MHD Flow of a Carreau Fluid Past a Stretching Cylinder with Cattaneo-Christov Heat Flux Using Spectral Relaxation Method

Article Preview

Abstract:

A theoretical investigation of a hydromagnetic boundary layer flow of Carreau fluid over a stretching cylinder with surface slippage and temperature jump is presented in this paper. It is assumed that heat transfer characteristics of the flow follows Cattaneo-Christov heat flux model base on conventional Fourier’s law with thermal relaxation time. The spectral relaxation method (SRM) is being utilized to provide the solution of highly nonlinear system of coupled partial differential equations converted into dimensionless governing equations. The behaviour of flow parameters on velocity, temperature distributions are sketched as well as analyzed physically. The result indicates that the temperature distribution decay for higher temperature jump and thermal relaxation parameters respectively.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

91-105

Citation:

Online since:

September 2018

Export:

Price:

* - Corresponding Author

[1] L.J. Crane, Flow past a stretching plate, Z. Angew. Math. Phys. 21(1970) 645-647.

Google Scholar

[2] P. S. Gupta, A.S. Gupta, Heat and mass transfer on a stretching sheet with suction or blowing, Can.J. Chem. Eng. 55 (1977) 744-746.

DOI: 10.1002/cjce.5450550619

Google Scholar

[3] B.K. Dutta, P. Roy, A.S. Gupta, Temperature field in flow over a stretching sheet with uniform heat flux, Int.Comm. Heat Mass Transfer, 12 (1985) 89–94.

DOI: 10.1016/0735-1933(85)90010-7

Google Scholar

[4] C.K. Chen, M.I. Char, Heat transfer of a continuous, stretching surface with suction or blowing, J. Math.Anal. Appl. 135 (1988), 568-580.

DOI: 10.1016/0022-247x(88)90172-2

Google Scholar

[5] H. Xu, S.J. Liao, Series solutions of unsteady magneto hydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate, J. Nonnewton. FluidMech.129 (2005) 46-55.

DOI: 10.1016/j.jnnfm.2005.05.005

Google Scholar

[6] R. Cortell, Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/absorption and suction/blowing,Fluid Dyn.Res. 37 (2005) 231-245.

DOI: 10.1016/j.fluiddyn.2005.05.001

Google Scholar

[7] R. Cortell, Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet, Phys. Lett. A. 357 (2006) 298-305.

DOI: 10.1016/j.physleta.2006.04.051

Google Scholar

[8] O.D. Makinde,P. Sibanda, Effects of chemical reaction on boundary layer flow past a vertical stretching surface in the presence of internal heat generation, International Journal of Numerical Methods for Heat& Fluid Flow, 21(2011) 779-792.

DOI: 10.1108/09615531111148509

Google Scholar

[9] O.D. Makinde, F. Mabood, W.A. Khan, M.S. Tshehla, MHD flow of a variable viscosity nanofluid over a radially stretching convective surface with radiative heat, Journal of Molecular Liquids, 219 (2016) 624-630.

DOI: 10.1016/j.molliq.2016.03.078

Google Scholar

[10] P.J. Carreau, Rheological Equations from Molecular Network Theories, Trans. Soc. Rheol. 116(1972) 99-127.

Google Scholar

[11] R.P. Chhabra, P.H.T. Uhlherr, Creeping Motion of Spheres Through Shear-Thinning Elastic Fluids Described by the Carreau Viscosity Equation, Rheol. Acta. 19(1980) 187–195.

DOI: 10.1007/bf01521930

Google Scholar

[12] M.B. Bush, N. Phan-Thein, Drag Force on a Sphere in Creeping Motion through a Carreau Model Fluid,J. Non-Newtonian Fluid Mech. 16 (1984) 303–313.

DOI: 10.1016/0377-0257(84)85016-8

Google Scholar

[13] K. Khellaf, G. Lauriat, Numerical Study of Heat Transfer in a Non-Newtonian Carreau-Fluid between Rotating Concentric Vertical Cylinders,J. Non-Newtonian Fluid Mech. 89 (2000) 45–61.

DOI: 10.1016/s0377-0257(99)00030-0

Google Scholar

[14] R.R. Martins, F.S. Silveira, M.L. Martins-Costa, S. Frey, Numerical Investigation of Inertia and Shear- Thinning Effects in Axisymmetric Flows of Carreau Fluids by a Galerkin Least-Squares Method, Latin Amer. Appl. Res. 38 (2008) 321–328.

Google Scholar

[15] C.Cattaneo, Sullaconduzionedelcalore. AttidelSeminario Matematicoe Fisico dell Universitadi Modenae Reggio Emilia.3 (1948) 83–101.

