Combined Effects of Hall Current and Radiation on MHD Free Convective Flow in a Vertical Channel with an Oscillatory Wall Temperature

Affiliation(s)

Department of Applied Mathematics, Vidyasagar University, Midnapore, India.

Department of Mathematics, University of Gour Banga, English Bazar, India.

Department of Applied Mathematics, Vidyasagar University, Midnapore, India.

Department of Mathematics, University of Gour Banga, English Bazar, India.

ABSTRACT

The combined effects of Hall current and radiation on an unsteady MHD free convective flow of a viscous incompressible electrically conducting fluid in a vertical channel with an oscillatory wall temperature have been studied. We have considered two different cases 1) flow due to the impulsive motion of one of the channel walls and 2) flow due to the accelerated motion of one of the channel walls. The governing equations are solved analytically using the Laplace transform technique. It is found that the primary velocity and the magnitude of the secondary velocity increase with an increase in Hall parameter for both the impulsive as well as the accelerated motions of one of the channel walls. An increase in either radiation parameter or frequency parameter leads to decrease in the primary velocity and the magnitude of the secondary velocity for both the impulsive as well as accelerated motions of one of the channel walls. The fluid temperature decreases with an increase in radiation parameter. Further, the shear stresses at the left wall reduce with an increase in either radiation parameter or frequency parameter for both the impulsive as well as the accelerated motions of one of the channel wall.

The combined effects of Hall current and radiation on an unsteady MHD free convective flow of a viscous incompressible electrically conducting fluid in a vertical channel with an oscillatory wall temperature have been studied. We have considered two different cases 1) flow due to the impulsive motion of one of the channel walls and 2) flow due to the accelerated motion of one of the channel walls. The governing equations are solved analytically using the Laplace transform technique. It is found that the primary velocity and the magnitude of the secondary velocity increase with an increase in Hall parameter for both the impulsive as well as the accelerated motions of one of the channel walls. An increase in either radiation parameter or frequency parameter leads to decrease in the primary velocity and the magnitude of the secondary velocity for both the impulsive as well as accelerated motions of one of the channel walls. The fluid temperature decreases with an increase in radiation parameter. Further, the shear stresses at the left wall reduce with an increase in either radiation parameter or frequency parameter for both the impulsive as well as the accelerated motions of one of the channel wall.

Cite this paper

S. Guchhait, S. Das and R. Jana, "Combined Effects of Hall Current and Radiation on MHD Free Convective Flow in a Vertical Channel with an Oscillatory Wall Temperature,"*Open Journal of Fluid Dynamics*, Vol. 3 No. 1, 2013, pp. 9-22. doi: 10.4236/ojfd.2013.31002.

S. Guchhait, S. Das and R. Jana, "Combined Effects of Hall Current and Radiation on MHD Free Convective Flow in a Vertical Channel with an Oscillatory Wall Temperature,"

References

[1] H. Sato, “The Hall Effects in the Viscous Flow of Ionized Gas between Parallel Plates under Transverse Magnetic Field,” Journal of Physical Society of Japan, Vol. 16, 1961, pp. 14-27. doi:10.1143/JPSJ.16.1427

[2] O. Miyatake and T. Fujii, “Free Convection Heat Transfer between Vertical Plates—One Plate Isothermally Heated and Other Thermally Insulated,” Heat Transfer—Japanese Research, Vol. 1, 1972, pp. 30-38.

[3] H. Tanaka, O. Miyatake, T. Fujii and M. Fujii, “Natural Convection Heat Transfer between Vertical Parallel Plates—One Plate with a Uniform Heat Flux and the Other Thermally Insulated,” Heat Transfer—Japanese Research, Vol. 2, 1973, pp. 25-33.

