Mhd And Radiation Effect On Heat Transfer In A Non-Newtonian Maxwell Fluid Over An Unsteady Stretching Sheet With Heat Source/Sink

S.Vijaya Lakshmi; T.Amaranatha Reddy; M. Suryanarayana Reddy

doi:https://doi.org/10.14445/22315373/IJMTT-V40P532

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 40 | Number 4 | Year 2016 | Article Id. IJMTT-V40P532 | DOI : https://doi.org/10.14445/22315373/IJMTT-V40P532

Mhd And Radiation Effect On Heat Transfer In A Non-Newtonian Maxwell Fluid Over An Unsteady Stretching Sheet With Heat Source/Sink

S.Vijaya Lakshmi, T.Amaranatha Reddy, M. Suryanarayana Reddy

Citation :

S.Vijaya Lakshmi, T.Amaranatha Reddy, M. Suryanarayana Reddy, "Mhd And Radiation Effect On Heat Transfer In A Non-Newtonian Maxwell Fluid Over An Unsteady Stretching Sheet With Heat Source/Sink," International Journal of Mathematics Trends and Technology (IJMTT), vol. 40, no. 4, pp. 255-261, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V40P532

Abstract

The effects of variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of, MHD, heat source/sink and radiation effects have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge–Kutta method coupled with the shooting technique using appropriate boundary conditions for various physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, radiation parameter, heat source/sink parameter, Deborah number, and Prandtl number on the velocity and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. The effects of variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of, MHD, heat source/sink and radiation effects have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge–Kutta method coupled with the shooting technique using appropriate boundary conditions for various physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, radiation parameter, heat source/sink parameter, Deborah number, and Prandtl number on the velocity and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. The effects of variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of, MHD, heat source/sink and radiation effects have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge–Kutta method coupled with the shooting technique using appropriate boundary conditions for various physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, radiation parameter, heat source/sink parameter, Deborah number, and Prandtl number on the velocity and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed.

Keywords

non- Newtonian Maxwell fluid, unsteady stretching sheet, radiation, variable fluid properties, variable heat flux.

References

1. Crane, L. J., (1970), Z. Angew. Math. Phys. 21 645

2. Gupta, P. S., and Gupta, A. S., (1977), Can. J. Chem. Eng. 55 744

3. Banks, W. H. H., (1983), J. Mec. Theor. Appl. 2 375

4. Magyari, E., and Keller, B., (1999), J. Phys. D: Appl. Phys. 32 2876

5. Mahapatra, T. R., and Gupta, A. S., (2003), Can. J. Chem. Eng. 81 258

6. Ahmed M. Megahed, (2013), Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity, Chin. Phys. B Vol. 22, No. 9, 094701, pp.1-6.

7. Sakiadis, B. C., (1961), Boundary layer behaviour on continuous solid surface: I. Boundary layer equations for two dimensional and axisymmetric flow, AIChE J. Vol.7, pp.26–28.

8. Alpher, R. A., (1961), Heat transfer in magnetohydrodynamic flow between parallel plates, Int. J. Heat Mass Transfer, Vol. 3, pp.108–112.

9. Andersson, H. I., and Kumaran, V., (2006), On sheet driven motion of power-law fluids, Int. J. Nonlin. Mech. Vol.41, pp.1228–1234.

10. Bird, R. B., Dai, G. C., and Yarusso, B. J., (1983), The rheology and flow of viscoplastic materials, Rev. Chem. Engng., Vol.1, pp.36–69.

11. Liao, S. J., (2003), Beyond Perturbation: Introduction to the Homotopy Analysis Method,

12. Chapman and Hall, CRC Press, Boca Raton.

13. Liao, S. J., (2003), On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet, J. Fluid Mech. Vol.488, pp.189– 212.

14. Hayat, T., Abbas, Z., and Sajid, M., (2006), Series solution for the upper convected Maxwell fluid over a porous stretching plate, Phys. Lett. A., Vol.358, pp.396– 403.

15. El-Aziz, M. A., (2010), Meccanica 45 97

16. Abdallah, A., (2009), Homotopy Analytical Solution of MHD Fluid Flow and Heat Transfer Problem, Applied Mathematics & Information Sciences, Vol. 3(2), 223-233

17. Bataller, R. C., (2011), Magnetohydrodynamic Flow and Heat Transfer of an Upper-Convected Maxwell Fluid Due to a Stretching Sheet, FDMP, Vol.7, no.2, pp.153- 173.

18. Das, K., (2011), Effect of chemical reaction and thermal radiation on heat and mass transfer flow of MHD micropolar fluid in a rotating frame of reference, Int. Jour. Heat Mass Transfer, Vol.54, pp.3505-3513.

19. Ishak, A., (2010), Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect, Meccanica, Vol.45, pp.367-373.

20. Pal, D. and Mondal, H., (2011), The influence of thermal radiation on hydromagnetic Darcy-Forchheimer mixed convection flow past a stretching sheet embedded in a porous medium, Meccanica, Vol.46, pp.739-753.

21. Mukhopadhyay, S., De, P.R., Bhattacharyya, K., and Layek, G.C., (2012), Forced convection flow and heat transfer over a porous plate in a Darcy-Forchheimer porous medium in presence of radiation, Meccanica, Vol.47, pp.153-161.

22. Olajuwon, B.I., and Oahimire, J.I., (2013), Unsteady free convection heat and mass transfer in an mhd micropolar fluid in the presence of thermo diffusion and thermal radiation, International Journal of Pure and Applied Mathematics, Vol. 84, No. 2, pp.15-37.

23. Prabir Kumar Kundu, Kalidas Das, Mr. S.Jana, (2010), mhd micropolar fluid flow with thermal radiation and thermal diffusion in a rotating frame, Mathematics Subject Classification. 76W05.

24. Tania S. Khaleque and Samad M.A., (2010), Effects of radiation, heat generation and viscous dissipation on MHD free convection flow along a stretching sheet, Research J of Appl. Sci., Eng. and Tech., Vol. 2, No. 4, pp. 368-377.

25. Moalem, D., (1976), Steady state heat transfer with porous medium with temperature dependent heat generation, Int. J.Heat and Mass Transfer, Vol. 19, No. 529–537.

26. Vajrevelu. K., Nayfeh, J., (1992), Hydro magnetic convection at a cone and a wedge, Int. Comm. Heat Mass Transfer, Vol. 19, pp. 701-710.

27. Elbashbeshy, E. M. A., and Bazid, M. A. A., (2003), Appl. Math. Comp. 138 239

28. Elbashbeshy, E. M. A., and Bazid, M. A. A., (2004), Heat Mass Tran. 41 1

29. Swati Mukhopadhyay, (2012), Heat Transfer Analysis of the Unsteady Flow of a Maxwell Fluid over a Stretching Surface in the Presence of a Heat

Source/Sink, Chin. Phys. Lett., Vol. 29, No. 5, 054703

30. Mahmoud M A A and Megahed A M 2009 Can. J. Phys. 87 1065

31. Megahed A M 2011 Eur. Phys. J. Plus 126 82, 094701- 6

32. Jain, M.K., Iyengar, S.R.K. and Jain, R.K., (1985), Numerical Methods for Scientific and Engineering Computation, Wiley Eastern Ltd., New Delhi, India

33. Abel M S, Tawade J and Nandeppanavar M M 2012 Meccanica 47 385