Computational Analysis of Hydromagnetic Flow of a Dissipative and Radiating Fluid Over a Stretching/ Shrinking Surface with Prescribed Heat Flux in the Presence of Heat Source/ Sink

Authors

  • J Wilfred Samuel Raj Department of Mathematics, The American College, Madurai-02, Tamil Nadu, India. https://orcid.org/0000-0001-5813-3023
  • SP Anjali Devi Department of Applied Mathematics, Bharathiar University, Coimbatore-46, Tamil Nadu, India.

Keywords:

Boundary Layer, Heat Source/ Sink, Heat Transfer, Magnetohydrodynamics, Prescribed Surface Heat Flux, Thermal Radiation

Abstract

Nonlinear hydromagnetic flow and heat transfer over a stretching/ shrinking surface with prescribed heat flux in the presence of viscous dissipation, radiation effects and heat source/ sink has been explored numerically. The basic equations comprising the balance laws of mass, linear momentum and energy are modified to include the viscous dissipation, heat source/ sink and radiation effects. A suitable similarity transformation is employed to reduce the nonlinear partial differential equations into nonlinear ordinary differential equations. Then the resultant third order momentum equation and second order energy equation are solved numerically using Nachtsheim Swigert Shooting iteration scheme for the satisfaction of asymptotic boundary conditions together with Runge Kutta Fourth Order integration method. The physical parameters like Suction parameter, Magnetic parameter, Stretching/ Shrinking parameter, Prandtl number, Radiation parameter, Heat source/ jsink parameter and Eckert number show significant effects on the flow and heat transfer. Numerical results are computed for dimensionless velocity, skin friction coefficient, dimensionless temperature and wall temperature and are depicted through graphs and tables. The temperature of the fluid is found to enhance apparently due to significant increase in Eckert number which ultimately leads to increase in the thermal boundary layer thickness.

How to cite this article: Raj JWS, Devi SPA. Computational Analysis of Hydromagnetic Flow of a Dissipative and Radiating Fluid Over a Stretching/ Shrinking Surface with Prescribed Heat Flux in the Presence of Heat Source/ Sink. J Adv Res Appl Mech Compu Fluid Dyna 2019; 6(3&4): 1-10.

