Volume 53 | Number 5 | Year 2018 | Article Id. IJMTT-V53P548 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P548
In this study, the unsteady magnetohydrodynamic (MHD) flow and heat trasnfer of a dusty, viscoelastic, incompressible and electrically conducting fluid in an inclined channel in the presence of thermal radiation and heat source has been investigated. The non-dimensional equations governing the flow are solved by parametric perturbation technique under the prescribed boundary conditions. The solutions of the equations governing the flow are obtained for fluid velocity, dust particle velocity, temperature and dust particle temperature profile.The results have been expressed graphically and in tabular form to observe the effects of different flow parameters. The effect of the various parameters entering in the governing equations on the flow are evaluated numerically and discussed with the help of graphs and tables.
[1] H. P. Greenspan and G. F. Carrier, “The MHD flow past a flat plate”, J. Fluid Mech., Vol.6, pp. 77-96, 1959.
[2] Y. J. Kim, “Unsteady MHD convective heat transfer past a semi-infinite vertical porous plate with variable suction”, Int. J.Engng. Sci., Vol. 38, pp. 833, 2000.
[3] H. A. Attia and N. A. Kotb, “MHD flow between two parallel plates with heat transfer”, Acta Mech., Vol.117, pp.215-220, 1996.
[4] M. A. Seddeek, “The effect of variable viscosity on hydromagnetic flow and heat transfer past a continuously moving porous boundary with radiation”, Int. Comm., Heat Mass Transfer, Vol. 27(7), pp. 1037-1046, 2000.
[5] O. D. Makinde and P.Y. Mhone, “Heat transfer to MHD oscillatory flow in a channel filled with a porous medium”, Rom. Journ. Phys., Vol.50, pp.931-938, 2005.
[6] S. Seth, R. Nandkeolyar and Md. S. Ansari, “Unsteady MHD convective flow within a parallel plate rotating channel with thermal source/sink in a porous medium under slip boundary conditions”, Int. J. of Engng., Sci. and Tech., Vol. 11, pp. 1-16, 2010.
[7] P. K. Sharma and S. K. Saini, “MHD Flow though Rotating Porous Medium with Radiating Heat Transfer in the Presence of Fluctuating Thermal Diffusion”, Universal Journal of Applied Mathematics, Vol. 2(2) pp. 92-98, http://www.hrpub.org DOI: 10.13189/ujam.2014.020203, 2014.
[8] D. Singh, “Effect of injection/ suction on convective oscillatory flow through porous medium bounded by two vertical porous plates”, Int. J. Physical and Mathematical Sciences, Vol. 2, pp. 140-147, 2011.
[9] S. T. Dinesh Kumar, P. Raveendra Nath, “A numerical study of convective heat transfer through a porous medium in a vertical channel with radiation effect”, International Conference computational, Heat and Mass Transfer, Vol. 127, pp.1281-1291, 2015.
[10] Z. Abbas, S.Rasool and M.M.Rashidi, “Heat transfer analysis due to an unsteady stretching/shrinking cylinder with partial slip condition and suction”, Ain Shams Engineering Journal, Vol. 6, pp. 939-945, 2015.
[11] M. S. Dada and A. B. Disu, “Heat transfer with radiation and temperature dependent heat source in MHD free convection flow in a porous medium between two vertical wavy walls”, Journal of Nigerian Society, Vol. 34, pp. 200-215, 2015.
[12] K. Walters, “Non- Newtonian effects in some general elastic-viscous liquids”, Proc. I.U.T.A.M. Symposium, Hafia, Isreal, pp.507-515, 1962.
[13] S. P. Mishra and T. C. Panda, “Effect of injection on the flow of second grade fluid in the inlet region of a channel”, Acta Mech., Vol.32, pp-11-17, 1979.
[14] P. D. Ariel, “The flow of a visco elastic fluid past a porous plate”, Acta Mech., Vol. 107, pp.199-204, 1984.
[15] C. E. Maneschy ,M. Massoudi and A. Ghoneimy, “Heat transfer analysis of a non-newtonian fluid past a porous plate”, International Journal of Non-linear Mechanics, Vol. 28(2), pp. 131-143, 1993.
[16] C. Kurtcebe and M. Z. Erim, “Heat transfer of a visco-elastic fluid in a porous channe”l, Int.J.Heat Mass Transfer, Vol. 48, pp. 5072-5077, 2005.
[17] Ali Attia Hazem, „Unsteady coquette flow with heat transfer of a visco elastic fluid considering the Hall Effect‟, Kragujevac J. Sci., Vol. 27, pp.5-22, 2005.
[18] P. R. Sharma and D. Pareek, “Unsteady flow and heat transfer through an elastico-viscous liquid along an infinite hot vertical porous moving plate with variable free stream and suction”, Bull. Cal. Math. Soc., Vol .98(2), pp.97-108, 2006.
