Computational Power Series Solution of Non- Linear Non-Darcy Momentum Transport and Heat Transport Equations through Cylindrical Porous Annulus

  IJCTT-book-cover
 
International Journal of Computer Trends and Technology (IJCTT)          
 
© 2016 by IJCTT Journal
Volume-36 Number-3
Year of Publication : 2016
Authors : Ashoka S. B.
  10.14445/22312803/IJCTT-V36P130

MLA

Ashoka S. B. "Computational Power Series Solution of Non- Linear Non-Darcy Momentum Transport and Heat Transport Equations through Cylindrical Porous Annulus". International Journal of Computer Trends and Technology (IJCTT) V36(3):167-171 June 2016. ISSN:2231-2803. www.ijcttjournal.org. Published by Seventh Sense Research Group.

Abstract -
The solution of the two-point boundary value problem arising in a fully-developed, nonlinear, non-Darcy flow through a cylindrical porous annulus is obtained using the uni-variate differential transform method. Radius of convergence of the power series solution is determined using the Domb-Sykes plot. For those combinations of parameters' values for which the series solution diverges, appropriate Padeapproximent is used to get a convergent solution. Numerical experimentation using a combination of choice of infinity, degree of the polynomial and order of the Pade-approximent is exhaustively performed to get the desired convergence in the solution for any given accuracy. Computation of the flow velocity is done using the free and open source software Maxima. The method successfully gives the required solution for large values of Forchheimer number when shooting method fails to do so. It is shown that Nusselt increases with individual increases in Darcy number, Forchheimer number and Brinkman number.

References
[1] D. A. Nield and A. Bejan, Convection in porous media, Springer Verlag, New York,2006.
[2] K. Vafai, Hand book of porous media, CRC Press, 2005.
[3] N. Rudraiah, P. G. Siddheshwar, D. Pal, and D. Vortmeyer, Non – Darcy effects on transient dispersion in porous media, ASME Proc.1988, Nat. Heat Trans. Conf.,Houston,Texas, USA (Ed. H. R. Jacobs), HTD – 96 (1) (1988) 623 - 629.
[4] E. Skjetne and J. L. Auriault, New insights on steady, nonlinear flow in porous media,Eur. J. Mech. B/Fluids, 18 (1999) 131-145.
[5] V. V. Calmidi and R. L. Mahajan, Forced convection in high porosity metal foams,ASME J. Heat Trans., 122(3) (2000) 557-565.
[6] A. R. A Khaled and K. Vafai., The role of porous media in modelling flow and heat transfer in biological tissues, Int. J. Heat Mass Trans., 46 (2003) 4989-5003.
[7] K. Vafai and S. J. Kim, Forced convection in a channel filled with a porous medium: An exact solution, ASME J. Heat Trans., 111 (1989) 1103-1106.
[8] D. A. Nield, S. L. M. Junqueira and J. L. Lage, Forced convection in a fluid-saturated porous-medium channel with isothermal or isoflux boundaries, J. Fluid Mech., 322 (1996) 201-214.
[9]P.H. Forcheimer, Wasserbewegug durch Buden, Z. Ver. Deutsch. Ing., 45 (1901) 1782- 1788.
[10] S. Ergun, Flow through packed columns, Chem. Eng. Prog., 48[2] (1952) 89-94.
[11] G. Lauriat and V. Prasad, Natural convection in a vertical porous cavity: A numerical study for Brinkman extended Darcy formulation, J. Heat Trans., 109 (1987) 295-330.
[12] R. C. Givler and S. A. Altobelli, A determination of the effective viscosity for the Brinkman – Forchheimer flow model, J. Fluid Mech., 258 (1994) 355-370.
[13] D. Poulikakos and K. Renken , Forced convection in a channel filled with porous medium, including the effect of flow inertia, variable porosity and Brinkman friction, ASME J. Heat Trans., 109 (1987) 880-888.
[14] M. Parang and M. Keyhany, Boundary and inertia effect on flow and heat transfer in porous media, Int. J. Heat Mass Trans., 24 (1987) 195-203.
[15] K. Hooman, A perturbation solution for forced convection in a porous saturated duct, J. Comput. Appl. Math., 211(1) (2008) 57-66.
[16] K. Hooman and H. Gurgenci, A theoretical analysis of forced convection in a porous saturated circular tube: Brinkman- Forchheimer model, Transport in Porous Media, 69(3) (2007) 289-300.

Keywords
It is shown that Nusselt increases with individual increases in Darcy number, Forchheimer number and Brinkman number.