Radiation Effects on Free Convection Flow Neara Vertical Plate with Ramped Wall Temperature

ABSTRACT

The effect of radiation on the unsteady natural convection flow past an infinite vertical plate is presented, wherein the plate temperature is a ramped one. The fluid considered here is a gray, absorbing/emitting but a non-scattering medium. The influence of the various parameters entering into the problem on the velocity field, temperature field, skin friction and Nusselt number is studied.

The effect of radiation on the unsteady natural convection flow past an infinite vertical plate is presented, wherein the plate temperature is a ramped one. The fluid considered here is a gray, absorbing/emitting but a non-scattering medium. The influence of the various parameters entering into the problem on the velocity field, temperature field, skin friction and Nusselt number is studied.

Cite this paper

nullR. Deka and S. Das, "Radiation Effects on Free Convection Flow Neara Vertical Plate with Ramped Wall Temperature,"*Engineering*, Vol. 3 No. 12, 2011, pp. 1197-1206. doi: 10.4236/eng.2011.312149.

nullR. Deka and S. Das, "Radiation Effects on Free Convection Flow Neara Vertical Plate with Ramped Wall Temperature,"

References

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[13] J. A. Schetz, “On the Approximate Solution of Viscous- flow Problems,” Journal of Applied Mechanics, Vol. 30, No. 2, 1963, pp. 263-268. doi:10.1115/1.3636522

[14] J. A. Schetz and R. Eichhorn, “Unsteady Natural Convection in the Vicinity of a Doubly Infinite Vertical Plate,” American Society of Mechanical Engineers Journal of Heat Transfer, Vol. 84, 1962, pp. 334-338.

[15] T. T. Kao, “Laminar Free Convective Heat Transfer Re- sponse along a Vertical Flat Plate with Step Jump in Sur- face Temperature,” Letters in Heat and Mass Transfer, Vol. 2, No. 5, 1975, pp. 419-428. doi:10.1016/0094-4548(75)90008-9

[16] V. M. Soundalgekar and H. S. Takhar, “Radiation Effects on Free Convection Flow Past a Semi-Infinite Vertical Plate,” Modeling Measurement and Control, Vol. B51, 1993, pp. 31-40.

[17] M. A. Hossain and H. S. Takhar, “Radiation Effects on Mixed Convection along a Vertical Plate with Uniform Surface Temperature,” Heat and Mass Transfer, Vol. 31, No. 4, 1996, pp. 243-248. doi:10.1007/BF02328616

[18] A. Raptis and C. Perdikis, “Radiation and Free Convection Flow Past a Moving Plate,” International Journal of Applied Mechanics and Engineering, Vol. 4, No. 4, 1999, pp. 817-821.

[19] U. N. Das, R. K. Deka and V. M. Soundalgekar, “Radiation Effects on Flow Past an Impulsively Started Vertical Infinite Plate,” Journal of Theoretical and Applied Mechanics, Vol. 1, 1996, pp. 111-115.

[20] R. Muthucumaraswamy and B. Janakiraman, “MHD and Radiation Effects on Moving Isothermal Vertical Plate with Variable Mass Diffusion,” Journal of Theoretical and Applied Mechanics, Vol. 33, No. 1, 2006, pp. 17-29. doi:10.2298/TAM0601017M

[21] S. C. Saha, C. Lei and J. C. Patterson, “On the Natural Convection Boundary Layer Adjacent to an Inclined Flat Plate Subject to Ramp Heating,” Proceedings of 16th Australian Fluid Mechanics Conference, Crown Plaza, Gold Coast, 11-16 September 2007, pp. 121-124.

[22] D. Deka and R. K. Deka, “Natural Convection near a Vertical Plate with Ramped Wall Temperature and Heat Source,” Far East Journal of Applied Mathematics, Vol. 1, No. 41, 2010, pp. 21-32.

[23] I. G. Currie, “Fundamental Mechanics of Fluids,” 3rd Edition, Marce-Dekker, New York, 2003.

[1] G. G. Stokes, “On the Effect of Internal Friction of Fluids on the Motion of Pendulums,” Mathematical and Physical Papers, Vol. 3, 1851, pp. 8-106.

[2] V. M. Soundalgekar, “Free Convection Effects on Stokes’s Problem for a Vertical Plate,” American Society of Me- chanical Engineers Journal of Heat Transfer, Vol. 99C, No. 3, 1977, pp. 499-501. doi:10.1115/1.3450729

[3] E. Pohlhausen, “Der Wareastausch Zwischen Festen Kor- penn und Flussigkeiten mit Kleineer Reibung und Klein- erwarmeletung,” Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 1, No. 2, 1921, pp. 115-121. doi:10.1002/zamm.19210010205

[4] S. Ostrach, “An Analysis of Laminar Free Convection Flow Heat Transfer about a Flat Plate Parallel to the Direction of the Generating Body Force,” NASA Report No. 1111, 1953.

