ORIGINAL PAPER
Melting Heat Transfer and MHD Boundary Layer Flow of Eyring-Powell Nanofluid Over a Nonlinear Stretching Sheet with Slip
 
More details
Hide details
1
Government Degree College (Autonomous) Siddipet Dist., Telangana, India, 502103
 
2
Department of Mathematics, University College of Science, Osmania University, Hyderabad, India, 500007
 
3
Government Degree College Mulugu, Warangal Dist., Telangana, India, 506343
 
 
Online publication date: 2019-03-12
 
 
Publication date: 2019-03-01
 
 
International Journal of Applied Mechanics and Engineering 2019;24(1):161-178
 
KEYWORDS
ABSTRACT
The steady laminar incompressible viscous magneto hydrodynamic boundary layer flow of an Eyring- Powell fluid over a nonlinear stretching flat surface in a nanofluid with slip condition and heat transfer through melting effect has been investigated numerically. The resulting nonlinear governing partial differential equations with associated boundary conditions of the problem have been formulated and transformed into a non-similar form. The resultant equations are then solved numerically using the Runge-Kutta fourth order method along with the shooting technique. The physical significance of different parameters on the velocity, temperature and nanoparticle volume fraction profiles is discussed through graphical illustrations. The impact of physical parameters on the local skin friction coefficient and rate of heat transfer is shown in tabulated form.
REFERENCES (48)
1.
Crane L.J. (1970): Flow past a stretching plate. – Zeitschrift fur Angewandte Mathematik und Physik, vol.21, pp.645-641.
 
2.
Vleggaar J. (1977): Laminar boundary layer behaviour on continuous accelerating surface. – Chem. Eng. Sci., vol.32, pp.1517–1525.
 
3.
Crane L.J. (1970): Flow past a stretching plate. – J. Appl. Math. Phys. (ZAMP), vol.21, pp.645-647.
 
4.
Wang C.Y. (1984): The three-dimensional flow due to a stretching flat surface. – Phys. Fluids, vol.27, pp.1915-1917.
 
5.
Andersson H.I. and Dandapat B.S. (1991): Flow of a power-law fluid over a stretching sheet. – SAACM 1, pp.339-347.
 
6.
Magyari E. and Keller B. (2000): Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls. – Eur. J. Mech. B Fluids, vol.19, pp.109-122.
 
7.
Sparrow E.M. and Abraham J.P. (2005): Universal solutions for the stream wise variation of the temperature of a moving sheet in the presence of a moving fluid. – Int. J. Heat Mass Transfer, vol.48, pp.3047-3056.
 
8.
Hunegnaw Dessie and Naikoti Kishan (2014): MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink. – Ain Shams Engineering Journal, vol.26, pp.967-977.
 
9.
Kishan N. and Amrutha P. (2011): Effects of viscous dissipation on MHD flow with heat and mass transfer over a stretching surface with heat source, thermal stratification and chemical reaction. – Journal of Naval Architecture and Marine Engineering, vol.7, No.1, pp.11-18..
 
10.
Turkyilmazoglu M. (2012): Dual and triple solutions for MHD slip flow of non-Newtonian fluid over a shrinking surface. – Comput. Fluids, vol.70, pp.53-58.
 
11.
Yin C., Niu J., Fu C. and Tan W.C. (2013): Thermal convection of a viscoelastic fluid in a fluid-porous system subjected to horizontal plane Couette flow. – Int. J. Heat Fluid Flow, vol.44, pp.711-718.
 
12.
Makinde O.D., Chinyoka T. and Rundora L. (2011): Unsteady flow of a reactive variable viscosity non-Newtonian fluid through a porous saturated medium with asymmetric convective boundary conditions. – Comput. Math. Appl., vol62, pp.3343-3352.
 
13.
Ellahi R. (2013): The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions. – Appl. Math. Model., vol.37, pp.1451-1467.
 
