On Spectral Relaxation Approach to Radiating Powell-Eyring Fluid Flow over a Stretching Disk with Newtonian Heating

Abstract:

In this study we use a new spectral relaxation method to investigate an axisymmetric law laminar boundary layer flow of a viscous incompressible non-Newtonian Eyring-Powell fluid and heat transfer over a heated disk with thermal radiation and Newtonian heating. The transformed boundary layer equations are solved numerically using the spectral relaxation method that has been proposed for the solution of nonlinear boundary layer equations. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity and temperature profiles. We show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to common numerical methods for solving nonlinear boundary value problems. We show that the convergence rate of the spectral relaxation method is significantly improved by using method in conjunction with the successive over-relaxation method. It is observed that CPU time is reduced in SOR method compare with SRM method.

• Periodical: Defect and Diffusion Forum (Volume 387)
• Pages: 461-473
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.387.461
• Online since: September 2018
• Authors: K. Gangadhar, D. Vijaya Kumar, S. Mohammed Ibrahim*, Oluwole Daniel Makinde
• Keywords: Heated Disk, Newtonian Heating, Powell-Eyring Fluid, Spectral Relaxation Method

References

[1] R. E. Powell, H. Eyring, Mechanisms for the relaxation theory of viscosity, Nature 154 (3909) (1944) 427–428.

DOI: 10.1038/154427a0

[2] M. Patel, M. G. Timol, Numerical treatment of Powell-Eyring fluid flow using method of satisfaction of asymptotic boundary conditions (MSABC), Appl. Numer. Math. 59 (2009) 2584– 2592.

DOI: 10.1016/j.apnum.2009.04.010

[3] V. Sirohi, M. G. Timol, N. L. Kalthia, Powell-Eyring model flow near an accelerated plate, Fluid Dyn. Res. 2 (3) (1987) 193–204.

DOI: 10.1016/0169-5983(87)90029-3

[4] H. K. Yoon, A. J. Ghajar, A note on the Powell-Eyring fluid model, Int. Commun. Heat Mass Transfer 14 (4) (1987) 381– 390.

DOI: 10.1016/0735-1933(87)90059-5

[5] S. Nadeem, N. S. Akbar, M. Ali, Endoscopic effects on the peristaltic flow of an Eyring-Powell fluid, Meccanica 47 (3) (2012) 687–697.

DOI: 10.1007/s11012-011-9478-1

[6] J. Rahimi, D. D. Ganji, M. Khaki, K. Hosseinzadeh, Solution of the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linear stretching sheet by collocation method, Alexandria Engineering Journal, (2017), 56, 621–627.

DOI: 10.1016/j.aej.2016.11.006

[7] T. Hayat, S. Nadeem, Flow of 3D Eyring-Powell fluid by utilizing Cattaneo-Christov heat flux model and chemical processes over an exponentially stretching surface, Results in Physics, 8, (2018), 397–403.

DOI: 10.1016/j.rinp.2017.12.038

[8] K. Parand, Z. Kalantari, M. Delkhosh, Solving the boundary layer flow of Eyring–Powell fluid problem via quasilinearization–collocation method based on Hermite functions, INAE Letters, 3(1) (2018) 11-19.

DOI: 10.1007/s41403-018-0033-4

[9] A. Rauf, Z. Abbas, S. A. Shehzad, A. Alsaedi, T. Hayat Numerical simulation of chemically reactive Powell-Eyring liquid flow with double diffusive Cattaneo-T.Christov heat and mass flux theories. Applied Mathematics and Mechanics (English Edition) 39(4) (2018).

DOI: 10.1007/s10483-018-2314-8

[10] S. Farooq, T. Hayat, B. Ahmad, A. Alsaedi, MHD flow of Eyring-Powell liquid in convectively curved configuration, Journal of the Brazilian Society of Mechanical Sciences and Engineering 40 (2018) 159, https://doi.org/10.1007/s40430-018-1071-2.

DOI: 10.1007/s40430-018-1071-2

[11] A. Hussain, M. Y. Malik, M. Awais, T. Salahuddin, S. Bilal, Computational and physical aspects of MHD Prandtl-Eyring fluid flow analysis over a stretching sheet, Neural Comput & Applic., (2017), pp.1-9, DOI 10.1007/s00521-017-3017-5.

DOI: 10.1007/s00521-017-3017-5

[12] W. Ibrahim, Three dimensional rotating flow of Powell-Eyring nanofluid with non-Fourier's heat flux and non-Fick's mass flux theory, Results in Physics 8 (2018) 569–577.

DOI: 10.1016/j.rinp.2017.12.034

[13] A. Ogulu, O. D. Makinde, Unsteady hydromagnetic free convection flow of a dissipative and radiating fluid past a vertical plate with constant heat flux. Chemical Engineering Communications 196(4) (2009) 454-462.

DOI: 10.1080/00986440802484531

[14] O. D. Makinde, MHD mixed-convection interaction with thermal radiation and nth order chemical reaction past a vertical porous plate embedded in a porous medium. Chemical Engineering Communications,198(4) (2011) 590-608.

DOI: 10.1080/00986445.2010.500151

[15] O. D. Makinde, R. J. Moitsheki, On non-perturbative techniques for thermal radiation effect on natural convection past a vertical plate embedded in a saturated porous medium. Mathematical Problems in Engineering, 2008 (2008) 689074 (11pages).

