American Journal of Mechanical Engineering
ISSN (Print): 2328-4102 ISSN (Online): 2328-4110 Website: http://www.sciepub.com/journal/ajme Editor-in-chief: Kambiz Ebrahimi, Dr. SRINIVASA VENKATESHAPPA CHIKKOL
Open Access
Journal Browser
Go
American Journal of Mechanical Engineering. 2015, 3(1), 16-20
DOI: 10.12691/ajme-3-1-3
Open AccessArticle

Flow of a Maxwell Fluid in a Porous Orthogonal Rheometer under the Effect of a Magnetic Field

H. Volkan Ersoy1,

1Department of Mechanical Engineering, Yildiz Technical University, Istanbul, Turkey

Pub. Date: February 12, 2014

Cite this paper:
H. Volkan Ersoy. Flow of a Maxwell Fluid in a Porous Orthogonal Rheometer under the Effect of a Magnetic Field. American Journal of Mechanical Engineering. 2015; 3(1):16-20. doi: 10.12691/ajme-3-1-3

Abstract

The steady flow of a Maxwell fluid in a porous orthogonal rheometer with the application of a magnetic field is studied. It is shown that there exists an exact solution for the problem. The effects of the parameters controlling the flow are analyzed by plotting graphs. It is observed that the effects of the Deborah number, the suction/injection velocity parameter, and the Reynolds number in the absence of a magnetic field are similar to those in the presence of a magnetic field. It is displayed that the Hartmann number that is based on the applied magnetic field reveals the tendency to slow down the flow.

Keywords:
magnetohydrodynamics Maxwell fluid orthogonal rheometer porous disk exact solution

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Maxwell, B. and Chartoff, R.P., “Studies of a polymer melt in an orthogonal rheometer,” Transactions of the Society of Rheology, 9 (1), 41-52, 1965.
 
[2]  Abbott, T.N.G. and Walters, K., “Rheometrical flow systems: Part2. Theory for the orthogonal rheometer, including an exact solution of the Navier-Stokes equations,” Journal of Fluid Mechanics, 40 (1), 205-213, 1970.
 
[3]  Rajagopal, K.R., “On the flow of a simple fluid in an orthogonal rheometer,” Archive for Rational Mechanics and Analysis, 79 (1) 39-47, 1982.
 
[4]  Rajagopal, K.R., “Flow of viscoelastic fluids between rotating disks,” Theoretical and Computational Fluid Dynamics, 3 (4), 185-206, 1992.
 
[5]  Srinivasa, A.R., “Flow characteristics of a multiconfigurational, shear thinning viscoelastic fluid with particular reference to the orthogonal rheometer,” Theoretical and Computational Fluid Dynamics, 13 (5), 305-325, 2000.
 
[6]  Ersoy, H.V., “On the locus of stagnation points for a Maxwell fluid in an orthogonal rheometer,” International Review of Mechanical Engineering, 3 (5), 660-664, 2009.
 
[7]  Mohanty, H.K., “Hydromagnetic flow between two rotating disks with noncoincident parallel axes of rotation,” Physics of Fluids, 15 (8), 1456-1458, 1972.
 
[8]  Rao, R. and Rao, P.R., “MHD flow of a second grade fluid in an orthogonal rheometer,” International Journal of Engineering Science, 23 (12), 1387-1395, 1985.
 
[9]  Kasiviswanathan, S.R. and Rao, A.R., “On exact solutions of unsteady MHD flow between eccentrically rotating disks,” Archiwum Mechaniki Stosowanej, 39 (4), 411-418, 1987.
 
[10]  Kasiviswanathan, S.R. and Gandhi, M.V., “A class of exact solutions for the magnetohydrodynamic flow of a micropolar fluid,” International Journal of Engineering Science, 30 (4), 409-417, 1992.
 
[11]  Ersoy, H.V., “MHD flow of an Oldroyd-B fluid between eccentric rotating disks,” International Journal of Engineering Science, 37 (15), 1973-1984, 1999.
 
