58 Downloads 376 Views
Author(s)
K.RAJESHWAR REDDY, Department of Mathematics, Malla Reddy College of Engg& Tech,Medchal500100, Telangana State, India.
M.CHENNA KRISHNA REDDY, Department of Mathematics, Osmania University, Hyderabad500007, Telangana State, India.
Abstract
A numerical investigation of an unsteady MHD natural convection flow past an impulsively moving plate with ramped temperature. The dimensionless governing coupled, non linear boundary layer partial differential equations are solved by a finite element method. The effects of the various dimensionless parameters entering into the problem on the primary velocity, secondary velocity, temperature and concentration profiles throughout the boundary layer are investigated through graphs. In addition, the analytical and numerical results of the local skin friction, couple stress coefficients, the rate of heat and mass transfers at the wall are prepared in tabular forms
Keywords
Unsteady, MHD, Natural convection,Ramped temperature,FEM
Cite this paper
K.RAJESHWAR REDDY,
M.CHENNA KRISHNA REDDY,
Unsteady MHD natural convection flow past an impulsively moving plate with ramped temperature, SCIREA Journal of Mathematics. Vol.
3
, No.
1
,
2018
, pp.
67

86
.
References
[ 1 ]  Cheng, P. and Minkowycz, W.J. Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res., 82, 20402044(1977) 
[ 2 ]  Nakayama, A and Koyama, H. A general similarity transformation for combined free and forced convection flows within a fluid saturated porous medium. ASME J. Heat Transfer, 109, 10411045(1987) 
[ 3 ]  Lai, F. C. andKulacki, F. A.NonDarcy Mixed Convection along a Vertical Wall in a Saturated Porous Medium, Trans. ASME J. Heat Transfer, 113, 252255(1991) 
[ 4 ]  Hsieh, J. C., Chen, T. S. and Armaly, B. F. Nonsimilarity solutions for mixed convection from vertical surfaces in porous media: variable surface temperature or heat flux. Int. J. Heat Mass Transfer, 36, 14851493(1993) 
[ 5 ]  Nield, D. A. and Kuznetsov, A. V. The ChengMinkowych problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid. Int. J. Heat Mass Transfer, 52, 57925795(2009) 
[ 6 ]  Gorla,R.S.R. andChamkha, A. J. Natural convective boundary layer flow over a nonisothermal vertical plate embedded in a porous medium saturated with nanofluid. Nanoscale and Microscale, Thermophys. Engng., 15, 8194(2011) 
[ 7 ]  Ingham, D. B. and Pop, I. Transport Phenomena in Porous Media, vol. III, Elsevier, Oxford, (2005) 
[ 8 ]  Vafai, K. Handbook of Porous Media, second ed., Taylor & Francis, New York, (2005) 
[ 9 ]  Nield, D. A. and Bejan, A. Convection in Porous Media, third ed., Springer, New York, (2006) 
[ 10 ]  Raptis, A. and Kafousias, N. Heat transfer in flow through a porous medium bounded by an infinite vertical plate under the action of magnetic field, Int. J. Energy Res., 6, 241245(1982) 
[ 11 ]  ]Raptis,A. Flow through a porous medium in the presence of a magnetic field. Int. J. Energy Res., 10, 97100(1986) 
[ 12 ]  Takhar, H. S. and Ram,P. C.Magnetohydrodynamic free convection flow of water at 4oC through a porous medium. Int. Comm. Heat Mass Transfer, 21,371376(1994) 
[ 13 ]  Chamkha,A. J. MHD Free Convection from a Vertical Plate Embedded in a Thermally Stratified Porous Medium, Fluid/Particle Separation Journal, 9, 195206(1996) 
[ 14 ]  Chamkha, A. J. and Khanafer, K. NonSimilar Combined Convection Flow Over a Vertical Surface Embedded in a Variable Porosity Medium. J. Porous Media, 2, 231249(1999 
[ 15 ]  Jha, B. K. MHD free convection and masstransform flow through a porous medium. Astrophys. Space Sci., 175, 283289(1991) 
[ 16 ]  Aldoss, T. K., AlNimr, M. A., Jarrah, M. A. and AlShaer, B. J. Magnetohydrodynamic mixed convection from a vertical plate embedded in a porous medium.Numer. Heat Transfer, 28, 635645(1995) 
[ 17 ]  Kim, Y. J. Unsteady MHD convective heat transfer past a semiinfinite vertical porous moving plate with variable suction. Int. J. Engng. Sci., 38, 833845(2000) 