[4] P. S. Gupta and A. S. Gupta, “Radiation Effect on Hydromantic Convection in a Vertical Channel,” International Journal of Heat Mass Transfer, Vol. 17, No. 12, 1974, pp. 1437-1442. doi:10.1016/0017-9310(74)90053-2

[5] N. Datta and R. N. Jana, “Hall Effects on Hydromagnetic Convective Flow through a Channel with Conducting Walls,” Internationa Journal of Engineering Science, Vol. 15, No. 9-10, 1977, pp. 561-567. doi:10.1016/0020-7225(77)90052-0

[6] A. R. Bestman and S. A. Adjepong, “Unsteady Hydromagnetic Free Convection Flow with Radiative Heat Transfer in a Rotating Fluid,” Space Science, Vol. 143, No. 1, 1988, pp. 73-80. doi:10.1007/BF00636756

[7] H. M. Joshi, “Transient Effects in Natural Convection Cooling of Vertical Parallel Plates,” International Communication Heat and Mass Transfer, Vol. 15, No. 2, 1988, pp. 227-238. doi:10.1016/0735-1933(88)90068-1

[8] A. K. Singh, “Natural Convection in Unsteady Couette Motion,” Defense Science Journal, Vol. 38, No. 1, 1988, pp. 35-41.

[9] A. K. Singh, H. K. Gholami and V. M. Soundalgekar, “Transient Free Convection Flow between Two Vertical Parallel Plates,” Heat and Mass Transfer, Vol. 31, No. 5, 1996, pp. 329-331. doi:10.1007/BF02184046

[10] B. K. Jha, “Natural Convection in Unsteady MHD Couette Flow,” Heat and Mass Transfer, Vol. 37, No. 4-5, 2001, pp. 329-331. doi:10.1007/PL00013295

[11] M. Narahari, S. Sreenadh and V. M. Soundalgekar, “Transient Free Convection Flow between Long Vertical Parallel Plates with Constant Heat Flux at One Boundary,” Journal of Thermophysics and Aeromechanics, Vol. 9, No. 2, 2002, pp. 287-293.

[12] B. K. Jha, A. K. Singh and H. S. Takhar, “Transient Free Convection Flow in a Vertical Channel Due to Symmetric Heating,” International Journal of Applied Mechichal Engineering, Vol. 8, No. 3, 2003, pp. 497-502.

[13] A. K. Singh and T. Paul, “Transient Natural Convection between Two Vertical Walls Heated/Cooled Asymetrically,” International Journal of Applied Mechanical Engineering, Vol. 11, No. 1, 2006, pp. 143-154.

[14] D. C. Sanyal and A. Adhikari, “Effects of Radiation on MHD Vertical Channel Flow,” Bulletin of Calcutta Mathematical Society, Vol. 98, No. 5, 2006, pp. 487-497.

[15] P. Mebine, “Radiation Effects on MHD Couette Flow with Heat Transfer between Two Parallel Plates,” Global Journal of Pure and Applied Mathematics, Vol. 3, No. 2, 2007, pp. 1-12.

[16] T. Grosan and I. Pop, “Thermal Radiation Effect on Fully Developed Mixed Convection Flow in a Vertical Channel,” Technische Mechanik, Vol. 27, No. 1, 2007, pp. 37-47.

[17] M. Guria and R. N. Jana, “Hall Effects on the Hydromagnetic Convective Flow through a Rotating Channel under General Wall Conditions,” Magnetohydrodynamics, Vol. 43, No. 3, 2007, pp. 287-300.

[18] B. K. Jha and A. O. Ajibade, “Unsteady Free Convective Couette Flow Of Heat Generating/Absorbing Fluid,” International Journal of Energy and Technology, Vol. 2, No. 12, 2010, pp. 1-9.

[19] M. Narahari, “Effects of Thermal Radiation and Free Convection Currents on the Unsteady Couette Flow between Two Vertical Parallel Plates with Constant Heat Flux at One Boundary,” WSEAS Transactions on Heat and Mass Transfer, Vol. 5, No. 1, 2010, pp. 21-30.

[20] U. S. Rajput and P. K. Sahu, “Transient Free Convection MHD Flow between Two Long Vertical Parallel Plates with Constant Temperature and Variable Mass Diffusion,” International Journal of Mathematical Analysis, Vol. 5, No. 34, 2011, pp. 1665-6671.

[21] S. Das, B. C. Sarkar and R. N. Jana, “Radiation Effects on Free Convection MHD Couette Flow Started Exponentially with Variable Wall Temperature in Presence of Heat Generation,” Open Journal of Fluid Dynamics, Vol. 2, No. 1, 2007, pp. 14-27.