[12]  Siddiqui, A.M., Rana, M.A. and Ahmed, N., “Magnetohydrodynamics flow of a Burgers' fluid in an orthogonal rheometer,” Applied Mathematical Modelling, 34 (10), 2881-2892, 2010.
 
[13]  Guria, M., Das, B.K., Jana, R.N. and Imrak, C.E., “Hydromagnetic flow between two porous disks rotating about non-coincident axes,” Acta Mechanica Sinica, 24 (5), 489-496, 2008.
 
[14]  Das, S., Jana, M. and Jana, R.N, “Unsteady hydromagnetic flow due to concentric rotation of eccentric disks,” Journal of Mechanics, 29 (1), 169-176, 2013.
 
[15]  Ersoy, H.V., “Unsteady flow due to a sudden pull of eccentric rotating disks,” International Journal of Engineering Science, 39 (3), 343-354, 2001.
 
[16]  Asghar, S., Mohyuddin, M.R. and Hayat, T., “Effects of Hall current and heat transfer on flow due to a pull of eccentric rotating disks,” International Journal of Heat and Mass Transfer, 48 (3-4), 599-607, 2005.
 
[17]  Siddiqui, A.M., Rana, M.A. and Ahmed, N., “Effects of Hall current and heat transfer on MHD flow of a Burgers' fluid due to a pull of eccentric rotating disks,” Communications in Nonlinear Science and Numerical Simulation, 13 (8), 1554-1570, 2008.
 
[18]  Hayat, T., Maqbool, K. and Khan, M., “Hall and heat transfer effects on the steady flow of a generalized Burgers' fluid induced by a sudden pull of eccentric rotating disks,” Nonlinear Dynamics, 51 (1-2), 267-276, 2008.
 
[19]  Hayat, T., Maqbool, K. and Asghar, S., “Hall and heat transfer effects on the steady flow of a Sisko fluid”, Zeitschrift für Naturforschung A, 64 (12), 769-782, 2009.
 
[20]  Ersoy, H.V., “Flow of a second order/grade fluid induced by a pull of disks in an orthogonal rheometer under the effect of a magnetic field,” International Review of Mechanical Engineering, 6 (5), 966-971, 2012.
 
[21]  Hsiao, K.-L., “MHD mixed convection for viscoelastic fluid past a porous wedge,” International Journal of Non-Linear Mechanics, 46 (1), 1-8, 2011.
 
[22]  Hsiao, K.-L., “MHD stagnation point viscoelastic fluid flow and heat transfer on a thermal forming stretching sheet with viscous dissipation,” The Canadian Journal of Chemical Engineering, 89 (5), 1228-1235, 2011.
 
[23]  Hsiao, K.-L., “Viscoelastic fluid over a stretching sheet with electromagnetic effects and non-uniform heat source/sink,” Mathematical Problems in Engineering, 2010 (Article ID 740943), 1-14, 2010.
 
[24]  Hsiao, K.-L., “Conjugate heat transfer for mixed convection and Maxwell fluid on a stagnation point,” Arabian Journal for Science and Engineering, 39 (6), 4325-4332, 2014.
 
[25]  Ersoy, H.V, “Flow of a Maxwell fluid between two porous disks rotating about noncoincident axes,” Advances in Mechanical Engineering, 2014 (Article ID 347196), 1-7, 2014.
 
[26]  Rajagopal, K.R. and Bhatnagar, R.K, “Exact solutions for some simple flows of an Oldroyd-B fluid,” Acta Mechanica, 113 (1-4), 233-239, 1995.
 
[27]  Hayat, T., Nadeem, S. and Asghar, S., “Hydromagnetic Couette flow of an Oldroyd-B fluid in a rotating system,” International Journal of Engineering Science, 42 (1), 65-78, 2004.
 
[28]  Hayat, T., Khan, M. and Ayub, M., “Exact solutions of flow problems of an Oldroyd-B fluid,” Applied Mathematics and Computation, 151 (1), 105-119, 2004.