[19] K. D. Singh, “Visco elastic mixed convection MHD oscillatory flow through a porous medium filled in a vertical channel”, Int. J. Physical and Mathematical Sciences, Vol. 3 pp.194-205, 2012.
[20] R. Choudhary and D. U. Jyoti, “Heat transfer to MHD oscillatory visco elastic flow in a channel filled with porous medium”, Physics Research International doi: 101155/ 2012/879537, 2012.
[21] A. A. Khan, R. Ellahi and M. Usman (2013), The effects of variable viscosity on the peristaltic flowof non-newtonian fluid through a porous medium in an inclined channel with slip boundary conditions, Journal of Porous Media, Vol.2, pp.16.
[22] B. P. Garg, K. D. Singh, A .K. Bansal, “An Oscillatory MHD Convective Flow of Viscoelastic Fluid through Porous Medium Filled in a Rotating Vertical Porous Channel with Heat Radiation”, International Journal of Engineering and Innovative Technology (IJEIT), Vol. 3, Issue 12, pp.273, 2014.
[23] P.G. Saffman , “ On the stability of laminar flow of a dusty gas”, Journal of Fluid Mechanics, Vol.13, pp.120, 1962.
[24] R. K. Gupta, S.C. Gupta , “Flow of a dusty gas through a channel with arbitrary time varying pressure gradient”, Journal of Applied Mathematics and Physics, Vol. 27, pp. 119, 1976.
[25] K. K. Singh, “Unsteady flow of a conducting dusty fluid through a rectangular channel with time dependent pressure gradient”, Indian Journal of Pure and Applied Mathematics, Vol. 8 (9) , pp.1124, 1976.
[26] V. R. Prasad, N. C. P. Ramacharyulu , “ Unsteady flow of a dusty incompressible fluid between two parallel plates under an impulsive pressure gradient”, Defence Science Journal, Vol. 30 , pp. 125, 1979.
[27] H. A. Attia, “Influence of temperature dependent viscosity on MHD channel flow of dusty fluid with heat transfer”, Acta Mech., Vol. 151, pp. 89-101, 2001.
[28] H. A. Attia, “Unsteady MHD flow and heat transfer of dusty fluid between parallel plates with variable physical properties”, Applied Mathematical Modelling, Vol. 26 pp. 863–875, 2002.
[29] H. A. Attia, “Influence of temperature-dependent viscosity on the MHD Couette flow of dusty fluid with heat transfer” , Differential Equations and Nonlinear Mechanics, Vol. 2006, Article ID 75290, Pages 1–14,DOI 10.1155/DENM/2006/75290.
[31] G. Palani and P. Ganesan, “ Heat transfer effect on dusty gas flow past a semi infinite inclined plate”, Forschung im Ingsenteurwesen, Vol.71(3-4),pp. 223-230, 2007.
[32] O.D. Makinde, T. Chinyoka, “MHD transient flows and heat transfer of dusty fluid in a channel with variable physical properties and Navier slip condition", Computers and Mathematics with Applications, Vol. 60, pp.660-669, 2010.
[33] K. Chand and S. Kumar, “Effect of hall current and rotation on chemically reacting and radiating MHD oscillatory dusty viscoelastic flow through porous vertical channel”, International Journal of Applied and Computation, Vol. 5(3), pp.17-32, 2013.
[34] K. Chand, K. D. Singh and S. Sharma, “Heat transfer in MHD oscillatory flow of dusty fluid in a rotating porous vertical channel”, Indian J. Pure Appl. Math., 819-835, 2014.
[35] H. A. Attia, A. L. Aboul- Hassan, M. A. M. Abdeen and A. El-Din Abdin, “MHD flow of a dusty fluid between two infinite parallel plates with temperature dependent physical properties under exponentially decaying pressure gradient”, Bulgarian Chemical Communications, Vol. 46(2) pp. 320 – 329, 2014.
[36] M. Jalil, S. Asghar and S. Yasmeen, “An exact solution of MHD boundary layer flow of Dusty fluid over a stretching surface”, Mathematical Problems in Engineering, Vol. 2017, Article ID 2307469, 5 pages, https://doi.org/10.1155/2017/2307469, 2017.
[37] A. C. Cogley, W. G. Vincenti, S. E. Gilles, “Differential approximation for radiative transfer in a non-gray gas near equilibrium”,Am. Inst. Aeronaut, Astronaut, Vol. 6, pp. 551-553, 1968.
[38] S. Sengupta and N. Ahmed, “MHD free convective Chemically reactive flow of a dissipative fluid with thermal diffusion, fluctuating wall temperature and concentration in velocity slip regime,” Int. J. of Appl. Math and Mech., vol. 10(4), pp.27-54, 2014.
Khem Chand, Sapna, "Hydromagnetic Oscillatory Flow and Heat Transfer in Dusty Viscoelastic Fluid Through Porous Medium in an Inclined Channel in The Presence of Thermal Radiation and Heat Sink," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 5, pp. 397-408, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P548