Google Scholar

[16] C.I. Christov, On frame in different formulation of the Maxwell–Cattaneo model of finite-speed heat conduction, Mech. Res. Commun. 36 (2009) 481–486.

DOI: 10.1016/j.mechrescom.2008.11.003

Google Scholar

[17] B. Straughan, Thermal convection with the Cattaneo–Christov model, Int. J. Heat Mass Transf. 53 (2010) 95–98.

DOI: 10.1016/j.ijheatmasstransfer.2009.10.001

Google Scholar

[18] T. Hayat,M. Imtiaz, A. Alsaedi,S. Almezal, On Cattaneo–Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous-heterogeneous reactions, J. Mag. Mat. 401 (2016) 296-303.

DOI: 10.1016/j.jmmm.2015.10.039

Google Scholar

[19] P.K. Kundu, T. Chakraborty, K. Das, Framing the Cattaneo–Christov heat flux phenomena on CNT- based maxwell nanofluid along stretching sheet with sultiple slips, Arab J Sci Eng.43 (2018) 1177-1188.

DOI: 10.1007/s13369-017-2786-6

Google Scholar

[20] S. Oyelakin, S. Mondal, P. Sibanda, Cattaneo–Christov Nanofluid Flow and Heat Transfer with Variable Properties Over a Vertical Cone in a Porous Medium, Int. J. Appl. Comput. Math.3 (2017) 1019-1034.

DOI: 10.1007/s40819-017-0396-3

Google Scholar

[21] M. Farooq, S. Ahmad, M. Javed, Aisha Anjum, Analysis of Cattaneo-Christov heat and mass fluxes in the squeezed flow embedded in porous medium with variable mass diffusivity, Results in Physics. 7 (2017) 3788–3796.

DOI: 10.1016/j.rinp.2017.09.025

Google Scholar

[22] J. H. Merkin, I. Pop, Conjugate free convection on a vertical surface, Int. J. Heat Mass Transf. 39 (1996) 1527–1534.

DOI: 10.1016/0017-9310(95)00238-3

Google Scholar

[23] J.H. Merkin, Natural convection boundary-layer flow on a vertical surface with Newtonian heating, Int. J. Heat Fluid Flow.15 (1994) 392–398.

DOI: 10.1016/0142-727x(94)90053-1

Google Scholar

[24] A. Aziz, A similarity solution for laminar thermal boundary layer over flat plate with convective surface boundary condition, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 1064–1068.

DOI: 10.1016/j.cnsns.2008.05.003

Google Scholar

[25] A. Ishak, Similarity solutions for flow and heat transfer over permeable surface with convective boundary conditions, Appl. Math. Comput. 217 (2010) 837-842.

DOI: 10.1016/j.amc.2010.06.026

Google Scholar

[26] E. Magyari, Comment on A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, by A. Aziz, Comm. Nonlinear Sci. Numer. Simul. 14 (2009).

DOI: 10.1016/j.cnsns.2010.03.020

Google Scholar

[27] R. C. Bataller, Similarity solutions for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface, J. Mater. Process. Technol. 203(2008) 176–183.

DOI: 10.1016/j.jmatprotec.2007.09.055

Google Scholar

[28] S. Yao, T. Fang, Y. Zhong, Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions, Commun. Nonlinear Sci. Numer. Simul. 16 (2011) 752–760.

DOI: 10.1016/j.cnsns.2010.05.028

Google Scholar

[29] M. M. Rahman, J.H. Merkin, I. Pop, Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition, Acta Mech., 226 (2015) 2441-2460.

DOI: 10.1007/s00707-015-1334-2

Google Scholar

[30] M. Ramzan, M. Bilal, Jae Dong Chung, A.B. Mann,On MHD radiative Jeffery nanofluid flow with convective heat and mass boundary conditions, Neural Comput & Applic., (2017)1-10. DOI 10.1007/s00521-017-2852-8.

DOI: 10.1007/s00521-017-2852-8

Google Scholar

[31] S.M. Ibrahim, P.V. Kumar, G. Lorenzini, E. Lorenzini, F. Mabood, Numerical Study of the Onset of Chemical Reaction and Heat Source on Dissipative MHD Stagnation Point Flow of Casson Nanofluid over a Nonlinear Stretching Sheet with Velocity Slip and Convective Boundary Conditions, Journal of Engineering Thermophysics.26 (2017).

