Unsteady Heat and Mass Transfer in MHD Viscoelastic Fluid Flow through Porous Medium between Two Inclined Porous Parallel Plates with Soret Effect and G-Jitter Force
Keywords:Free Convection, Inclined Channel, MHD (Magneto Hydro-Dynamics), Viscoelastic Fluid, Soret Effect.
AbstractThe unsteady two-dimensional convective flow of a viscous incompressible, electrically conducting, viscoelastic fluid (Rivlin-Ericksen Model) through porous medium bounded between two inclined porous plates with time dependent injection and same suction velocity has been investigated. At the first plate where injection and same suction velocity has been investigated. At the first plate where injection is taking place is assumed to have a slip property while the other plate is moving with a constant velocity. A first order chemical reaction is considered. Magnetic field is applied transversely to the channel, and assumed so strong that the induced magnetic field is negligibly small. The inclination of channel with direction of gravity is assumed to be between 0 and 90 (acute angle). The effects of a number of non-dimensional parameters namely; Prandtl number (Pr), Grashof number (Gr), modified Grashof number (Gc), frequency of oscillation (Ï‰), viscoelastic parameter (Rc), Soret number (S0) and heat absorption coefficient (Q0) entering into the problem on the velocity, temperature and concentration profiles are stud- ied in detail. Solution of the present problem is found analytically by the method of perturbation technique. Pertinent results regarding the effect of above said non-dimensional numbers for velocity, temperature and concentration profiles are concluded from graphs and tables. Scientific software and Origin software are used for numerical calculations and plot of graphs respectively. The contribution of the temperature gradient to the flux of matter (Soret effect), the effect of angle of inclination of channel and effect of g-jitter are the leading phenomenon.
S. M. Alharbi, M. A. A. Bazid, and M. S. E. Glendy, Heat and mass transfer in MHD viscoelastic fluid through porous medium over a stretching sheet with chemical reaction. Applied Mathematics, 1 (2010), 446-455.
F. Ali, I. Khan and S. Shafie, Closed form solutions for unsteady free convective flow of a second grade fluid over an oscillating vertical plate, PLOS ONE 9 (2014) 1-15.
K. Chand, K. D. Singh and S. Sharma, Combined effects of chemical reaction and radiation on heat and mass transfer in oscillatory MHD flow of viscoelastic fluid through vertical channel, Research J. Science and Tech. 5 (2013), 77-84.
C. H. Chen, Heat and mass transfer in MHD flow by natural convection from a permeable, inclined surface with variable wall temperature and concentration. Acta Mechanica 172 (2004), 219-235.
T. Chinyoka, S. P. Goqo, and B. I. Olajuwon, Computational analysis of gravity driven flow of a variable viscosity viscoelastic fluid down an inclined plane. Computers and Fluids, 84 (2013), 315-326.
C. I. Christov and G. M. Homsy, Nonlinear dynamics of two dimensional convection in a vertically stratified slot with and without gravity modulation. J Fluid Mech 430 (2001), 335-360.
K. R. Crammer and S. Pai, Magneto fluid dynamics for engineers and Applied Physicist, McGraw Hill New York (1973).
A. C. Cogley, W. G. Vincent, and S. E. Giles, Differential approximation to radiative heat transfer in a non-grey gas near equilibrium. AIAA, 6 (1968), 551-553.
G. C. Dash, P. K. Rath and N. Mahapatra, Unsteady free convection MD flow and mass transfer through porous media of a second order fluid between two heated plates with source/sink, Proc Nat Acad Sci., India section A, 80 (2010) 203-212.
A. Farooq and G. M. Homsy, Streaming flows due to g-jitter induced natural convection, J Fluid Mech, 271 (1994), 351-378.
A. Farooq and G. M. Homsy, Linear and nonlinear dynamics of a differentially heated slot under gravity modulation, J Fluid Mech, 313 (1996), 1-38.
M. Farooq, M. T. Rahim, S. Islam, and A. M. Siddiqui, Steady Poiseulle flow and heat transfer of couple stress fluids between two parallel inclined plates with variable viscosity. Journal of the Association of Arab Universities for Basic and Applied Sciences, 14 (2013), 9-18.
A. V. Glazunov and Dymnikov, Spatial spectra and characteristic horizontal scales of temperature and velocity fluctuations in convective boundary layer of the atmosphere. Izvestiya, Atmospheric and oceanic physics, 49 (2013), 33-54.
P. M. Gresho and R. L. Sani, The effects of gravity modulation on the stability of a heated fluid layer. J Fluid Mech, 40 (1970) 783-806.
T. Hayat, F. M. Abbasi, Al. M. Yami, and S. Monquel, Slip and joule heating effects in mixed convection peristaltic transport of nano-fluid with Soret and Dufour effects. Journal of Molecular liquids, 194 (2014), 93-99.
S. Jothimani, and S. P. A. Devi, Hydromagnetic slip flow with heat transfer in an inclined channel. Czechoslovak Journal of Physics, 48 (1998), 89-96.
J. P. Mahato, Unsteady free convective flow and mass transfer in a rotating porous medium, Indian J Technol, 26 (1988), 225-234.
A. Manglesh, and M. G. Gorla, MHD free convective flow through porous medium in the presence of Hall current, radiation and thermal diffusion. Indian J. Pure and Appl. Math., 44 (2013), 743-756.
H. Neff, Lima, A. M. N., Loureiro, F. C. C. L. and Almeida, L. A. L. Transient response analysis and modeling of near wall flow conditions in micro channel: evidence of slip flow, Micro fluid Nano fluid, 3 (2007), 591-602.
J. Prakash, D. Bhanumathi, A. G. V. Kumar, and S. V. K. Varma, Diffusion- Thermo and radiation effects on unsteady MHD flow through porous medium past an impulsively started infinite vertical plate with variable temperature and mass diffusion. Transp. Porous Med. 96 (2013), 135-151.
M. M. Rashidi, T. Hayat, E. P. Erfani, S. A. M. Pour and A. A. Hendi, Simultaneous effects of partial slip and thermal-diffusion and diffusion-thermo on steady MHD convective flow due to a rotating disk. Commun Nonlinear Sci Numer Simulat, 16 (2011), 4303-4317.
M. C. Raju, S. V. K. Varma, P. V. Reddy, and S. Saha, Soret effect due to natural convection between heated inclined plates with magnetic field. Journal of Mechanical Engineering, 39 (2008), 65-70.
H. Schlichting, Boundary layer theory, Mc Graw-Hill, New York (1960).
C. Seis, Laminar Boundary layers in convective heat transport. Communications in Mathematical Physics, 324 (2013), 995-1031.
V. Shevtsova, I. I. Ryzkov, D. E. Melnikov, Y. A. Gaponenko and A. Mialdun, Experimental and theoretical study of vibration-induced thermal convection in low gravity, J Fluid Mech, 648 (2010), 53-82.
S. Srinivas, T. Malathy and A. S. Reddy, A note on thermal-diffusion and chemical reaction effects on MHD pulsating flow in a porous channel with slip and convective boundary conditions. Journal of King Saud University- Engineering Sciences. http://dx.doi.org/10.1016/j.jksues.2014.03.011.
K. D. Singh, Visco-elastic MHD convective periodic flow through porous medium in a rotating vertical channel with thermal radiation, Journal of Global Research in Mathematical Archives, 1(2013), 8-20.