14.
Srinivas Reddy C. and Kishan N. (2015): MHD Boundary layer flow and heat transfer of a nanofluid over a shrinking sheet with mass suction and chemical reaction. – Journal of Nanofluids, vol.4, pp.518-527.
 
15.
Madhu M. and Kishan N. (2016): Finite element analysis of heat and mass transfer by MHD mixed convection stagnation-point flow of a non-Newtonian power-law nanofluid towards a stretching surface with radiation. – Journal of the Egyptian Mathematical Society, vol.24, No.3, pp.458-470.
 
16.
Madhu M., Kishan N. and Chamka A. (2016): Boundary layer flow and heat transfer of a non-Newtonian nanofluid over a non-linearly stretching sheet. – International Journal of Numerical Methods for Heat and Fluid Flow, vol.26, No.7, pp.2198-2217.
 
17.
Madhu M. and Kishan N. (2016): MHD boundary-layer flow of a non-Newtonian nanofluid past a stretching sheet with a heat source/sink. – Journal of Applied Mechanics and Technical Physics, vol.57, No.5, pp.908-915.
 
18.
Patel M. and Timol M.G. (2009): Numerical treatment of Powell-Eyring fluid flow using method of satisfaction of asymptotic boundary conditions (MSABC). – Appl. Numer. Math., vol.59, pp.2584-2592.
 
19.
Hayat T., Iqbal Z., Qasim M. and Obidat S. (2012): Steady flow of an Eyring Powell fluid over a moving surface with convective boundary conditions. – Int. J. Heat Mass Transf., vol.55, pp.1817-1822.
 
20.
Rosca A.V. and Pop I.M. (2014): Flow and heat transfer of Powell-Eyring fluid over a shrinking surface in a parallel free stream. – Int. J. Heat Mass Transfer, vol.71, pp.321-327.
 
21.
Jalil M., Asghar S. and Imran S.M. (2013): Self similar solutions for the flow and heat transfer of Powell-Eyring fluid over a moving surface in a parallel free stream. – Int. J. Heat Mass Transfer, vol.65, pp.73-79.
 
22.
Islam S., Shah A., Zhou C.Y. and Ali I. (2009): Homotopy perturbation analysis of slider bearing with Powell- Eyring fluid. – Z. Angew. Math. Phys., vol.60, pp.1178-1193.
 
23.
Sirohi V., Timol M.G. and Kalathia N.L. (1984): Numerical treatment of Powell-Eyring fluid flow past a 90 degree wedge. – Reg. J. Energy Heat Mass Transfer, vol.6, No.3, pp.219-228.
 
24.
Powell R.E. and Eyring H. (1944): Mechanism for relaxation theory of viscosity. – Nature, vol.154, pp.427-428.
 
25.
Hayat T., Iqbal Z., Qasim M. and Obaidat S. (2012): Steady flow of an Eyring-Powell fluid over a moving surface with convective boundary conditions. – Int. J. Heat Mass Transfer, vol.55, pp.1817-1822.
 
26.
Choi S.U.S. and Eastman J.A. (1995): Enhancing thermal conductivity of fluids with nanoparticles. – Exposition. ASME, San Francisco, USA, FED 231/MD66, pp.99-105.
 
27.
Khan W.A. and Pop I. (2010): Boundary layer flow of a nanofluid past a stretching sheet. – Int. J. Heat Mass Transfer, vol.53, pp.2477-2483.
 
28.
Kuznetsov A.V. and Nield D.A. (2010): Natural convective boundary-layer flow of a nanofluid past a vertical plate. – Int. J. Therm. Sci., vol.49, pp.243-247.
 
29.
Gorla R.S.R., Kabeir S.M.M.E.L, and Rashad A.M. (2011): Heat transfer in the boundary layer on a stretching circular cylinder in a nanofluid. – J. Thermophys. Heat Transfer, vol.25, pp.183-186.
 
30.
Aziz A. (2010): Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition. – Comm. Nonlinear Num. Simu., vol.15, pp.573-580.
 
