Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-17T21:25:13.012Z Has data issue: false hasContentIssue false
  • English
  • Français

Heat Transfer in an Upper Convected Maxwell Fluid with Fluid Particle Suspension

Published online by Cambridge University Press:  28 May 2015

K. Vajravelu ,
K. V. Prasad  and
S. R. Santhi
K. Vajravelu*
Affiliation:
Department of Mathematics, Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, USA
K. V. Prasad
Affiliation:
Department of Mathematics, VSK University, Vinayaka Nagar, Bellary-583104, Karnataka, India
S. R. Santhi
Affiliation:
Department of Mathematics, Bangalore University, Bangalore-560001, Karnataka, India
*
*Corresponding author. Email: kuppalapalle.vajravelu@ucf.edu (K. Vajravelu)
Get access

Abstract

An analysis is carried out to study the magnetohydrodynamic (MHD) flow and heat transfer characteristics of an electrically conducting dusty non-Newtonian fluid, namely, the upper convected Maxwell (UCM) fluid over a stretching sheet. The stretching velocity and the temperature at the surface are assumed to vary linearly with the distance from the origin. Using a similarity transformation, the governing nonlinear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and the equations are solved numerically by a second order finite difference implicit method known as the Keller-box method. Comparisons with the available results in the literature are presented as a special case. The effects of the physical parameters on the fluid velocity, the velocity of the dust particle, the density of the dust particle, the fluid temperature, the dust-phase temperature, the skin friction, and the wall-temperature gradient are presented through tables and graphs. It is observed that, Maxwell fluid reduces the wall-shear stress. Also, the fluid particle interaction reduces the fluid temperature in the boundary layer. Furthermore, the results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the dusty UCM fluid flow phenomena.

Keywords

76W0576T2080A10Heat transferhydromagnetic flowUCM fluiddusty fluidfluid particle interaction
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 3 , June 2015 , pp. 369 - 386
Copyright
Copyright © Global-Science Press 2015 

