Entropy Generation on MHD Flow of Powell-Eyring Fluid Between Radially Stretching Rotating Disk with Diffusion-Thermo and Thermo-Diffusion Effects

Khan, Najeeb Alam; Aziz, Shahnila; Ullah, Saif

doi:10.1515/ama-2017-0004

Abstract

An investigation is performed for an alyzing the effect of entropy generation on the steady, laminar, axisymmetric flow of an incompressible Powell-Eyring fluid. The flow is considered in the presence of vertically applied magnetic field between radially stretching rotating disks. The Energy and concentration equation is taking into account to investigate the heat dissipation, Soret, Dufour and Joule heating effects. To describe the considered flow non-dimensionalized equations, an exact similarity function is used to reduce a set of the partial differential equation into a system of non-linear coupled ordinary differential equation with the associated boundary conditions. Using homotopy analysis method (HAM), an analytic solution for velocity, temperature and concentration profiles are obtained over the entire range of the imperative parameters. The velocity components, concentration and temperature field are used to determine the entropy generation. Plots illustrate important results on the effect of physical flow parameters. Results obtained by means of HAM are then compared with the results obtained by using optimized homotopy analysis method (OHAM). They are in very good agreement.

References

1. Abolbashari M.H., Freidoonimehr N., Nazari F., Rashidi M.M. (2014), Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nano-fluid, Powder Technology, 267, 256–267.10.1016/j.powtec.2014.07.028
Search in Google Scholar Back to article
2. Afify A.A. (2009), Similarity solution in MHD: effects of thermal diffusion and diffusion thermo effects on free convective heat and mass transfer over a stretching surface considering suction or injection, Communications in Nonlinear Science and Numerical Simulation, 14, 2202–2214.10.1016/j.cnsns.2008.07.001
Search in Google Scholar Back to article
3. Anjali Devi S.P., Uma Devi R. (2011), Soret and Dufour effects on MHD slip flow with thermal radiation over a porous rotating infinite disk, Communications in Nonlinear Science and Numerical Simulation, 16, 1917–1930.10.1016/j.cnsns.2010.08.020
Search in Google Scholar Back to article
4. Ariel P.D. (2001), Axisymmetric Flow of a Second Grade Fluid Past a Stretching Sheet, International Journal of Engineering Science, 39, 529-553.10.1016/S0020-7225(00)00052-5
Search in Google Scholar Back to article
5. Arikoglu A., Ozkol I. (2008), Komurgoz G. Effect of slip on entropy generation in a single rotating disk in MHD flow, Appl. Energy, 85, 1225-1236.
Search in Google Scholar Back to article
6. Asghar S., Jalil M., Hussan M., Turkyilmazoglu M. (2014), Lie group analysis of flow and heat transfer over a stretching rotating disk, International Journal of Heat and Mass Transfer, 69, 140–146.10.1016/j.ijheatmasstransfer.2013.09.061
Search in Google Scholar Back to article
7. Ashraf M., Batool K. (2013), MHD flow and heat transfer of a micropolar fluid over a stretchable disk, Journal of Theoretical and Applied Mechanics, 51, 25-38.
Search in Google Scholar Back to article
8. Banks W. (1983), Similarity solutions of the boundary-layer equations for a stretching wall, Journal de. Mécaniqe, Théorique et Appliquee, 2, 375–392.
Search in Google Scholar Back to article
9. Bataller R.C. (2007), Viscoelastic fluid flow and heat transfer over a stretching sheet under the effects of a non-uniform heat source, viscous dissipation and thermal radiation, International Journal of Heat and Mass Transfer, 50, 3152–3162.10.1016/j.ijheatmasstransfer.2007.01.003
Search in Google Scholar Back to article
10. Bejan A. (1982), Entropy generation through heat fluid flow, 2^nd ed., New York, Wiley.10.1115/1.3167072
Search in Google Scholar Back to article
11. Bejan A. (1996), Entropy generation minimization: the method of thermodynamic optimization of finite-size systems and finite-time processes, CRC Press.10.1063/1.362674
Search in Google Scholar Back to article