DOI: 10.1155/2008/689074

[16] R. P. Sharma, K. Avinash, N. Sandeep, O.D. Makinde, Thermal radiation effect on non-Newtonian fluid flow over a stretched sheet of non-uniform thickness. Defect and Diffusion Forum, 377 (2017) 242-259.

DOI: 10.4028/www.scientific.net/ddf.377.242

[17] M. A. El-Aziz, Radiation effect on the flow and heat transfer over an unsteady stretching sheet. Int. Commun. Heat Mass Transf. 36 (2009)521-524.

DOI: 10.1016/j.icheatmasstransfer.2009.01.016

[18] R. S. Telles, O. V. Trevisan, Dispersion in heat and mass transfer natural convection along vertical boundaries in porous media. Int. J. Heat Mass Transf. 36 (1993)1357-1365.

DOI: 10.1016/s0017-9310(05)80103-6

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

DOI: 10.1186/1687-2770-2013-242

[20] O.D. Makinde, I. L. Animasaun, Bioconvection in MHD nanofluid flow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolution. International Journal of Thermal Sciences, 109 (2016).

DOI: 10.1016/j.ijthermalsci.2016.06.003

[21] 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

[22] 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

[23] O.D. Makinde, Effects of viscous dissipation and Newtonian heating on boundary layer flow of nanofluids over a flat plate. International Journal of Numerical Methods for Heat and Fluid flow, 23(8) (2013) 1291-1303.

DOI: 10.1108/hff-12-2011-0258

[24] O.D. Makinde, Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating. Applied Mathematics and Mechanics, English Edition, 33(12) (2012) 1545–1554.

DOI: 10.1007/s10483-012-1642-8

[25] O.D. Makinde, P.O. Olanrewaju, Combined effects of internal heat generation and buoyancy force on boundary layer flow over a vertical plate with a convective surface boundary condition.Canadian Journal of Chemical Engineering, 90(2012) 1289–1294.

DOI: 10.1002/cjce.20614

[26] G. Singh, O. D. Makinde, Computational dynamics of MHD free convection flow along an inclined plate with Newtonian heating in the presence of volumetric heat generation, Chemical Engineering Communications, 199(9) (2012) 1144-1154.

DOI: 10.1080/00986445.2011.651184

[27] S. Das, R. N. Jana, O. D. Makinde, Natural convection near a moving vertical plate with ramped heat and mass fluxes in the presence of thermal radiation. Defect and Diffusion Forum, 377(2017) 211-232.

DOI: 10.4028/www.scientific.net/ddf.377.211

[28] S. Das, R. N. Jana, O. D. Makinde, MHD Boundary layer slip flow and heat transfer of nanofluid past a vertical stretching sheet with non-uniform heat generation/absorption. International Journal of Nanoscience, 13(3) (2014) 1450019(12pages).

DOI: 10.1142/s0219581x14500197

[29] 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(3) (2017) 568 -574.

DOI: 10.1007/s10891-017-1602-1

[30] I. Ullah, S. Shafie, I. Khan, Effects of slip condition and Newtonian heating on MHD flow of Casson fluid over a nonlinearly stretching sheet saturated in a porous medium, Journal of King Saud University - Science 29 (2017) 250–259.

DOI: 10.1016/j.jksus.2016.05.003

[31] I. Khan, M. Y. Malik, T. Salahuddin, M. Khan, K. U. Rehman, Homogenous-heterogeneous reactions in MHD flow of Powell-Eyring fluid over a stretching sheet with Newtonian heating, Neural Comput & Applic., (2017) 1-8, DOI 10.1007/s00521-017-2943-6.

DOI: 10.1007/s00521-017-2943-6

[32] S. S. Motsa, O. D. Makinde, S. Shateyi, On the successive linearisation approach to the flow of reactive third-grade liquid in a channel with isothermal walls. Mathematical Problems in Engineering,2013 (2013) 635392(7pages).

DOI: 10.1155/2013/635392

[33] S. S. Motsa (2014), a new spectral relaxation method for similarity variable nonlinear boundary layer flow systems, Chemical Engineering Communications, 201(2) (2014) 241-256.

DOI: 10.1080/00986445.2013.766882

[34] C. Canuto, M. V. Hussaini, A. Quarteroni, T. A. Zang, Spectral Methods in Fluid Dynamics. Springer, Berlin, (1988).

DOI: 10.1007/978-3-642-84108-8

[35] L. N. Trefethen, Spectral methods in MATLAB. SIAM, Philadelphia, (2000).

[36] A. A. Aly, Heat treatment of polymers: a review. Int. J. Mater. Chem. Phys. 1(2) (2015) 132–140.

[37] T. Hayat, S. Makhdoom, M. Awais, S. Saleem, M. M. Rashidi, Axisymmetric Powell-Eyring fluid flow with convective boundary condition: optimal analysis, Appl. Math. Mech. -Engl. Ed., 37(7) (2016) 919–928.

DOI: 10.1007/s10483-016-2093-9

[38] C. Y. Wang, Natural convection on a vertical radially stretching sheet, Journal of Mathematical Analysis and Applications, 332 (2007) 877–883.

DOI: 10.1016/j.jmaa.2006.11.006