Radiative Heat Transfer of an Optically Thick Gray Gas in The Presence of Indirect Natural Convection

ABSTRACT

We study the effects of thermal radiation of a viscous incompressible fluid occupying a semi-infinite region of space bounded by an infinite horizontal moving hot flat plate in the presence of indirect natural convection by way of an induced pressure gradient. The fluid is a gray, absorbing emitting radiation but a non scattering medium. An exact solution is obtained by employing Laplace transform technique. Since temperature field depends on Reynold number the flow is considered to be non-isothermal case (the temperature of the plate Tw ≠ constant) and for an isothermal case (Tw = constant) the flow is determined by the Reynold number which is equal to 1.

We study the effects of thermal radiation of a viscous incompressible fluid occupying a semi-infinite region of space bounded by an infinite horizontal moving hot flat plate in the presence of indirect natural convection by way of an induced pressure gradient. The fluid is a gray, absorbing emitting radiation but a non scattering medium. An exact solution is obtained by employing Laplace transform technique. Since temperature field depends on Reynold number the flow is considered to be non-isothermal case (the temperature of the plate Tw ≠ constant) and for an isothermal case (Tw = constant) the flow is determined by the Reynold number which is equal to 1.

KEYWORDS

Thermal Radiation, Indirect Natural Convection, Reynold Number, Stefan-Boltzman Radiation Parameter

Thermal Radiation, Indirect Natural Convection, Reynold Number, Stefan-Boltzman Radiation Parameter

Cite this paper

nullR. Jana and S. Ghosh, "Radiative Heat Transfer of an Optically Thick Gray Gas in The Presence of Indirect Natural Convection,"*World Journal of Mechanics*, Vol. 1 No. 2, 2011, pp. 64-69. doi: 10.4236/wjm.2011.12009.

nullR. Jana and S. Ghosh, "Radiative Heat Transfer of an Optically Thick Gray Gas in The Presence of Indirect Natural Convection,"

References

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[3] H. Naroua, P. C. Ram, A. S. Sambo and H. S. Takhar, “Finite Element Analysis of Natural Convection Flow in a Rotating Fluid with Radiative Heat Transfer,” Journal of Magnetohydrodynamics and Plasma Research, Vol. 7, No. 4, 1998, pp. 257-274.

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

[5] H. S. Takhar, R. S. S. Gorla and V. M. Soundalgekar, “Radiation Effects on MED Free Convection Flow of a Radiating Gas Past a Semi-Infinite Vertical Plate,” Inter- national Journal of Numerical Methods for Heat & Fluid Flow, Vol. 6, 1996, pp. 77-83.

[6] M. A. Hossain and H. S. Takhar, “Radiation Efeects 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

[7] A. Raptis and C. Perdikis, “Radiation and Free Con- vection Flow past a Moving Plate,” Applied Mechanics and Engineering, Vol. 4, No. 4, 1990, pp. 817-821.

[8] A. Raptis and C. Perdikis, “Thermal Radiation of an Optically Thin Gray Gas,” International Journal of Applied Mechanics and Engineering, Vol. 8, No. 1, 2003, pp. 131-134.

[9] R. Madhucumaraswamy and P. Ganesan, “Radiation Effects on Flow past an Impulsively Started Infinite Ver- tical Plate with Variable Temperature,” International Journal of Applied Mechanics and Engineering, Vol. 8, No. 1, 2003, pp. 125-129.

[10] S. K. Ghosh and I. Pop, “Thermal Radiation of an Opti- cally Thick Gray Gas in the Presence of Indirect Natural Convection,” International Journal of Fluid Mechanics Research, Vol. 34, No. 6, 2007, pp. 515-520.

