A theoretical study is carried out to obtain an analytic solution of heat and mass transfer in a vertical porous channel with rotation and Hall current. A constant suction and injection is applied to the two insulating porous plates. A strong magnetic field is applied in the transverse direction. The entire system rotates with uniform angular velocity about the axis normal to the plates. The governing equations are solved by perturbation technique to obtain the analytical results for velocity, temperature, and concentration fields and shear stresses. The steady and unsteady resultant velocities along with the phase differences for various values of physical parameters are discussed in detail. The effects of rotation, buoyancy force, magnetic field, thermal radiation, and heat generation parameters on resultant velocity, temperature, and concentration fields are analyzed. 1. Introduction Free convection in channel flow has many important applications in designing ventilating and heating of buildings, cooling of electronic components of a nuclear reactor, bed thermal storage, and heat sink in the turbine blades. Convective flows driven by temperature difference of the bounding walls of channels are important in industrial applications. El-Hakiem [1] studied the unsteady MHD oscillatory flow on free convection radiation through a porous medium with a vertical infinite surface that absorbs the fluid with a constant velocity. Jaiswal and Soundalgekar [2] analyzed the effects of suction with oscillating temperature on a flow past an infinite porous plate. Singh et al. [3] studied the unsteady free convective flow in a porous medium bounded by an infinite vertical porous plate in the presence of rotation. Pal and Shivakumara [4] studied the mixed convection heat transfer from a vertical plate in a porous medium. Hydromagnetic convection with heat transfer in a rotating medium has important applications in MHD generators and accelerators design, geophysics, and nuclear power reactors. MHD free convection and mass transfer flows in a rotating system have diverse applications. The effects of Hall currents cannot be neglected as the conducting fluid when it is an ionized gas, and applied field strength is strong then the electron cyclotron frequency (where , , and denote the electron charge, the applied magnetic field, and mass of an electron, resp.) exceeds the collision frequency so that the electron makes cyclotron orbit between the collisions which will divert in a direction perpendicular to the magnetic and electric fields directions. Thus, if an electric
References
[1]
M. A. El-Hakiem, “MHD oscillatory flow on free convection-radiation through a porous medium with constant suction velocity,” Journal of Magnetism and Magnetic Materials, vol. 220, no. 2-3, pp. 271–276, 2000.
[2]
B. S. Jaiswal and V. M. Soundalgekar, “Oscillating plate temperature effects on a flow past an infinite vertical porous plate with constant suction and embedded in a porous medium,” Heat and Mass Transfer, vol. 37, no. 2-3, pp. 125–131, 2001.
[3]
K. D. Singh, M. G. Gorla, and H. Raj, “A periodic solution of oscillatory couette flow through porous medium in rotating system,” Indian Journal of Pure and Applied Mathematics, vol. 36, no. 3, pp. 151–159, 2005.
[4]
D. Pal and I. S. Shivakumara, “Mixed convection heat transfer from a vertical heated plate embedded in a sparsely packed porous medium,” International Journal of Applied Mechanics and Engineering, vol. 11, no. 4, pp. 929–939, 2006.
[5]
T. G. Cowling, Magnetohydrodynamics, Interscience Publishers, New York, NY, USA, 1957.
[6]
A. S. Gupta, “Hydromagnetic flow past a porous flat plate with hall effects,” Acta Mechanica, vol. 22, no. 3-4, pp. 281–287, 1975.
[7]
R. N. Jana, A. S. Gupta, and N. Datta, “Hall effects on the hydro magnetic flow past an infinite porous flat plate,” Journal of the Physical Society of Japan, vol. 43, no. 5, pp. 1767–1772, 1977.
[8]
O. D. Makinde and P. Y. Mhone, “Heat transfer to MHD oscillatory flow in a channel filled with porous medium,” Romanian Journal of Physics, vol. 50, pp. 931–938, 2005.
[9]
Z. Zhang and J. Wang, “On the similarity solutions of magnetohydrodynamic flows of power-law fluids over a stretching sheet,” Journal of Mathematical Analysis and Applications, vol. 330, no. 1, pp. 207–220, 2007.
[10]
M. Hameed and S. Nadeem, “Unsteady MHD flow of a non-Newtonian fluid on a porous plate,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 724–733, 2007.
[11]
O. D. Makinde, O. A. Beg, and H. S. Takhar, “Magnetohydrodynamic viscous flow in a rotating porous medium cylindrical annalus with on applied radial magnetic field,” International Journal of Applied Mathematics and Mechanics, vol. 5, pp. 68–81, 2009.
[12]
P. Sibanda and O. D. Makinde, “On steady MHD flow and heat transfer past a rotating disk in a porous medium with ohmic heating and viscous dissipation,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 20, no. 3, pp. 269–285, 2010.
[13]
I. Pop and T. Watanabe, “Hall effects on magnetohydrodynamic free convection about a semi-infinite vertical flat plate,” International Journal of Engineering Science, vol. 32, no. 12, pp. 1903–1911, 1994.
[14]
L. K. Saha, S. Siddiqa, and M. A. Hossain, “Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux,” Applied Mathematics and Mechanics (English Edition), vol. 32, no. 9, pp. 1127–1146, 2011.
[15]
D. Pal, B. Talukdar, I. S. Shivakumara, and K. Vajravelu, “Effects of Hall current and chemical reaction on oscillatory mixed convection-radiation of a micropolar fluid in a rotating system,” Chemical Engineering Communications, vol. 199, pp. 943–965, 2012.
[16]
A. C. Cogley, W. C. Vincenti, and S. E. Gilles, “Differential approximation for radiation transfer in a nongray gas near equilibrium,” American Institute of Aeronautics and Astronautics Journal, vol. 6, pp. 551–555, 1968.