[ 18 ]  Makinde, O. D. and Sibanda, P.Magneto hydrodynamic Mixed Convective Flow and Heat and Mass Transfer Past a Vertical Plate in a Porous Medium with Constant Wall Suction. J. Heat Transf., 130 Article No. 112602, 8 pages(2008) 
[ 19 ]  Makinde, O. D. On MHD boundarylayer flow and mass transfer past a vertical plate in a porous medium with constant heat flux. Int. J. Numer. Methods Heat Fluid Flow, 19, 546554(2009) 
[ 20 ]  Vajravelu, K. and Nayfeh, J.Hydromagnetic convection at a cone and a wedge. Int. Comm. Heat Mass Transfer, 19, 701710(1992) 
[ 21 ]  Crepeau, J. C. and Clarksean, R. Similarity solutions of natural convection with internal heat generation. ASME J. Heat Transfer, 119, 183185(1997) 
[ 22 ]  Mckenzie, D. P., Roberts, J. M. and Weiss, N. O. Convection in the Earth’s mantle: towards a numerical simulation. J. Fluid. Mech., 62, 465538(1974) 
[ 23 ]  Baker, L., Faw, R. E. and Kulacki, F. A. Postaccident heat removal partI: heat transfer within an internally heated nonboiling liquid layer. J. Nucl. Sci. Eng., 61, 222230(1976) 
[ 24 ]  Delichatsios, M. A. Air entrainment into buoyant jet flames and pool fires in DiNenno, P.J, et al (Eds.) The SFPA handbook of fire protection engineering, NFPA publications, Quincy, M.A., 306314(1988) 
[ 25 ]  Westphal, B. R., Keiser, D. D., Rigg, R. H. and Loug, D. V. Production of metal waste forms from spent nuclear fuel treatment, DOE Spent Nuclear Fuel Conference, Salt Lake City, UT, 288294(1994) 
[ 26 ]  Moalem, D. Steady state heat transfer with porous medium with temperature dependent heat generation. Int. J. Heat Mass Transfer, 19, 529537(1976) 
[ 27 ]  Chamkha, A.J. Unsteady MHD convective heat and mass transfer past a semiinfinite vertical permeable moving plate with heat absorption. Int. J. Engng Sci., 42, 217230(2004) 
[ 28 ]  Ibrahim, F. S., Hassanien, I. A. and Bakr, A. A. Unsteady magnetohydrodynamic micropolar fluid flow and heat transfer over a vertical porous plate through a porous medium in the presence of thermal and mass diffusion with a constant heat source. Canadian J. Phys., 82, 775790(2004) 
[ 29 ]  Rahman, M. M. and Sattar, M. A.Magnetohydrodynamic convective flow of a micropolar fluid past a continuously moving vertical porous plate in the presence of heat generation/absorption, ASME J. Heat Trans., 128, 142152(2006) 
[ 30 ]  Jha, B. K. and Ajibade, A. O. Free convective flow of heat generating/absorbing fluid between vertical porous plates with periodic heat input. Int. Comm. Heat Mass Transfer, 36 624631(2009) 
[ 31 ]  Pop, I. and Watanabe, T. Hall effect on magnetohydrodynamic free convection about a semiinfinite vertical flat plate. Int. J. Eng .Sci., 32, 1903(1994) 
[ 32 ]  AboEldahab, E. M., Elbarbary, E. M. E. Hall current effect on magnetohydrodynamic freeconvection flow past a semiinfinite vertical plate with mass transfer. Int. J. Eng Sci., 39, 1641(2001) 
[ 33 ]  Takhar, H. S., Roy, S., Nath, G. Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and Hall currents. Heat Mass Transfer, 39, 825(2003) 
[ 34 ]  Saha, L. K., Siddiqa, S., Hossain, M. A. Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux. Appl Math MechEngl Ed, 32, 1127(2011) 
[ 35 ]  Siva Reddy Sheri.,Chamkha Ali J. and Anjan Kumar Suram. Thermaldiffusion and diffusionthermo effects on MHD natural convective flow through porous medium in a rotating system with ramped temperature.Int. J. Numerical Methods for Heat & Fluid Flow,27(11), 25412480(2017). 
[ 36 ]  Siva Reddy Sheri.,Anjan Kumar Suram. andPrashanthiModugula. Heat and mass transfer effects on MHD natural convection Flow past an infinite inclined plate with ramped temperature, J. Korean Society for Industrial and Applied Mathematics, 20(4), 355–374 (2016) 
[ 37 ]  Siva Reddy Sheri,.andAnjan Kumar Suram. Finite element analysis of heat and mass transfer past an impulsively moving vertical plate with ramped temperature, Tamkang J. Sci. Eng., 19(4), 385392(2016) 
[ 38 ]  Bathe, K. J. Finite Element Procedures, Prentice – Hall, New Jersey, (1996) 
[ 39 ]  Reddy, J. N. An Introduction to the Finite Element Method, McGraw – Hill Book Company, New York, 3rd Edition(2006) 