31.
Nield D.A. and Kuznetsov A.V. (2006): Forced convection with slip-flow in a channel or duct occupied by a hyper-porous medium saturated by a rarefied gas. – Transp. Porous Media, vol.64, pp.161-170.
 
32.
Beavers G.S. and Joseph D.D. (1967): Boundary condition at a naturally permeable wall. – J. Fluid Mech., vol.30, pp.197-207.
 
33.
Hamdan M.A., Al-Nimr M.A. and Hammoudeh V.A. (2010): Effect of second order velocity-slip/temperaturejump on basic gaseous fluctuating micro-flows. – J. Fluids Eng., vol.132, 074503.
 
34.
Bhattacharyya K., Mukhopadhyay S. and Layek G.C. (2011): Slip effects on boundary layer stagnation-point flow and heat transfer towards a shrinking sheet. – Int. J. Heat Mass Transfer, vol.54, pp.308-313.
 
35.
Roberts L. (1958): On the melting of a semi-infinite body of ice placed in a hot stream of air. – J. Fluid Mech., vol.4, pp.505-528.
 
36.
Hayat T., Farooq M. and Alsaedi A. (2014): Melting heat transfer in the stagnation point flow of Maxwell fluid with double diffusive convection. – Int. J. Numer. Methods Heat Fluid Flow, vol.24, pp.760-774.
 
37.
Das K. (2014): Radiation and melting effects on MHD boundary layer flow over a moving surface. – Ain Shams Eng. J., vol.5, pp.1207-1214.
 
38.
Epstein E.M. and Cho D.H. (1976): Melting heat transfer in steady laminar flow over a flat plate. – J. Heat Transfer, vol.98, pp.531-533.
 
39.
Kazmierczak M., Poulikakos D. and Pop I. (1986): Melting from a flat plate embedded in a porous medium in the presence of steady convection. – Numer. Heat Transfer, vol.10, pp.571-581.
 
40.
Gorla R.S.R., Mansour M.A., Hussanien I.A. and Bakier A.Y. (1999): Mixed convection effect on melting from a vertical plate. – Transport Porous Med., vol.36, pp.245-254.
 
41.
Bachock N., Ishak A. and Pop I. (2010): Melting heat transfer in boundary layer stagnation point flow towards a stretching/shrinking sheet. – Phys. Lett. A 374, pp.4075-4079.
 
42.
Anuar Ishak and Roslinda Nazar (2010): Melting heat transfer in steady laminar flow over a moving surface. – Heat Mass Transfer, vol.46, pp.463-468.
 
43.
Gireesha B.J., Mahanthesh B., Shivakumara I.S. and. Eshwarappa K.M. (2016): Melting heat transfer in boundary layer stagnation-point flow of nanofluid toward a stretching sheet with induced magnetic field. – Engineering Science and Technology an International Journal, vol.19, pp.313-321.
 
44.
Chamkha A.J., Rashad A.M. and Al-Meshaiei E. (2011): Melting effect on unsteady hydrodynamic flow of a nanofluid past a stretching sheet. – Int. J. Chem. React. Eng., vol.9, pp.1-13.
 
45.
Gorla R.S.R., Chamkha A. and Aloraier A. (2011): Melting heat transfer in a nanofluid flow past a permeable continuous moving surface. – J. Nav. Arch. Mar. Eng., vol.2, pp.83-92.
 
46.
Panigrahi S., Reza M. and Mishra A.K. (2014): MHD effect of mixed convection boundary-layer flow of Powell- Eyring fluid past nonlinear stretching surface. – Vol.35, No.12, pp.1525-1540.
 
47.
Cortell R. (2007): Viscous flow and heat transfer over a nonlinearly stretching sheet. – Applied Mathematics and Computation, vol.184, pp.864-873.
 
48.
Rana P. and Bhargava R. (2012): Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study. – Communications in Nonlinear Science and Numerical Simulation, vol.17, pp.212-226.
 
eISSN:2353-9003
ISSN:1734-4492
Journals System - logo
Scroll to top