[17]
M. A. Mansour, “Radiative and free-convection effects on the oscillatory flow past a vertical plate,” Astrophysics and Space Science, vol. 166, no. 2, pp. 269–275, 1990.
[18]
M. A. Hossain and H. S. Takhar, “Radiation effect on mixed convection along a vertical plate with uniform surface temperature,” Heat and Mass Transfer, vol. 31, no. 4, pp. 243–248, 1996.
[19]
M. A. Hossain, M. A. Alim, and D. A. S. Rees, “The effect of radiation on free convection from a porous vertical plate,” International Journal of Heat and Mass Transfer, vol. 42, no. 1, pp. 181–191, 1999.
[20]
M. A. Seddeek, “Effects of radiation and variable viscosity on a MHD free convection flow past a semi-infinite flat plate with an aligned magnetic field in the case of unsteady flow,” International Journal of Heat and Mass Transfer, vol. 45, no. 4, pp. 931–935, 2002.
[21]
R. Muthucumaraswamy and G. K. Senthil, “Studied the effect of heat and mass transfer on moving vertical plate in the presence of thermal radiation,” Journal of Theoretical And Applied Mechanics, vol. 31, no. 1, pp. 35–46, 2004.
[22]
D. Pal, “Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of buoyancy force and thermal radiation,” Meccanica, vol. 44, no. 2, pp. 145–158, 2009.
[23]
O. Aydin and A. Kaya, “Radiation effect on MHD mixed convection flow about a permeable vertical plate,” Heat and Mass Transfer, vol. 45, no. 2, pp. 239–246, 2008.
[24]
R. A. Mohamed, “Double-diffusive convection-radiation interaction on unsteady MHD flow over a vertical moving porous plate with heat generation and Soret effects,” Applied Mathematical Sciences, vol. 3, no. 13–16, pp. 629–651, 2009.
[25]
D. S. Chauhan and P. Rastogi, “Radiation effects on natural convection MHD flow in a rotating vertical porous channel partially filled with a porous medium,” Applied Mathematical Sciences, vol. 4, no. 13–16, pp. 643–655, 2010.
[26]
S. Y. Ibrahim and O. D. Makinde, “Radiation effect on chemically reacting magnetohydrodynamics (MHD) boundary layer flow of heat and mass transfer through a porous vertical flat plate,” International Journal of Physical Sciences, vol. 6, no. 6, pp. 1508–1516, 2011.
[27]
D. Pal and H. Mondal, “The influence of thermal radiation on hydromagnetic darcy-forchheimer mixed convection flow past a stretching sheet embedded in a porous medium,” Meccanica, vol. 46, no. 4, pp. 739–753, 2011.
[28]
G. Palani and K. Y. Kim, “Influence of magnetic field and thermal radiation by natural convection past vertical cone subjected to variable surface heat flux,” Applied Mathematics and Mechanics (English Edition), vol. 33, pp. 605–620, 2012.
[29]
M. A. A. Mahmoud and S. E. Waheed, “Variable fluid properties and ther-28 mal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite flat plate with slip velocity,” Applied Mathematics and Mechanics (English Edition), vol. 33, pp. 663–678, 2012.
[30]
E. M. Aboeldahab and E. M. E. Elbarbary, “Hall current effect on magnetohydrodynamic free-convection flow past a semi-infinite vertical plate with mass transfer,” International Journal of Engineering Science, vol. 39, no. 14, pp. 1641–1652, 2001.
[31]
E. M. Abo-Eldahab and M. A. El Aziz, “Viscous dissipation and Joule heating effects on MHD-free convection from a vertical plate with power-law variation in surface temperature in the presence of Hall and ion-slip currents,” Applied Mathematical Modelling, vol. 29, no. 6, pp. 579–595, 2005.
[32]
R. Kandasamy, K. Periasamy, and K. K. Sivagnana Prabhu, “Chemical reaction, heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification effects,” International Journal of Heat and Mass Transfer, vol. 48, no. 21-22, pp. 4557–4561, 2005.
[33]
R. Muthucumaraswamy and B. Janakiraman, “Mass transfer effects on isothermal vertical oscillating plate in the presence of chemical reaction,” International Journal of Applied Mathematics and Mechanics, vol. 4, no. 1, pp. 66–74, 2008.
[34]
P. R. Sharma and K. D. Singh, “Unsteady MHD free convective flow and heat transfer along a vertical porous plate with variable suction and internal heat generation,” International Journal of Applied Mathematics and Mechanics, vol. 4, no. 5, pp. 1–8, 2009.
[35]
M. Sudheer Babu and P. V. Satya Narayan, “Effects of the chemical reaction and radiation absorption on free convection flow through porous medium with variable suction in the presence of uniform magnetic field,” Journal of Heat and Mass Transfer, vol. 3, pp. 219–234, 2009.
[36]
O. D. Makinde and T. Chinyoka, “Numerical study of unsteady hydromagnetic Generalized Couette flow of a reactive third-grade fluid with asymmetric convective cooling,” Computers and Mathematics with Applications, vol. 61, no. 4, pp. 1167–1179, 2011.
[37]
D. Pal and B. Talukdar, “Combined effects of Joule heating and chemical reaction on unsteady magnetohydrodynamic mixed convection of a viscous dissipating fluid over a vertical plate in porous media with thermal radiation,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 3016–3036, 2011.
[38]
K. D. Singh and R. Kumar, “Combined effects of hall current and rotation on free convection MHD flow in a porous channel,” Indian Journal of Pure and Applied Physics, vol. 47, no. 9, pp. 617–623, 2009.
[39]
R. C. Meyer, “On reducing aerodynamic heat transfer rates by magnetohydrodynamic techniques,” Journal of the Aerospace Sciences, vol. 25, p. 561, 1958.