[5] R. Siegel, “Transient Free Convection from a Vertical Flat Plate,” Transactions of the American Society of Me- chanical Engineers, Vol. 80, 1958, pp. 347-359.

[6] B. Gebhart, “Transient Natural Convection from Vertical Elements,” American Society of Mechanical Engineers Journal of Heat Transfer, Vol. 83C, 1961, pp. 61-67.

[7] P. Chandran, N. C. Sacheti and A. K. Singh, “Exact Solu- tions for the Convective Flow of Fluids of Different Prandtl Numbers Near an Infinite Vertical Plate in a Rotating System,” International Journal of Applied Mechanics and Engineering, Vol. 6, No. 3, 2001, pp. 573- 590.

[8] P. Chandran, N. C. Sacheti and A. K. Singh, “Natural Convection Near a Vertical Plate with Ramped Wall Temperature,” Heat and Mass Transfer, Vol. 41, No. 5, 2005, pp. 459-464. doi:10.1007/s00231-004-0568-7

[9] P. Ganesan and G. Palani, “Natural Convection Effects on Impulsively Started Inclined Plate with Heat and Mass Transfer,” Heat Mass Transfer, Vol. 39, 2003, pp. 277-283.

[10] A. A. Hayday, D. A. Bowlus and R. A. McGraw, “Free Convection from a Vertical Flat Plate with Step Disconti- nuities in Surface Temperature,” American Society of Mechanical Engineers Journal of Heat Transfer, Vol. 89, No. 3, 1967, pp. 244-250.

[11] M. Kelleher, “Free Convection from a Vertical Plate with Discontinuous Wall Temperature,” American Society of Mechanical Engineers Journal of Heat Transfer, Vol. 93, 1971, 349-356.

[12] S. Lee and M. M. Yovanovich, “Laminar Natural Convection from a Vertical Plate with a Step Change in Wall Temperature,” American Society of Mechanical Engineers Journal of Heat Transfer, Vol. 113, 1991, pp. 501- 504.

[13] J. A. Schetz, “On the Approximate Solution of Viscous- flow Problems,” Journal of Applied Mechanics, Vol. 30, No. 2, 1963, pp. 263-268. doi:10.1115/1.3636522

[14] J. A. Schetz and R. Eichhorn, “Unsteady Natural Convection in the Vicinity of a Doubly Infinite Vertical Plate,” American Society of Mechanical Engineers Journal of Heat Transfer, Vol. 84, 1962, pp. 334-338.

[15] T. T. Kao, “Laminar Free Convective Heat Transfer Re- sponse along a Vertical Flat Plate with Step Jump in Sur- face Temperature,” Letters in Heat and Mass Transfer, Vol. 2, No. 5, 1975, pp. 419-428. doi:10.1016/0094-4548(75)90008-9

[16] V. M. Soundalgekar and H. S. Takhar, “Radiation Effects on Free Convection Flow Past a Semi-Infinite Vertical Plate,” Modeling Measurement and Control, Vol. B51, 1993, pp. 31-40.

[17] M. A. Hossain and H. S. Takhar, “Radiation Effects on Mixed Convection along a Vertical Plate with Uniform Surface Temperature,” Heat and Mass Transfer, Vol. 31, No. 4, 1996, pp. 243-248. doi:10.1007/BF02328616

[18] A. Raptis and C. Perdikis, “Radiation and Free Convection Flow Past a Moving Plate,” International Journal of Applied Mechanics and Engineering, Vol. 4, No. 4, 1999, pp. 817-821.

[19] U. N. Das, R. K. Deka and V. M. Soundalgekar, “Radiation Effects on Flow Past an Impulsively Started Vertical Infinite Plate,” Journal of Theoretical and Applied Mechanics, Vol. 1, 1996, pp. 111-115.

[20] R. Muthucumaraswamy and B. Janakiraman, “MHD and Radiation Effects on Moving Isothermal Vertical Plate with Variable Mass Diffusion,” Journal of Theoretical and Applied Mechanics, Vol. 33, No. 1, 2006, pp. 17-29. doi:10.2298/TAM0601017M

[21] S. C. Saha, C. Lei and J. C. Patterson, “On the Natural Convection Boundary Layer Adjacent to an Inclined Flat Plate Subject to Ramp Heating,” Proceedings of 16th Australian Fluid Mechanics Conference, Crown Plaza, Gold Coast, 11-16 September 2007, pp. 121-124.

[22] D. Deka and R. K. Deka, “Natural Convection near a Vertical Plate with Ramped Wall Temperature and Heat Source,” Far East Journal of Applied Mathematics, Vol. 1, No. 41, 2010, pp. 21-32.

[23] I. G. Currie, “Fundamental Mechanics of Fluids,” 3rd Edition, Marce-Dekker, New York, 2003.