DOI: 10.1134/s1810232817020096

Google Scholar

[32] O.D. Makinde, N. Sandeep, I.L. Animasaun, M.S. Tshehla, Numerical exploration of Cattaneo-Christov heat flux and mass transfer in magnetohydrodynamic flow over various geometries, Defect and Diffusion Forum, 374 (2017) 67-82.

DOI: 10.4028/www.scientific.net/ddf.374.67

Google Scholar

[33] S. Das, R.N. Jana, O.D. Makinde, Slip flow and radiative heat transfer on a convectively heated vertical cylinder, Journal of Engineering Physics and Thermophysics. 90 (2017) 568-574.

DOI: 10.1007/s10891-017-1602-1

Google Scholar

[34] K.U. Rehman, A.A. Khan, M.Y. Malik, O.D. Makinde, Thermophysical aspects of stagnation point magnetonanofluid flow yields by an inclined stretching cylindrical surface: a non-Newtonian fluid model, Journal of Braz. Soc. Mech. Sci. Eng. 39 (2017).

DOI: 10.1007/s40430-017-0860-3

Google Scholar

[35] P.R. Sharma, S. Choudhary, O.D. Makinde, MHD slip flow and heat transfer over an exponentially stretching permeable sheet embedded in a porous medium with heat source, Frontiers in Heat and Mass Transfer, 9 (2017) 1-7.

DOI: 10.5098/hmt.9.18

Google Scholar

[36] S.U. Mamatha, Mahesha, C.S.K. Raju, O.D. Makinde, Effect of convective boundary conditions on MHD Carreau dusty fluid over a stretching sheet with heat source, Defect and Diffusion Forum, 377 (2017) 233-241.

DOI: 10.4028/www.scientific.net/ddf.377.233

Google Scholar

[37] O.D. Makinde, Computational modelling of MHD unsteady flow and heat transfer over a flat plate with Navier slip and Newtonian heating. Brazilian Journal of Chemical Engineering, 29 (2012) 159-166.

DOI: 10.1590/s0104-66322012000100017

Google Scholar

[38] O.D. Makinde, Heat and mass transfer by MHD mixed convection stagnation point flow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation, Meccanica, 47 (2012) 1173-1184.

DOI: 10.1007/s11012-011-9502-5

Google Scholar

[39] R.R. Rangi, N. Ahmad, Boundary layer flow past a stretching cylinder and heat transfer with variable thermal conductivity, Applied Mathematics, 3 (2012) 205–209.

DOI: 10.4236/am.2012.33032

Google Scholar

[40] V. Poply, P. Singh, K.K. Chaudhary, Analysis of laminar boundary layer flow along a stretching cylinder in the presence of thermal radiation, WSEAS Trans Fluid Mech. 4 (2013) 159-164.

Google Scholar

[41] Hashim, M. Khan, A. Saleh Alshomrani, Characteristics of melting heat transfer during flow of Carreau fluid induced by a stretching cylinder, Eur. Phys. J. E.40 (2017) 8, DOI 10.1140/epje/i2017-11495-6.

DOI: 10.1140/epje/i2017-11495-6

Google Scholar

[42] R.B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids (Wiley, New York, 1987).

Google Scholar

[43] S.S. Motsa, Z.G. Makukula, On spectral relaxation method approach for steady von kárman flow of a reiner-rivlin fluid with joule heating, viscous dissipation and suction/injection, Cent. Eur. J. Phys. 11(2013) 363–374.

DOI: 10.2478/s11534-013-0182-8

Google Scholar

[44] P. Kameswaran, P. Sibanda, S.S. Motsa, A spectral relaxation method for thermal dispersion and radiation effects in a nanofluid flow, Boundary Value Problems, 242 (2013).

DOI: 10.1186/1687-2770-2013-242

Google Scholar

[45] O.D. Makinde, W.A. Khan, Z.H. Khan, Stagnation point flow of MHD chemically reacting nanofluid over a stretching convective surface with slip and radiative heat.Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering. 231(4) (2017).

DOI: 10.1177/0954408916629506

Google Scholar

[46] A. Alizadeh-Pahlavan, V. Aliakbar, F. Vakili-Farahani, K. Sadeghy, MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method, Commun Nonlinear Sci Numer Simul. 14 (2009) 473–488.

DOI: 10.1016/j.cnsns.2007.09.011

Google Scholar

[47] M. Naseer, M. Y. Malik, S. Nadeem, A. Rehman, The boundary layer flow of hyperbolic tangent fluid over a vertical exponentially stretching cylinder, Alexandria Engineering Journal. 53 (2014) 747–750.

DOI: 10.1016/j.aej.2014.05.001

Google Scholar