12. Bhatti M.M., Abbas T., Rashidi M.M., Ali M.E.S. (2016), Numerical Simulation of Entropy Generation with Thermal Radiation on MHD Carreau nanofluid towards a Shrinking Sheet, Entropy, 18(6), 200.10.3390/e18060200
Search in Google Scholar Back to article
13. Butt A.S., Ali A. (2014), Entropy analysis of magnetohydrodynamic flow and heat transfer due to a stretching cylinder, Journal of Taiwan institute of chemical engineers, 45, 780-786.10.1016/j.jtice.2013.08.018
Search in Google Scholar Back to article
14. Butt A.S., Munawar S., Ali A., Mehmood A. (2012), Entropy generation in hydrodynamic slip flow over a vertical plate with convective boundary, Journal of Mechanical Science and Technology, 26, 2977-298410.1007/s12206-012-0701-3
Search in Google Scholar Back to article
15. Crane L.J. (1970), Flow past a stretching plate, ZAMP, 21, 645-647.10.1007/BF01587695
Search in Google Scholar Back to article
16. Eckert E.R.G., Drake R.M. (1972), Analysis of heat and mass transfer, New York: McGraw-Hill.
Search in Google Scholar Back to article
17. Fang T. (2007), Flow over a stretchable disk, Physics of Fluids, 19, 128105.10.1063/1.2823572
Search in Google Scholar Back to article
18. Fang T., Zhang J. (2008), Flow between two stretchable disks-an exact solution of the Navier–Stokes equations, International Communication of Heat and Mass Transfer, 35, 892–895.10.1016/j.icheatmasstransfer.2008.04.018
Search in Google Scholar Back to article
19. Gaikwad S.N., Malashetty M.S., Prasad Rama K. (2007), An analytical study of linear and nonlinear double diffusive convection with Soret and Dufour effects in couple stress fluid, International Journal of Non-Linear Mechanics, 42, 903-913.10.1016/j.ijnonlinmec.2007.03.009
Search in Google Scholar Back to article
20. Gorder R.V., Sweet E., Vajravelu K. (2010), Analytical solutions of a coupled nonlinear system arising in a flow between stretching disks, Applied Mathematics and Computation, 216, 1513–1523.10.1016/j.amc.2010.02.053
Search in Google Scholar Back to article
21. Grubka L.J., Bobba K.M. (1985), Heat transfer characteristic of a continuous stretching surface with variable temperature, International Journal of Heat and Mass Transfer, 107, 248–250.10.1115/1.3247387
Search in Google Scholar Back to article
22. Guo J., Xu M., Cai J., Huai X. (2011), Viscous dissipation effect on entropy generation in curved square microchannels, Energy, 36, 5416-5423.10.1016/j.energy.2011.06.060
Search in Google Scholar Back to article
23. Gupta P., Gupta A. (1977), Heat and mass transfer on a stretching sheet with suction or blowing, Candian Journal of Chemical Engineers, 55, 744–746.10.1002/cjce.5450550619
Search in Google Scholar Back to article
24. Hayat T., Mustafa M., Pop I. (2010), Heat and mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid, Communications in Nonlinear Science and Numerical Simulation, 15, 1183–1196.10.1016/j.cnsns.2009.05.062
Search in Google Scholar Back to article
25. Khan N.A., Aziz S., Khan N.A. (2014), MHD flow of Powell-Eyring fluid over a rotating disk, Journal of the Taiwan Institute of Chemical Engineers, 45, 2859-2867.10.1016/j.jtice.2014.08.018
Search in Google Scholar Back to article
26. Khan N.A., Aziz S., Khan N.A. (2014), Numerical Simulation for the Unsteady MHD Flow and Heat Transfer of Couple Stress Fluid over a Rotating Disk, Plos One..10.1371/journal.pone.0095423
Search in Google Scholar Back to article
27. Li X., Faghri A. (2011), Local entropy generation analysis on passive high-concentration DMFCs (direct methanol fuel cell) with different cell structures, Energy, 36, 403-414.10.1016/j.energy.2010.10.024
Search in Google Scholar Back to article
28. Liao S.J. (2003), Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall CRC Press, Boca Raton.
Search in Google Scholar Back to article
29. Liao S.J. (2004), On the Homotopy Analysis Method for nonlinear problems, Applied Mathematics and Computation, 147, 499–513.10.1016/S0096-3003(02)00790-7
Search in Google Scholar Back to article
