Radiation Effects on Free Convection MHD Couette Flow Started Exponentially with Variable Wall Temperature in Presence of Heat Generation

ABSTRACT

Radiation effects on free convection MHD Couette flow started exponentially with variable wall temperature in the presence of heat generation have been studied. The governing equations are solved analytically using the Laplace transform technique. The variations of velocity and fluid temperature are presented graphically. It is observed that the velocity decreases with an increase in either magnetic parameter or radiation parameter or Prandtl number. It is also observed that the velocity increases with an increase in either heat generation parameter or Grashof number or accelerated parameter or time. An increase in either radiation parameter or Prandtl number leads to fall in the fluid temperature. It is seen that the fluid temperature increases with an increase in either heat generation parameter or time. Further, it is seen that the shear stress at the moving plate decreases with an increase in either magnetic parameter or radiation parameter while it increases with an increase in either heat generation parameter or Prandtl number. The rate of heat transfer increases with an increase in either Prandtl number or time whereas it decreases with an increase in heat generation parameter.

Radiation effects on free convection MHD Couette flow started exponentially with variable wall temperature in the presence of heat generation have been studied. The governing equations are solved analytically using the Laplace transform technique. The variations of velocity and fluid temperature are presented graphically. It is observed that the velocity decreases with an increase in either magnetic parameter or radiation parameter or Prandtl number. It is also observed that the velocity increases with an increase in either heat generation parameter or Grashof number or accelerated parameter or time. An increase in either radiation parameter or Prandtl number leads to fall in the fluid temperature. It is seen that the fluid temperature increases with an increase in either heat generation parameter or time. Further, it is seen that the shear stress at the moving plate decreases with an increase in either magnetic parameter or radiation parameter while it increases with an increase in either heat generation parameter or Prandtl number. The rate of heat transfer increases with an increase in either Prandtl number or time whereas it decreases with an increase in heat generation parameter.

Cite this paper

S. Das, B. Sarkar and R. 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, 2012, pp. 14-27. doi: 10.4236/ojfd.2012.21002.

S. Das, B. Sarkar and R. Jana, "Radiation Effects on Free Convection MHD Couette Flow Started Exponentially with Variable Wall Temperature in Presence of Heat Generation,"

References

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[2] A. K. Singh and T. Paul, “Transient Natural Con-vection between Two Vertical Walls Heated/Cooled Asymetri-cally,” International Journal of Applied Mechanics and Engi-neering, Vol. 11, No. 1, 2006, pp. 143-154.

[3] 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 Mechanics and Engineering, Vol. 8, No. 3, 2003, pp. 497-502.

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

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

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

[7] H. K. Mohanty, “Transient Free Convection Horizontal Laminar Flow between Two Parallel Plates,” Acta Me- chanica, Vol. 15, No. 3-4, 1972, pp. 273-293. doi:10.1007/BF01304296

[8] 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

[9] A. Ogulu and S. Motsa, “Ra-diative Heat Transfer to Mag- netohydrodynamic Couette Flow with Variable Wall Temperature,” Physica Scripta, Vol. 71, No. 4, 2005, pp. 336-339. doi:10.1238/Physica.Regular.071a00336

[10] R. C. Chaudhary and P. Jain, “Exact Solutions of Incompressible Couette Flow with Constant Temperature and Constant Heat Flux on Walls in the Presence of Radiation,” Turkish Journal of Engineering & Environmental Sciences, Vol. 3, No. 1, 2007, pp. 297-304.

[11] 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.

[12] B. K. Jha and A. O. Ajibade, “Free Con-vective Flow of Heat Generating/Absorbing Fluid between Vertical Porous Plates with Periodic Heat Input,” International Communications in Heat and Mass Transfer, Vol. 36, No. 6, 2009, pp. 624-631. doi:10.1016/j.icheatmasstransfer.2009.03.003

[13] 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.

[14] C. Israel-Cookey, E. Amos and C. Nwaigwe, “MHD Oscillatory Couette Flow of a Radiating Viscous Fluid in a Porous Medium with Periodic Wall Temperature,” American Journal of Scien-tific Industrial Research, Vol. 1, No. 2, 2010, pp. 326-331.