[11] A. Raptis, C. Perdikis and H. S. Takhar, “Effect of Ther- mal Radiation on MHD Flow,” Applied Mathematics and Computation, Vol. 153, No. 3, 2004, pp. 645-649. doi:10.1016/S0096-3003(03)00657-X

[12] H. M. Duwairi and R. M. Duwairi, “Thermal Radiation Effect on Mhd Rayleigh Flow with Constant Surface Heat Flux,” Heat and Mass Transfer, Vol. 41, No. 1, 2005, pp. 51-57.

[13] E. N. Vasil’ev and D. A. Nesterov, “The Effect of Ra- diative — Convective Heat Transfer on the Formation of Current Layer,” High Temperature, Vol. 43, No. 3, 2005, pp. 396-403.

[14] H. M. Duwairi, “Viscous and Joule Heating Effects on Forced Convection Flow From Radiate Isothermal Porous Surface,” International Journal of Numerical methods Heat Fluid Flow, Vol. 15, No. 5, 2005, pp. 429-440. doi:10.1108/09615530510593620

[15] M. E. M. Quaf, “Exact Solution of Thermal Radiation on Mhd Flow over a Stretching Porous Sheet,” Applied Ma- thematics and Computation, Vol. 170, No. 2, 2005, pp. 1117-1125.

[16] S. K. Ghosh, “Radiative Heat Transfer Aspect of an Optically Thick Gray Gas in the Presence of a Magnetic Field,” International Journal of Applied Mechanics and Engineering, Vol. 12, No. 3, 2007, pp. 849-855.

[17] S. K. Ghosh, “Radiative Heat Transfer Aspect of an Opti- cally Thick Gray Gas in the Presence of a Magnetic Field,” International Journal of Applied Mechanics and Engineering, Vol. 12, No. 4, 2007, pp. 1181.

[18] J. Zueco, “Network Simulation Method Applied to Ra- diation and Viscous Dissipation Effects on MHD Un- steady Free Convection Over a Vertical Porous Plate,” Applied Mathematical Modelling, Vol. 31, No. 9, 2007, pp. 2019-2033.

[19] M. A. Samad and M. M. Rahman, “Thermal Radiation Interaction with Unsteady MHD Flow past a Vertical Porous Plate Immersed in a Porous Medium,” Journal of Naval Architecture and Marine Engineering, Vol. 3, No. 1, 2006, pp. 7-14.

[20] O. A. Beg and S. K. Ghosh, “Analytical Study of Magne- tohydrodynamic Radiation — Convection with Surface Temperature Oscillation and Secondary Flow Effects,” International Journal of Applied Mathematics and Me- chanics, Vol. 6, No. 6, 2010, pp. 1-22.

[21] V. P. Isachenko, V. A. Osipova and A. S. Sukomel, “Heat Transfer,” Mir Publishers, Moscow, 1969, pp. 341-451.

[1] W. G. England and A. F. Emery, “Thermal Radiation Effects on the Laminear Free Convection Boundary Layer of an Absorbing Gas,” Journal of Heat Transfer, Vol. 91, 1969, pp. 37-44.

[2] A. R. Bestman and S. K. Adiepong, “Unsteady Hydro- magnetic Free-Convection Flow with Radiation Heat Transfer in a Rotating Fluid,” Astrophysics and Space Science, Vol. 143, No. 1, 1988, pp. 73-80. doi:10.1007/BF00636756

[3] H. Naroua, P. C. Ram, A. S. Sambo and H. S. Takhar, “Finite Element Analysis of Natural Convection Flow in a Rotating Fluid with Radiative Heat Transfer,” Journal of Magnetohydrodynamics and Plasma Research, Vol. 7, No. 4, 1998, pp. 257-274.

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

[5] H. S. Takhar, R. S. S. Gorla and V. M. Soundalgekar, “Radiation Effects on MED Free Convection Flow of a Radiating Gas Past a Semi-Infinite Vertical Plate,” Inter- national Journal of Numerical Methods for Heat & Fluid Flow, Vol. 6, 1996, pp. 77-83.