30. Mahian O., Oztop H., Pop I. Mahmud S., Wongwises S. (2013), Entropy generation between two vertical cylinders in the presence of MHD flow subjected to constant wall temperature, International Communications in Heat and Mass Transfer, 44, 87-92.10.1016/j.icheatmasstransfer.2013.03.005
Search in Google Scholar Back to article
31. Munawar S., Mehmood A., Ali A. (2011), Effects of slip on flow between two stretchable disks using optimal homotopy analysis method, Canadian Journal of Applied Sciences, 1, 50-68.10.21065/19257430.50.1
Search in Google Scholar Back to article
32. Osalusi E., Side J., Harris R. (2008), Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer of a steady MHD convective and slip flow due to a rotating disk with viscous dissipation and Ohmic heating, International Journal of Heat and Mass Transfer, 35, 908–915.10.1016/j.icheatmasstransfer.2008.04.011
Search in Google Scholar Back to article
33. Parvin S., Chamkha A.J. (2014), An analysis on free convection flow, heat transfer and entropy generation in an odd-shaped cavity filled with nanofluid, International Communications in Heat and Mass Transfer, 54, 8-17.10.1016/j.icheatmasstransfer.2014.02.031
Search in Google Scholar Back to article
34. Powell R.E., Eyring H. (1944), Mechanism for the relaxation theory of viscosity, Nature, 154, 427–428.10.1038/154427a0
Search in Google Scholar Back to article
35. Rashidi M.M., Hayat T., Erfani E., Mohimanian Pour S.A., Awatif Hendi A. (2011), Simultaneous effects of partial slip and thermal-diffusion and diffusion-thermo on steady MHD convective flow due to a rotating disk, Communications in Nonlinear Science and Numerical Simulation, 16, 4303–4317.10.1016/j.cnsns.2011.03.015
Search in Google Scholar Back to article
36. Rashidi M.M., Kavyani N., Abelman S. (2014), Investigation of entropy generation in MHD and slip flow over a rotating porous disk with variable properties, International Journal of Heat and Mass Transfer, 70, 892-917.10.1016/j.ijheatmasstransfer.2013.11.058
Search in Google Scholar Back to article
37. Sajid M., Hayat T., Ayub M. (2008), Series Solution for Unsteady Axisymmetric Flow and Heat Transfer over a Radially Stretching Sheet, Communications in Nonlinear Science and Numerical Simulation, 13, 2193-2202.10.1016/j.cnsns.2007.06.001
Search in Google Scholar Back to article
38. Sakiadis B.C. (1961), Boundary layer behavior on continuous solid surfaces: I boundary layer on a continuous flat surface, AICHE J., 7, 221-225.10.1002/aic.690070211
Search in Google Scholar Back to article
39. Shateyi S., Motsa S.S., Makukula Z. (2015), On Spectral Relaxation Method for Entropy Generation on a MHD Flow and Heat Transfer of a Maxwell Fluid, Journal of Applied Fluid Mechanics, 8, 21-31.10.36884/jafm.8.01.20273
Search in Google Scholar Back to article
40. Torabi M., Zhang K. (2015), Heat transfer and thermodynamic performance of convective-radiative cooling double layer walls with temperature-dependent thermal conductivity and internal heat generation, Energy Conversion and Management, 89, 12-2310.1016/j.enconman.2014.09.032
Search in Google Scholar Back to article
41. Tsai R., Huang J.S. (2009), Heat and mass transfer for Soret and Dufour’s effects on Hiemenz flow through porous medium onto a stretching surface, International Journal of Heat and Mass Transfer, 52, 2399–2406.10.1016/j.ijheatmasstransfer.2008.10.017
Search in Google Scholar Back to article
42. Turkyilmazoglu M. (2012), MHD fluid flow and heat transfer due to a stretching rotating disk, International Journal of Thermal Science, 51, 195–201.10.1016/j.ijthermalsci.2011.08.016
Search in Google Scholar Back to article
43. Wang C.Y. (1984), The three-dimensional flow due to a stretching flat surface, Physics of Fluids, 27, 1915.10.1063/1.864868
Search in Google Scholar Back to article
44. Wang C.Y. (1988), Stretching a surface in a rotating fluid, Journal of Applied Mathematics and Physics, ZAMP, 39, 177–185.10.1007/BF00945764
Search in Google Scholar Back to article

Entropy Generation on MHD Flow of Powell-Eyring Fluid Between Radially Stretching Rotating Disk with Diffusion-Thermo and Thermo-Diffusion Effects

Abstract

Paradigm

My account