parametric study for the flow field, temperature variation and magnetic field are performed from the set of Navier-Stokes, Energy and from the Maxwell equations. Coupled system of PDE’s are converted into system of ODE’s by means of similarity transformations. Effects of various parameters, like, squeezing parameter S, Hartman number M, Reynolds number R and Prandtl number P_{r} on the physical properties of flow, temperature variation and magnetic field are discussed and graphed. For comparison numerical results obtained by Parametric Continuation Method and BVP4C package results are compared.

#### Keywords

#### Full Text:

PDF#### References

M. J. Stefan, VersuchÜber die scheinbare adhesion, Akademie der Wissenschaften, Mathematische – Naturwissenschaftliche, 69 (1874), 713–721.

J. Engmann, C. Servais, A. S. Burbidge, Squeeze flow theory and applications to rheometry: A review, Journal of Non-Newtonian Fluid Mechanics, 132 (2005), 1– 27.

P. S. Gupta, A.S. Gupta, Squeezing flow between parallel plates, Wear, 45 (2) (1977), 177-185.

A. R. A. Khaled, K. Vafai, Hydromagnetic squeezed flow and heat transfer over a sensor surface, Int. J. Eng. Sci. 42 (2004) 509–519.

M. M. Rashidi, H. Shahmohamadi, S. Dinarvand, Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates, Math. Prob. Eng. (2008) 935-945.

R. L. Verma, A numerical solution for squeezing flow between parallel channels, Wear,72(1981)89-95.

K. R. Rajagopal, R. Kumbakonam, A. S. Gupta, On a class of exact solutions to the equations of motion of a second grade fluid International Journal of Engineering Science,19(1981) 1009-1014.

M. M. Rashidi, H. Shahmohamadi, S. Dinarvard,Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates, Journal of Mathematical Problems in Engineering,(2008) https://doi.org/10.1155/2008/935095.

G. Domairry, A. Aziz, Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by homotopy perturbation method journal of Mathematical Problems in Engineering, 2009(603-916).

R. U. Haq, Z.Hammouch, W. A. Khan, water-based squeezing flow in the presence of carbon nanotubesbetween two parallel disks, Thermal Science. 20 (6) (2016) 1973-1981.

B. Hoffner, O. H. Campanella, M. G. Corradini, M. Peleg, Rheol. Acta 40, 289 (2001).

He JH. Some asymptotic methods for strongly nonlinear equations. International journal of Modern physics B. 2006 Apr 20;20(10):1141-99.

Sparrow EM, Beavers GS and Hung LY. Flow about a porous-surface rotating disk. Int J Heat Mass Transf 1971, 14 993–996.

Stuart JT. On the effect of uniform suction on the steady flow due to a rotating disk. Q. J Mech Appl Math 1954, 7 446–457.

Kuiken HK. The effect of normal blowing on the flow near a rotating disk of infinite extent. J. Fluid Mech 1971, 47 789–798.

M. Tabassum and M. Mustafa. A numerical treatment for partial slip flow and heat transferof non-Newtonian Reiner-Rivlin fluid due to rotating disk. Int J Heat Mass Transf 2018, 123 979–987.

A. Rauf, Z. Abbas and SA. Shehzad. Interactions of active and passive control of nanoparticles on radiative magnetohydrodynamics flow of nanofluid over oscillatory rotating disk in porous medium. J Nanofluids 2019, 8 1385–1396.

T.V. Karman, Uber laminare und turbulenteReibung, Z. Angew. Math. Mech. 1 (1921) 1233–1255.

G.N. Lance, M.M. Rogers, The axially symmetric flow of a viscous fluid between two infinite rotating disks, Proc. R. Soc. A 266 (1962) 109–121.

M. Holodniok, M. Kubicek, V. Hlavacek, Computation of the flow between two rotating coaxial disks, J. Fluid Mech. 81 (4) (1977) 689–699.

M. Mustafa, T. Hayat, S. Obaidat, On heat and mass transfer in the unsteady squeezing flow between parallel plates, Meccanica 47 (2012) 1581–1589.

### Refbacks

- There are currently no refbacks.

Copyright (c) 2022 Recent Trends in Fluid Mechanics