Convection of Radiating Gas in a Vertical Channel through Porous Media

ABSTRACT

The free convection flow of radiating gas between two vertical thermally conducting walls through porous medium in the presence of a uniform gravitational field has been studied. Closed form solutions for the velocity and temperature have been obtained in the optically thin limit case when the wall temperatures are varying linearly with the vertical distance. It is observed that the fluid velocity increases and the temperature difference between the walls and the fluid decreases with an increase in the radiation parameter. It is also observed that both the fluid velocity and temperature in the flow field increase with an increase in the porosity parameter. It is found that the fluid velocity decreases while the temperature increases with an increase in the thermal conductance of the walls. Further, it is found that radiation causes to decrease the rate of heat transfer to the fluid, thereby reducing the effect of natural convection.

The free convection flow of radiating gas between two vertical thermally conducting walls through porous medium in the presence of a uniform gravitational field has been studied. Closed form solutions for the velocity and temperature have been obtained in the optically thin limit case when the wall temperatures are varying linearly with the vertical distance. It is observed that the fluid velocity increases and the temperature difference between the walls and the fluid decreases with an increase in the radiation parameter. It is also observed that both the fluid velocity and temperature in the flow field increase with an increase in the porosity parameter. It is found that the fluid velocity decreases while the temperature increases with an increase in the thermal conductance of the walls. Further, it is found that radiation causes to decrease the rate of heat transfer to the fluid, thereby reducing the effect of natural convection.

Cite this paper

nullM. Jana, S. Maji, S. Das and R. Jana, "Convection of Radiating Gas in a Vertical Channel through Porous Media,"*World Journal of Mechanics*, Vol. 1 No. 6, 2011, pp. 275-282. doi: 10.4236/wjm.2011.16034.

nullM. Jana, S. Maji, S. Das and R. Jana, "Convection of Radiating Gas in a Vertical Channel through Porous Media,"

References

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[20] C. L. Tien, “Thermal Radiation Properties of Gases,” Advan- ces in Heat Transfer, Vol. 5, 1968, pp. 253-324.

[1] D.A. Nield and A.Bejan, “Convection in Porous Media,” Springer, Berlin, Heidelberg, New York, 1971.

[2] E. M. Sparrrow and R. D. Cess, “Radiation Heat Transfer,” Hemispherer Publication Corp., Washington DC, 1978.

[3] L. C. Burmeister, “Convective Heat Transfer,” Wiley, New York, 1983.

[4] A. Bejan, “Convection Heat Transfer,” Wiley, New York, 1994.

[5] M. Kavinay, “Principles of Heat Transfer in porous Me- dia,” Springer-Verlay, New York, 1995.

[6] K. Vafai, “Handbook of Porous Media,” 2nd Edition, Taylor and Francis, New York, 2005. doi:10.1201/9780415876384

[7] A. Raptis, “Radiation and Free Convection Flow through a Porous Medium,” International Communications in Heat and Mass Transfer, Vol. 25, No. 2, 1998, pp. 289- 295. doi:10.1016/S0735-1933(98)00016-5

[8] A. Raptis, “Radiation and Flow through a Porous Me- dium,” Journal of Porous Media, Vol. 4, No. 3, 2001, pp. 271-273.

[9] D. Hall, G. C. Vliet and T. L. Bergman, “Natural Convec- tion Cooling of Vertical Rectangular Channels in Air Con- sidering Radiation and Wall Conduction,” Journlaof Electronic Packaging, Vol. 121, No. 2, 1999, pp. 75-84. doi:10.1115/1.2792671

[10] M. A. Al-Nimr and O. H. Haddad, “Fully Developed Free Convection in Open-Ended Vertical Channels Partially Fil- led with Porous Material,” Journal of Porous Media, Vol. 2, No. 2, 1999, pp. 179-189.

[11] A. A. Mohammadein and M. F. El-Amin, “Thermal Dis- persion-Radiation Effects on Non-Darcy Natural Convec- tion in a Fluid Saturated Porous Medium,” Transport in Porous Medium, Vol. 40, No. 2, 2000, pp. 153-163. doi:10.1023/A:1006654309980

[12] S. H. Kim, N. K. Anand and W. Aung, “Effect of Wall Conduction on Free Convection between Asymmetrically Heated Vertical Plates, Uniform Wall Heat Flux,” International Communications in Heat and Mass Transfer, Vol. 33, No. 5, 1990, pp. 1013-1023. doi:10.1016/0017-9310(90)90082-6

[13] R. Greif, I. S. Habib and J. C. Lin, “Laminar Convection of a Radiating Gas in a Vertical Channel,” Journal of Fluid Mechanics, Vol. 46, No. 3, 1971, pp. 513-520. doi:10.1017/S0022112071000673

[14] C. P. Yu and K. K. Yang, “Effect of Wall Conductances on Convective Magnetohydrodynamic Channel Flow,” Ap- plied Scietific Research, Vol. 20, No. 1, 1969, pp. 16-23. doi:10.1007/BF00382379

[15] N. Datta and R. N Jana, “Effect of Wall Conductances on Hydromagnetic Convection of a Radiation Gas in a Ver- tical Channel,” International Communications in Heat and Mass Transfer, Vol. 19, No. 9, 1974, pp. 1015-1019. doi:10.1016/0017-9310(76)90184-8

[16] P. S. Gupta and A. S. Gupta, “Radiation Effect on Hydro- magnetic Convection in a Vertical Channel,” International Communications in Heat and Mass Transfer, Vol. 17, No. 12, 1973, pp. 1437-1442. doi:10.1016/0017-9310(74)90053-2

[17] O. D. Makinde and P. Y. Mhone, “Heat Transfer to MHD Oscillatory Flow in a Channel Filled with Porous Me- dium,” Romanian Journal of Physics, Vol. 50, No. 9-10, 2005, pp. 931-938.

[18] M. Narahari, “Effects of Thermal Radiation and Free Con- vection 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. 1, No. 5, 2010, pp. 21-30.

[19] A. C. Cogley, W. C. Vincenti and S. E. Gilles, “Differen- tial Approximation for Radiative Transfer in a Non-Grey Gas near Equilibrium,” AIAA Journal, Vol. 6, No. 3, 1968, pp. 551-553. doi:10.2514/3.4538

[20] C. L. Tien, “Thermal Radiation Properties of Gases,” Advan- ces in Heat Transfer, Vol. 5, 1968, pp. 253-324.