[6] M. A. Hossain and H. S. Takhar, “Radiation Efeects 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

[7] A. Raptis and C. Perdikis, “Radiation and Free Con- vection Flow past a Moving Plate,” Applied Mechanics and Engineering, Vol. 4, No. 4, 1990, pp. 817-821.

[8] A. Raptis and C. Perdikis, “Thermal Radiation of an Optically Thin Gray Gas,” International Journal of Applied Mechanics and Engineering, Vol. 8, No. 1, 2003, pp. 131-134.

[9] R. Madhucumaraswamy and P. Ganesan, “Radiation Effects on Flow past an Impulsively Started Infinite Ver- tical Plate with Variable Temperature,” International Journal of Applied Mechanics and Engineering, Vol. 8, No. 1, 2003, pp. 125-129.

[10] S. K. Ghosh and I. Pop, “Thermal Radiation of an Opti- cally Thick Gray Gas in the Presence of Indirect Natural Convection,” International Journal of Fluid Mechanics Research, Vol. 34, No. 6, 2007, pp. 515-520.

[11] A. Raptis, C. Perdikis and H. S. Takhar, “Effect of Ther- mal Radiation on MHD Flow,” Applied Mathematics and Computation, Vol. 153, No. 3, 2004, pp. 645-649. doi:10.1016/S0096-3003(03)00657-X

[12] H. M. Duwairi and R. M. Duwairi, “Thermal Radiation Effect on Mhd Rayleigh Flow with Constant Surface Heat Flux,” Heat and Mass Transfer, Vol. 41, No. 1, 2005, pp. 51-57.

[13] E. N. Vasil’ev and D. A. Nesterov, “The Effect of Ra- diative — Convective Heat Transfer on the Formation of Current Layer,” High Temperature, Vol. 43, No. 3, 2005, pp. 396-403.

[14] H. M. Duwairi, “Viscous and Joule Heating Effects on Forced Convection Flow From Radiate Isothermal Porous Surface,” International Journal of Numerical methods Heat Fluid Flow, Vol. 15, No. 5, 2005, pp. 429-440. doi:10.1108/09615530510593620

[15] M. E. M. Quaf, “Exact Solution of Thermal Radiation on Mhd Flow over a Stretching Porous Sheet,” Applied Ma- thematics and Computation, Vol. 170, No. 2, 2005, pp. 1117-1125.

[16] S. K. Ghosh, “Radiative Heat Transfer Aspect of an Optically Thick Gray Gas in the Presence of a Magnetic Field,” International Journal of Applied Mechanics and Engineering, Vol. 12, No. 3, 2007, pp. 849-855.

[17] S. K. Ghosh, “Radiative Heat Transfer Aspect of an Opti- cally Thick Gray Gas in the Presence of a Magnetic Field,” International Journal of Applied Mechanics and Engineering, Vol. 12, No. 4, 2007, pp. 1181.

[18] J. Zueco, “Network Simulation Method Applied to Ra- diation and Viscous Dissipation Effects on MHD Un- steady Free Convection Over a Vertical Porous Plate,” Applied Mathematical Modelling, Vol. 31, No. 9, 2007, pp. 2019-2033.

[19] M. A. Samad and M. M. Rahman, “Thermal Radiation Interaction with Unsteady MHD Flow past a Vertical Porous Plate Immersed in a Porous Medium,” Journal of Naval Architecture and Marine Engineering, Vol. 3, No. 1, 2006, pp. 7-14.

[20] O. A. Beg and S. K. Ghosh, “Analytical Study of Magne- tohydrodynamic Radiation — Convection with Surface Temperature Oscillation and Secondary Flow Effects,” International Journal of Applied Mathematics and Me- chanics, Vol. 6, No. 6, 2010, pp. 1-22.

[21] V. P. Isachenko, V. A. Osipova and A. S. Sukomel, “Heat Transfer,” Mir Publishers, Moscow, 1969, pp. 341-451.