[22] C. Mandal, S. Das and R. N. Jana, “Effect of Radiation on Transient Natural Convection Flow between Two Vertical Walls,” International Journal of Applied Information Systems, Vol. 2, No. 2, 2012, pp. 49-56.

[23] S. Das, S. K. Guchhait and R. N. Jana, “Radiation Effects on Unsteady MHD Free Convective Couette Flow of Heat Generation/Absorbing Fluid,” International Journal of Computer Applications, Vol. 39, No. 3, 2012, pp. 42-51.

[24] B. C. Sarkar, S. Das and R. N. Jana, “Effects of Radiation on MHD Free Convective Couette Flow in a Rotating System,” International Journal of Engineering Research and Application, Vol. 2, No. 4, 2012, pp. 2346-2359.

[25] B. C. Sarkar, S. Das and R. N. Jana, “Oscillatory MHD Free Convective Flow between Two Vertical Walls in a Rotating System,” Advance in Applied Science Research, Vol. 3, No. 5, 2012, pp. 3311-3325.

[26] A. C. Cogley, W. C. Vincentine and S. E. Gilles, “A Differential Approximation for Radiative Transfer in a NonGray Gas Near Equilibrium,” American Institute of Aeronautics and Astronautics Journal, Vol. 6, No. 3, 1968, pp. 551-555.

[27] T. G. Cowling, “Magnetohydrodynamics,” Interscience, New York, 1957.

[1] H. Sato, “The Hall Effects in the Viscous Flow of Ionized Gas between Parallel Plates under Transverse Magnetic Field,” Journal of Physical Society of Japan, Vol. 16, 1961, pp. 14-27. doi:10.1143/JPSJ.16.1427

[2] O. Miyatake and T. Fujii, “Free Convection Heat Transfer between Vertical Plates—One Plate Isothermally Heated and Other Thermally Insulated,” Heat Transfer—Japanese Research, Vol. 1, 1972, pp. 30-38.

[3] H. Tanaka, O. Miyatake, T. Fujii and M. Fujii, “Natural Convection Heat Transfer between Vertical Parallel Plates—One Plate with a Uniform Heat Flux and the Other Thermally Insulated,” Heat Transfer—Japanese Research, Vol. 2, 1973, pp. 25-33.

[4] P. S. Gupta and A. S. Gupta, “Radiation Effect on Hydromantic Convection in a Vertical Channel,” International Journal of Heat Mass Transfer, Vol. 17, No. 12, 1974, pp. 1437-1442. doi:10.1016/0017-9310(74)90053-2

[5] N. Datta and R. N. Jana, “Hall Effects on Hydromagnetic Convective Flow through a Channel with Conducting Walls,” Internationa Journal of Engineering Science, Vol. 15, No. 9-10, 1977, pp. 561-567. doi:10.1016/0020-7225(77)90052-0

[6] A. R. Bestman and S. A. Adjepong, “Unsteady Hydromagnetic Free Convection Flow with Radiative Heat Transfer in a Rotating Fluid,” Space Science, Vol. 143, No. 1, 1988, pp. 73-80. doi:10.1007/BF00636756

[7] H. M. Joshi, “Transient Effects in Natural Convection Cooling of Vertical Parallel Plates,” International Communication Heat and Mass Transfer, Vol. 15, No. 2, 1988, pp. 227-238. doi:10.1016/0735-1933(88)90068-1

[8] A. K. Singh, “Natural Convection in Unsteady Couette Motion,” Defense Science Journal, Vol. 38, No. 1, 1988, pp. 35-41.

[9] A. K. Singh, H. K. Gholami and V. M. Soundalgekar, “Transient Free Convection Flow between Two Vertical Parallel Plates,” Heat and Mass Transfer, Vol. 31, No. 5, 1996, pp. 329-331. doi:10.1007/BF02184046

[10] B. K. Jha, “Natural Convection in Unsteady MHD Couette Flow,” Heat and Mass Transfer, Vol. 37, No. 4-5, 2001, pp. 329-331. doi:10.1007/PL00013295

[11] M. Narahari, S. Sreenadh and V. M. Soundalgekar, “Transient Free Convection Flow between Long Vertical Parallel Plates with Constant Heat Flux at One Boundary,” Journal of Thermophysics and Aeromechanics, Vol. 9, No. 2, 2002, pp. 287-293.

