Communications on Advanced Computational Science with Applications
Volume 2016, No. 1 (2016), Pages 32-46
Article ID cacsa-00038, 15 Pages
Studying influence of the wicking process on the heat transfer in a homogeneous inclined porous medium
Alireza Rahbari1,2, Mohammad Abdollahzadeh2 *
1Department of Mechanical Engineering, Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran.
2Department of Mechanical Engineering, Tehran Science and Research Branch, Islamic Azad University, Damavand, Iran.
* Corresponding author. Email address: firstname.lastname@example.org
Received: 24 March 2015; Accepted: 08 June 2015
Copyright © 2016 Alireza Rahbari and Mohammad Abdollahzadeh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this research, we study the spontaneous wicking process of a fluid in a homogeneous porous medium taking into account that the medium is subject to the presence of a temperature gradient, including the gravity effects. We assume that the porous medium is initially at temperature $T_0$ and pressure $P_0$ ; then the lower part of the porous medium faces a liquid reservoir with temperature $T_1$ and pressure $P_0$ and begins the spontaneous wicking process into the porous medium. The physical influence of two nondimensional parameters like the ratio of the characteristic thermal time to the characteristic wicking time, $\beta$ and $\alpha$ are defined as the ratio of the hydrostatic head of the imbibed fluid to the characteristic pressure difference between the wicking front and the dry zone of the porous medium, serves us to evaluate the velocity of the wicking front as well as the temperature profiles and the corresponding Nusselt numbers in the wetting zone. Influence of the heat dissipation and slope of porous medium on temperature and velocity profile is studied. In particular, for small values of time the well-known Washburn law is recovered. The numerical predictions show that the the velocity and temperature profiles depend on the above nondimensional parameters, revealing a clear deviation of the simple Washburn law.
Keywords: porous media; heat transfer; wicking; homogeneous; numberical.
C. J. van Oss, R. F. Giese, Z. Li, K. Murphy, J. Norris, M. K. Chaudhury, R. J. Good, Determination of contact angles and pore sizes of porous media column and thin layer wicking, J. Adhes. Sci. Technol, 6 (1992) 413-428.
E. Chibowski, L. Holysz, Use of the Washburn equation for surface fee energy determination, Langmuir, 8 (1992) 710-716.
E. P. Kalogianni, T. Savopoulos, T. D. Karapantsios, S. N. Raphaelides, A dynamic wicking technique for determining the effective pore radius of pregelatinized starch sheets, Colloids Surf. B 35 (2004) 159-167.
J. Navas, R. Alcantara, C. Fernandez-Lorenzo, J. Martin-Calleja, Pore characterization methodology by means of capillary sorption tests, Transp. Porous Med, 86 (2011) 333-351.
E. W. Washburn, The dynamics of capillary flow, Phys. Rev, 17 (1921) 273.
P. Cheng, W. J. Minkowycz, Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike, J. Geophys. Res, 82 (1977) 2040-2044.
W. J. Minkowycz, P. Cheng, Free convection about a vertical cylinder embedded in a porous medium, Int. J. Heat Mass Transfer, 19 (1987) 805-813.
H. M. Badr, I. Pop, Combined convection from an isothermal horizontal rod buried in a porous medium, Int. J. Heat Mass Transfer, 31 (1988) 2527-2541.
A. Nakayama, H. Koyama, A general similarity transformation for combined free and forced convection flows within a fluid saturated porous medium, J. Heat Mass Transfer, 28 (1995) 1041-1045.
M. Sanchez, F. Sanchez, C. Pérez-Rosales, A. Medina, C. Treviño, Imbibition in a Hele-Shaw cell under a temperature gradient, Phys. Lett. A 324 (2004) 14-21.
E. W. Washburn, The Dynamics of Capillary Flow, Phys. Rev, 17 (1921) 273.
M. Alava, M. Dubé, M. Rost, Imbibition in disordered media, Adv. Phys, 53 (2004) 83-175.
O. M. Phillips, Flow and Reactions in Permeable Rocks, Cambridge University Press, Cambridge, (1991).
T. J. Babadagli, Temperature effect on heavy-oil recovery by imbibition in fractured reservoirs, Journal of Petroleum Science and Engineering, 14 (1996) 197-208.
T. J. Babadagli, Scaling capillary imbibition during static thermal and dynamic fracture flow conditions, Journal of Petroleum Science and Engineering, 33 (2002) 223-239.