A numerical study on slip flow in packed hyper-porous media inside micro-channels using differential transformation method

  • Authors

    • Puyan Saffari PHD student,Department of Mechanical Engineering, Islamic Azad University of Lahijan,Guilan, Iran
    • Esmaeel Fatahian PHD student,Department of Mechanical Engineering, Islamic Azad University of Nour,Mazandaran, Iran
    • Peyman Saffari PHD student,Department of Mechanical Engineering, Islamic Azad University of Nour,Mazandaran, Iran
    • Hossein Fatahian PHD student,Department of Mechanical Engineering, Islamic Azad University of Shahroud,Semnan, Iran
    2016-11-03
    https://doi.org/10.14419/ijsw.v4i2.6736
  • Slip Flow, Hyper-Porous Media, Differential Transformation Method.
  • Velocity slip boundary condition in parallel-plate micro-channels filled with hyper-porous media is studied using differential transformation method (DTM) in order to find an analytical approximate solution. The results focus on slip flow regime (i.e., for Knudsen numbers in the range 10−3 < Kn < 10−1). The Darcy-Brinkman-Forchheimer model is applied to study the effect of nonlinear drag term further boundary-friction effects on hydrodynamic of gas flow in micro-channels. The results show that DTM results are in good agreement with numerical ones. Also, it is observed that decreasing the value of Darcy number flattens the velocity profile while this trend is opposite for decreasing the Forchheimer number. Also, increasing the value of  causes to increase the velocity slip at the wall.

  • References

    1. [1] Nield, D. A., and A. V. Kuznetsov. "Forced convection with slip-flow in a channel or duct occupied by a hyper-porous medium saturated by a rarefied gas." Transport in porous media 64.2 (2006): 161-170. http://dx.doi.org/10.1007/s11242-005-2341-x.

      [2] Haddad, O. M., and Yazan Taamneh. "Hydrodynamic and thermal behavior of gas flow in micro-channels filled with porous media." Journal of Porous Media 9.5 (2006).

      [3] Haddad, O. M., M. A. Al-Nimr, and M. S. Sari. "Forced convection gaseous slip flow in circular porous micro-channels." Transport in Porous Media 70.2 (2007): 167-179. http://dx.doi.org/10.1007/s11242-006-9093-0.

      [4] Zhou, J. K. "Differential transformation and its applications for electrical circuits." (1986): 1279-1289.

      [5] Kundu, B., and D. Barman. "Analytical study on design analysis of annular fins under dehumidifying conditions with a polynomial relationship between humidity ratio and saturation temperature." International Journal of Heat and Fluid Flow 31.4 (2010): 722-733. http://dx.doi.org/10.1016/j.ijheatfluidflow.2010.01.010.

      [6] Yaghoobi, Hessameddin, and Mohsen Torabi. "The application of differential transformation method to nonlinear equations arising in heat transfer." International Communications in Heat and Mass Transfer 38.6 (2011): 815-820. http://dx.doi.org/10.1016/j.icheatmasstransfer.2011.03.025.

      [7] Rashidi, M. M. "The modified differential transform method for solving MHD boundary-layer equations." Computer Physics Communications 180.11 (2009): 2210-2217. http://dx.doi.org/10.1016/j.cpc.2009.06.029.

      [8] Rashidi, Mohammad Mehdi, and Mohammad Keimanesh. "Using differential transform method and padé approximant for solving mhd flow in a laminar liquid film from a horizontal stretching surface." Mathematical Problems in Engineering 2010 (2010). http://dx.doi.org/10.1155/2010/491319.

      [9] Rashidi, M. M., and S. M. Sadri. "Solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the differential transform method." Int. J. Contemp. Math. Sciences 5.15 (2010): 711-720.

      [10] Chamkha, Ali J. "Non-Darcy hydromagnetic free convection from a cone and a wedge in porous media." International communications in heat and mass transfer 23.6 (1996): 875-887. http://dx.doi.org/10.1016/0735-1933(96)00070-X.

      [11] Chamkha, Ali J. "Hydromagnetic plane and axisymmetric flow near a stagnation point with heat generation." International Communications in Heat and Mass Transfer 25.2 (1998): 269-278. http://dx.doi.org/10.1016/S0735-1933(98)00014-1.

      [12] Desseaux, André. "Influence of a magnetic field over a laminar viscous flow in a semi-porous channel." International journal of engineering science 37.14 (1999): 1781-1794. http://dx.doi.org/10.1016/S0020-7225(99)00003-8.

  • Downloads

  • How to Cite

    Saffari, P., Fatahian, E., Saffari, P., & Fatahian, H. (2016). A numerical study on slip flow in packed hyper-porous media inside micro-channels using differential transformation method. International Journal of Scientific World, 4(2), 57-60. https://doi.org/10.14419/ijsw.v4i2.6736