Effects of Radiation on Free Convection Non-Darcy Flow along Non-isothermal Vertical Wall Embedded in a Porous Medium with Heat Generation

Abstract

This work presents a numerical study to simulate the effect of thermal radiation on natural convection non-Darcy flow along non-isothermal vertical plate embedded in a porous medium with heat generation. Similarity solution is used to convert the governing differential equations from its dimensional form to its dimensionless form.  Finite difference method is used to convert the dimensionless governing differential equations of the problem to its numerical form, and then it’s programmed by using Fortran language. The work of the program is tested by making a comparison between present work and previously published work, and the result of the comparison is good, after that the program is run to give the results related to this study. Dimensionless velocity and temperature profiles as well as local Nusselt number are presented and discussed in detail for various values of involved parameters. From this result it can infer that the raise in the power law index of variable wall temperature, radiation parameter, and radiation parameter but in presence of heat generation enhances the amount of heat transfer. The increase in the Forchheimer parameter, Rayleigh number, and heat generation parameter lead to lessen the amount of heat transfer.  

Country : Iraq

1 Rafee Mohammad Al-kazzaz2 Saddam Atteyia Mohammad

  1. MSc. Student, Department of Mechanical Engineering, College of Engineering, University of Mosul, Mosul, Iraq
  2. Lecturer, Department of Mechanical Engineering, College of Engineering, University of Mosul, Mosul, Iraq

IRJIET, Volume 6, Issue 6, June 2022 pp. 99-107

doi.org/10.47001/IRJIET/2022.606013

References

  1. Nield, D. A., &Bejan, A. (2006). Convection in porous media (Vol. 3). New York: Springer.
  2. Kaviany, M., 2012. Principles of heat transfer in porous media. Springer Science & Business Media.
  3. Su, B.L., Sanchez, C. and Yang, X.Y. eds., 2012. Hierarchically structured porous materials: from nanoscience to catalysis, separation, optics, energy, and life science. John Wiley & Sons.
  4. Burden, R. L., & Faires, J. D. (2011). Numerical differentiation & integration numerical differentiation I. Numerical analysis, 174-184.
  5. Bear, J. (1988). Dynamics of fluids in porous media. Courier Corporation.
  6. XIAOBING, C. (2009). A Numerical Study of Heat and Mass Transfer in Porous-Fluid Coupled Domains.
  7. Bejan, A. (2013). Convection heat transfer. John wiley& sons.
  8. Wu, Y. S. (2002). Numerical simulation of single-phase and multiphase non-Darcy flow in porous and fractured reservoirs. Transport in Porous Media, 49(2), 209-240.
  9. Kaviany, M., & Mittal, M. (1987). Natural convection heat transfer from a vertical plate to high permeability porous media: an experiment and an approximate solution. International Journal of heat and mass transfer, 30(5), 967-977.
  10. Murthy, P. V. S. N., & Singh, P. (1997). Effect of viscous dissipation on a non-Darcy natural convection regime. International journal of heat and mass transfer, 40(6), 1251-1260.
  11. Hossain, M. A., Alim, M. A., & Rees, D. A. S. (1999). The effect of radiation on free convection from a porous vertical plate. International Journal of Heat and Mass Transfer, 42(1), 181-191.
  12. Murthy, P. V. S. N., & Singh, P. (1997). Thermal dispersion effects on non-Darcy natural convection with lateral mass flux. Heat and Mass Transfer, 33(1), 1-5.
  13. Hung, C. I., & Chen, C. B. (1997).Non-Darcy free convection in a thermally stratified porous medium along a vertical plate with variable heat flux.Heat and mass transfer, 33(1), 101-107.
  14. Mohammadien, A. A., & El-Amin, M. F. (2000). Thermal dispersion–radiation effects on non-Darcy natural convection in a fluid saturated porous medium. Transport in porous media, 40(2), 153-163.
  15. Grosan, T., & Pop, I. (2001). Free Convection over 3 Vertical Flat Plate with a Variable Wall Temperature and Internal Heat Generation in a Porous Medium Saturated with a Non-Newtonian Fluid. Technische Mechanik-European Journal of Engineering Mechanics, 21(4), 313-318.
  16. El-Hakiem, M. A., & El-Amin, M. F. (2001). Thermal radiation effect on non-Darcy natural convection with lateral mass transfer. Heat and Mass Transfer, 37(2), 161-165.
  17. Ali, M. E. (2007). The effect of lateral mass flux on the natural convection boundary layers induced by a heated vertical plate embedded in a saturated porous medium with internal heat generation. International Journal of Thermal Sciences, 46(2), 157-163.
  18. Ibrahim, S. M. (2013). Radiation effects on mass transfer flow through a highly porous medium with heat generation and chemical reaction. International Scholarly Research Notices, 2013.
  19. Beg, O. A., Rao, A. S., Nagendra, N., Amanulla, C. H., & Reddy, M. S. N. (2017). Computational analysis of non-Newtonian boundary layer flow of nanofluid past a vertical plate with partial slip. Modelling, Measurement and Control B, 86(1), 271-295.
  20. M.ELharoui, M.Sriti, D.Achemlal, 2015, "Double Diffusive Free Convection over a Heated Vertical Plate in a Saturated Porous Medium with Soret Effect and Variable Heat Source", AMSEJORNALS –Series: Modelling B; Vol. 84; N 1; pp 23-37.
  21. Beg, O. A., Rao, A. S., Nagendra, N., Amanulla, C. H., & Reddy, M. S. N. (2017). Computational analysis of non-Newtonian boundary layer flow of nanofluid past a vertical plate with partial slip. Modelling, Measurement and Control B, 86(1), 271-295.
  22. Neagu, M. (2015). Free Convection in a Darcy Thermally Stratified Porous Medium That Embeds a Vertical Wall of Constant Heat Flux and Concentration. International Journal of Mechanical and Mechatronics Engineering, 10(1), 65-74.
  23. Huang, C. J., Hsu, H. P., & Ay, H. C. (2019). Influence of mhd on free convection of non-newtonian fluids over a vertical permeable plate in porous media with internal heat generation. Frontiers in Heat and Mass Transfer (FHMT), 13.
  24. Bejan, A. (2013). Convection heat transfer. John wiley & sons.
  25. Hsieh, J. C., Chen, T. S., & Armaly, B. F. (1993). Mixed convection along a nonisothermal vertical flat plate embedded in a porous medium: the entire regime. International journal of heat and mass transfer, 36(7), 1819-1825.
  26. Khan, W. A., & Gorla, R. S. R. (2010). Mixed convection of power-law fluids along a vertical wedge with convective boundary condition in a porous medium. Journal of Mechanical Science and Technology, 24(9), 1919-1925.