[15] M. Narahari, “Effects Of Thermal Radiation and Free Convection Currents on the Unsteady Couette Flow be-tween 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.

[16] R. K. Deka and A. Bhattacharya, “Unsteady Free Convective Couette Flow of Heat Generating/Absorbing Fluid in Porous Medium,” Interna-tional Journal of Mathematical Archive, Vol. 2, No. 6, 2011, pp. 853-863.

[17] A. G. V. Kumar and S. V. K. Varma, “Radiation Effects on MHD Flow Past an Impulsively Started Exponen-tially Accelerated Vertical Plate with Variable Temperature in the Presence of Heat Generation,” International Journal of Engineering Science and Technology, Vol. 3, No. 4, 2011, pp. 2897-2909.

[18] R. Grief, I. S. Habib and J. C. Lin, “Laminar Convection of a Radiating Gas in a Vertical Channel,” Journal of Fluid Mechanics, Vol. 46, 1970, pp. 513-520. doi:10.1017/S0022112071000673

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

[2] A. K. Singh and T. Paul, “Transient Natural Con-vection between Two Vertical Walls Heated/Cooled Asymetri-cally,” International Journal of Applied Mechanics and Engi-neering, Vol. 11, No. 1, 2006, pp. 143-154.

[3] 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 Mechanics and Engineering, Vol. 8, No. 3, 2003, pp. 497-502.

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

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

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

[7] H. K. Mohanty, “Transient Free Convection Horizontal Laminar Flow between Two Parallel Plates,” Acta Me- chanica, Vol. 15, No. 3-4, 1972, pp. 273-293. doi:10.1007/BF01304296

[8] 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

[9] A. Ogulu and S. Motsa, “Ra-diative Heat Transfer to Mag- netohydrodynamic Couette Flow with Variable Wall Temperature,” Physica Scripta, Vol. 71, No. 4, 2005, pp. 336-339. doi:10.1238/Physica.Regular.071a00336

[10] R. C. Chaudhary and P. Jain, “Exact Solutions of Incompressible Couette Flow with Constant Temperature and Constant Heat Flux on Walls in the Presence of Radiation,” Turkish Journal of Engineering & Environmental Sciences, Vol. 3, No. 1, 2007, pp. 297-304.

[11] 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.

[12] B. K. Jha and A. O. Ajibade, “Free Con-vective Flow of Heat Generating/Absorbing Fluid between Vertical Porous Plates with Periodic Heat Input,” International Communications in Heat and Mass Transfer, Vol. 36, No. 6, 2009, pp. 624-631. doi:10.1016/j.icheatmasstransfer.2009.03.003

[13] 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.

[14] C. Israel-Cookey, E. Amos and C. Nwaigwe, “MHD Oscillatory Couette Flow of a Radiating Viscous Fluid in a Porous Medium with Periodic Wall Temperature,” American Journal of Scien-tific Industrial Research, Vol. 1, No. 2, 2010, pp. 326-331.

[15] M. Narahari, “Effects Of Thermal Radiation and Free Convection Currents on the Unsteady Couette Flow be-tween 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.

[16] R. K. Deka and A. Bhattacharya, “Unsteady Free Convective Couette Flow of Heat Generating/Absorbing Fluid in Porous Medium,” Interna-tional Journal of Mathematical Archive, Vol. 2, No. 6, 2011, pp. 853-863.

[17] A. G. V. Kumar and S. V. K. Varma, “Radiation Effects on MHD Flow Past an Impulsively Started Exponen-tially Accelerated Vertical Plate with Variable Temperature in the Presence of Heat Generation,” International Journal of Engineering Science and Technology, Vol. 3, No. 4, 2011, pp. 2897-2909.

[18] R. Grief, I. S. Habib and J. C. Lin, “Laminar Convection of a Radiating Gas in a Vertical Channel,” Journal of Fluid Mechanics, Vol. 46, 1970, pp. 513-520. doi:10.1017/S0022112071000673