References

1. Ali FM, Nazar R, Arifin NM. MHD viscous flow and heat transfer due to a permeable shrinking sheet with prescribed surface heat flux. WSEAS Transactions on Mathematics 2010; 9: 365-375. (ISSN: 1109-2769).
2. Devi ASP, Raj JWS. Numerical simulation of magnetohydrodynamic forced convective boundary layer flow past a stretching/shrinking sheet prescribed with variable heat flux in the presence of heat source and constant suction. Journal of Applied Fluid Mechanics 2014; 7: 415-423.
3. Babu PR, Rao JA, Sheri S. Radiation effect on MHD heat and mass transfer flow over a shrinking sheet with mass suction. Journal of Applied Fluid Mechanics 2014; 7: 641-650.
4. Badruddin IA, Zainal ZA, Zahid A et al. Effect of viscous dissipation and radiation on natural convection in a porous medium embedded within vertical annulus. Int J of Thermal Sciences 2007; 46: 221-227.
5. Bhattachaarya K, Layek GC. Effects of suction/ blowing on steady boundary layer stagnation point flow and heat transfer towards a shrinking sheet with thermal radiation. Int J Heat Mass Transfer 2011; 54: 302-307.
6. Brewster MQ. Thermal Radiative Transfer Properties. Wiley, Canada. 1992.
7. Chen CK, Char MI. Heat transfer of a continuously stretching surface with suction and blowing. J Math Anal Appl 1988; 135: 560-580.
8. Crane LJ. Flow past a stretching plate. Z Angew Math Physics 1970; 21: 645-647.
9. Danberg JS, Fansler KS. A non similar moving wall boundary layer problem. Quart Appl Math 1976; 34: 305-309. 10. Erickson LE, Fan TI, Fox VG. Heat and mass transfer on a moving continuous flat plate with suction or injection. Ind Eng Chem Fundam 1966; 5: 19-25.
11. Fang T, Zhang J. Thermal boundary layers over a shrinking sheet: an analytical solution. Acta Mech 2010; 209: 325-343.
12. Fang T, Zhang J. Closed-form exact solutions of MHD viscous flow over a shrinking sheet. Communications in Nonlinear Science and Numerical Simulation 2009; 14: 2853-2857.
13. Gupta PS, Gupta AS. Heat and mass transfer on a stretching sheet with suction or blowing. Can J Chem Eng 1977; 55: 744–746.
14. Hayat TM, Hussain AA, Hendi et al. MHD stagnation point flow towards heated shrinking surface subjected to heat generation/ absorption. Applied Mathematics and Mechanics 2012; 33: 631-648.
15. Hayat TZ, Abbas T, Sajid M. On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet. Journal of Applied Mechanics 2007; 74: 1165-1171.
16. Hayat TZ, Abbas T, Sajid M et al. Three-dimensional rotating flow induced by a shrinking sheet for suction. Chaos, Solitons & Fractals 2009; 39: 1615-1626.
17. Ismaila NS, Norihan MA, Nazar R et al. Stability analysis of unsteady MHD stagnation point flow and heat transfer over a shrinking sheet in the presence of viscous dissipation. Chinese Journal of Physics 2019; 57: 116-126.
18. Javed TZ, Abbas T, Sajid M et al. Heat transfer analysis for a hydromagnetic viscous fluid over a non-linear shrinking sheet. Int J of Heat and Mass transf 2011; 54: 2034-2042.
19. Jhankal AK, Kumar M. MHD boundary layer flow past over a shrinking sheet with heat transfer and mass suction. Int J of Computational and Applied Mathematics 2017; 12: 441-448. (ISSN 1819-4966).
20. Mahantesh MM, Nandeppanavar K, Abel S et al. Flow and heat transfer characteristics of a viscoelastic fluid in a porous medium over an impermeable stretching
sheet with viscous dissipation. Int J of Heat and Mass Transfer 2010; 53: 4707-4713.
21. Mahmoud EM, Ouaf. Exact solution of thermal radiation on MHD flow over a stretching porous sheet. Applied Mathematics and Computation 2005; 170: 1117-1125.
22. Miklavcic M, Wang CY. Viscous flow due to a shrinking sheet. Quart Appl Math 2006; 64: 83-290.
23. Nadeem S, Hussain A. MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method. Applied Mathematics and Mechanics 2009; 30: 1569-1578.
24. Fadiya N, Mohod N, Hasim I. MHD flow and heat transfer adjacent to a permeable shrinking sheet embedded in a porous medium. Sains Malaysains 2009; 38: 559-565.
25. Cortell R. Effect of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys Lett A 2008; 372: 631-636.
26. Cortell R. Internal heat generation and radiation effects on a certain free convective flow. Int J of nonlinear science 2010; 9: 468-479.
27. Raptis A, Perdikis C, Takhar HS. Radiation effects on flow past a stretching plate with temperature dependent viscosity. Appl Math Comput 2004; 153: 645-649.
28. Sajid M, Javed T, Hayat T. MHD rotating flow of a viscous fluid over a shrinking surface. Nonlinear dyn 2008; 51: 259-265.
29. Sakiadis BC. Boundary layer behaviour on continuous solid surface: I Boundary layer equations for two dimensional and axisymmetric flow. J AIChe 1961; 7: 26-28.
30. Khalid S, Hussain S, Waqas H. Numerical solution of MHD flow and heat transfer in porous medium over a porous shrinking surface with radiation and viscous dissipation. Sci Int (Lahore) 2016; 28: 4297-4302.
31. Sonth RM, Khan Sk, Abel MS et al. Heat and mass transfer in a viscoelastic fluid over an accelerating surface with heat source/ sink and viscous dissipation. Heat Mass Transfer 2002; 38: 213-220.
32. Tak SS, Lodha A. Flow and heat transfer in presence of transverse magnetic field. Acta Ciencia Indica 2005; 31: 657-663.
33. Vajravelu K, Hadjinicolaou A. Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation. International Communications in Heat and Mass Transfer 1993; 20: 417-430.
34. Wang CY. Liquid film on an unsteady stretching sheet. Q Appl Math 1990; 48: 601-610.

Published

2020-01-27

Issue

Vol. 6 No. 3&4 (2019): Journal of Advanced Research in Applied Mechanics & Computational Fluid Dynamics

Section

Research Article