[12] B. K. Jha, A. K. Singh and H. S. Takhar, “Transient Free Convection Flow in a Vertical Channel Due to Symmetric Heating,” International Journal of Applied Mechichal Engineering, Vol. 8, No. 3, 2003, pp. 497-502.

[13] A. K. Singh and T. Paul, “Transient Natural Convection between Two Vertical Walls Heated/Cooled Asymetrically,” International Journal of Applied Mechanical Engineering, Vol. 11, No. 1, 2006, pp. 143-154.

[14] D. C. Sanyal and A. Adhikari, “Effects of Radiation on MHD Vertical Channel Flow,” Bulletin of Calcutta Mathematical Society, Vol. 98, No. 5, 2006, pp. 487-497.

[15] P. Mebine, “Radiation Effects on MHD Couette Flow with Heat Transfer between Two Parallel Plates,” Global Journal of Pure and Applied Mathematics, Vol. 3, No. 2, 2007, pp. 1-12.

[16] T. Grosan and I. Pop, “Thermal Radiation Effect on Fully Developed Mixed Convection Flow in a Vertical Channel,” Technische Mechanik, Vol. 27, No. 1, 2007, pp. 37-47.

[17] M. Guria and R. N. Jana, “Hall Effects on the Hydromagnetic Convective Flow through a Rotating Channel under General Wall Conditions,” Magnetohydrodynamics, Vol. 43, No. 3, 2007, pp. 287-300.

[18] B. K. Jha and A. O. Ajibade, “Unsteady Free Convective Couette Flow Of Heat Generating/Absorbing Fluid,” International Journal of Energy and Technology, Vol. 2, No. 12, 2010, pp. 1-9.

[19] M. Narahari, “Effects of Thermal Radiation and Free Convection Currents on the Unsteady Couette Flow between Two Vertical Parallel Plates with Constant Heat Flux at One Boundary,” WSEAS Transactions on Heat and Mass Transfer, Vol. 5, No. 1, 2010, pp. 21-30.

[20] U. S. Rajput and P. K. Sahu, “Transient Free Convection MHD Flow between Two Long Vertical Parallel Plates with Constant Temperature and Variable Mass Diffusion,” International Journal of Mathematical Analysis, Vol. 5, No. 34, 2011, pp. 1665-6671.

[21] S. Das, B. C. Sarkar and R. N. Jana, “Radiation Effects on Free Convection MHD Couette Flow Started Exponentially with Variable Wall Temperature in Presence of Heat Generation,” Open Journal of Fluid Dynamics, Vol. 2, No. 1, 2007, pp. 14-27.

[22] C. Mandal, S. Das and R. N. Jana, “Effect of Radiation on Transient Natural Convection Flow between Two Vertical Walls,” International Journal of Applied Information Systems, Vol. 2, No. 2, 2012, pp. 49-56.

[23] S. Das, S. K. Guchhait and R. N. Jana, “Radiation Effects on Unsteady MHD Free Convective Couette Flow of Heat Generation/Absorbing Fluid,” International Journal of Computer Applications, Vol. 39, No. 3, 2012, pp. 42-51.

[24] B. C. Sarkar, S. Das and R. N. Jana, “Effects of Radiation on MHD Free Convective Couette Flow in a Rotating System,” International Journal of Engineering Research and Application, Vol. 2, No. 4, 2012, pp. 2346-2359.

[25] B. C. Sarkar, S. Das and R. N. Jana, “Oscillatory MHD Free Convective Flow between Two Vertical Walls in a Rotating System,” Advance in Applied Science Research, Vol. 3, No. 5, 2012, pp. 3311-3325.

[26] A. C. Cogley, W. C. Vincentine and S. E. Gilles, “A Differential Approximation for Radiative Transfer in a NonGray Gas Near Equilibrium,” American Institute of Aeronautics and Astronautics Journal, Vol. 6, No. 3, 1968, pp. 551-555.

[27] T. G. Cowling, “Magnetohydrodynamics,” Interscience, New York, 1957.