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

[1]Sakiadis, B.C.Boundary-layer behavior on continuous solid surfaces I, The boundary layer on a equations for two dimensional and axisymmetricflow, AIChE. J., 7 (1961), pp. 26–28.CrossRefGoogle Scholar
[2]Crane, L.J.Flow past a stretching plate, ZAMP, 1 (1970), pp. 645–647.Google Scholar
[3]Grubka, L.G. and Bobba, K.M.Heat transfer characteristics of a continuous stretching surface with variable temperature, ASME J. Heat Trans., 107 (1985), pp. 248–250.CrossRefGoogle Scholar
[4]Dutta, B.K.Roy, P. and Gupta, A.S.Temperature field inflow over a stretching sheet with uniform heat flux, Int. Comm. Heat Mass Trans., 12 (1985), pp. 89–94.CrossRefGoogle Scholar
[5]Chen, C.K. and Char, M.I.Heat transfer of a continuous stretching surface with suction or blowing, J. Math. Anal. Appl., 135 (1988), pp. 568–580.CrossRefGoogle Scholar
[6]Ali, M.E.Heat transfer characteristics of a continuous stretching surface, Heat Mass Trans., 29 (1994), pp. 227–234.Google Scholar
[7]Ishak, A.Nazar, R. and Pop, I.Boundary layer flow and heat transfer over an unsteady stretching vertical surface, Meccanica, 44 (2009), pp. 369–375.Google Scholar
[8]Pavlov, K.B.Magnetohydrodynamicflow of an incompressible viscous fluid caused by deformation of a plane surface, Magnitnaya Gidrodinamika (USSR), 4 (1974), pp. 146–147.Google Scholar
[9]Chakrabarti, A. and Gupta, A.S.Hydromagnetic flow and heat transfer over a stretching sheet, Quart. Appl. Math., 37 (1979), pp. 73–78.CrossRefGoogle Scholar
[10]Rajagopal, K.R.Na, T.Y. and Gupta, A.S.Flow of a visco-elastic fluid over a stretching sheet, Rheol. Acta, 23 (1984), pp. 213–215.CrossRefGoogle Scholar
[11]Dandapat, B.S. and Gupta, A.S.Flow and heat transfer in a visco-elastic fluid over a stretching sheet, Int. J. Non-Linear Mech., 24 (1989), pp. 215–219.CrossRefGoogle Scholar
[12]Char, M.I.Heat and mass transfer in a hydromagnetic flow of a visco-elastic fluid over a stretching sheet, J. Math. Anal. Appl., 186 (1994), pp. 674–689.Google Scholar
[13]Cortell, R.A note on magnetohydrodynamic flow of a power law fluid over a stretching sheet, Appl. Math. Comput., 168 (2005), pp. 557–566.Google Scholar
[14]Bhatnagar, R.K.Gupt, G. and Rajagopal, K.R.Flow of an Oldroyd-B fluid due to a stretching sheet in the presence of a free stream velocity, Int. J. Non-Linear Mech., 30 (1995), pp. 391–405.CrossRefGoogle Scholar
[15]Renardy, M.High weissenberg number boundary layers for upper convected Maxwell fluid, J. Non-Newtonian Mech., 68 (1997), pp. 125–132.Google Scholar
[16]Hayat, T.Abbas, Z. and Sajid, M.Series solution for the upper-convected Maxwell fluid over a porous stretching plate, Phys. Lett. A, 358 (2006), pp. 396–403.CrossRefGoogle Scholar
[17]Sadeghy, K.Najafi, A.H. and Saffaripour, M.Sakiadis flow of an upper-convected Maxwell fluid, Int. J. Non-Linear Mech., 40 (2005), pp. 1220–1228Google Scholar
[18]Aliakbar, V.Alizadeh-Pahlavan, A. and Sadeghy, K.The influence of thermal radiation on MHD flow of Maxwellian fluids above stretching sheets, Comm. Non-linear Sci. Numer. Simulation, 14 (2009), pp. 779–794.Google Scholar
[19]Vajravelu, K.Prasad, K.V. and Sujatha, A.Convection heat transfer in a Maxwell fluid at a non-isothermal surface, Cent. Euro. J. Phys., 9 (2011), pp. 807–815.Google Scholar
[20]Prasad, K.V.Sujatha, A.Vajravelu, K. and Pop, I.MHD flow and heat transfer of a UCM fluid over a stretching surface with variable thermophysical properties, Meccanica, 47 (2012), pp. 1425–1439.CrossRefGoogle Scholar
[21]Saffman, P.G.On the stability of laminar flow of a dusty gas, J. Fluid. Mech., 13 (1962), pp. 120–128.CrossRefGoogle Scholar
[22]Datta, N. and Mishra, S.K.Boundary layer flow of a dusty fluid over a semi-infinite flat plate, Acta Mech., 42 (1982), pp. 71–83.CrossRefGoogle Scholar
[23]Vajravelu, K. and Nayfeh, J.Hydromagnetic flow of a dusty fluid over a stretching sheet, Int. J. Non-Linear Mech. 27 (1992), pp. 937–945.CrossRefGoogle Scholar
[24]Ming-Liang, XIE.Jian-Zhong, LIN and Fu-Tang, XINGOn the hydrodynamic stability of a particle-laden flow in growing flat plate boundary layer, J. Zhejiang Uni. SCI. A, 8 (2007), pp. 275–284.Google Scholar
[25]Vajravelu, K.Prasad, K.V. and Datti, P.S.Hydromagnetic fluid flow and heat transfer at a stretching sheet with fluid-particle suspension and variable fluid properties, J. Fluids Eng., 134 (2012), pp. 121001–121003.Google Scholar
[26]Chiam, T.C.Heat transfer in afluid with variable thermal conductivity over a stretching sheet, Acta Mech., 29 (1998), pp. 63–72.Google Scholar
[27]Vajravelu, K.Prasad, K.V. and Santhi, S.R.Axisymmetric magneto-hydrodynamic (MHD) flow and heat transfer at a non-isothermal stretching cylinder, Appl. Math. Comput., 219 (2012), pp. 3993–4005.Google Scholar
[28]Cebeci, T. and Bradshaw, P.Physical and Computational Aspects of Convective Heat Transfer, Springer-Verlag, New York, 1984.CrossRefGoogle Scholar
[29]Keller, H.B.Numerical Methods for Two-Point Boundary Value Problems, Dover Publ., New York, 1992.Google Scholar
[30]Andersson, H.I.Bech, K.H. and Dandapat, B.S.Magneto-hydrodynamic flow of a power law fluid over a stretching sheet, Int. J. Non-Linear Mech., 27 (1992), pp. 929–936.CrossRefGoogle Scholar