Transp Porous Med (2013) 98:35–57
DOI 10.1007/s11242-013-0131-4
Effect of an Inserted Porous Layer Located at a Wall
of a Parallel Plate Channel on Forced Convection Heat
Transfer
Eren Ucar · Moghtada Mobedi · Ioan Pop
Received: 8 October 2012 / Accepted: 25 January 2013 / Published online: 14 February 2013
© Springer Science+Business Media Dordrecht 2013
Abstract A theoretical study is performed on heat and fluid flow in partially porous medium
filled parallel plate channel. A uniform symmetrical heat flux is imposed onto the boundaries
of the channel partially filled with porous medium. The dimensional forms of the governing
equations are solved numerically for different permeability and effective thermal conduc-
tivity ratios. Then, the governing equations are made dimensionless and solved analytically.
The results of two approaches are compared and an excellent agreement is observed, indicat-
ing correctness of the both solutions. An overall Nusselt number is defined based on overall
thermal conductivity and difference between the average temperature of walls and mean
temperature to compare heat transfer in different channels with different porous layer thick-
ness, Darcy number, and thermal conductivity ratio. Moreover, individual Nusselt numbers
for upper and lower walls are also defined and obtained. The obtained results show that the
maximum overall Nusselt number is achieved for thermal conductivity ratio of 1. At specific
values of Darcy number and thermal conductivity ratio, individual Nusselt numbers approach
to infinity since the value of wall temperatures approaches to mean temperature.
Keywords Porous medium · Partially filled porous media · Channel flow · Fully developed.
List of Symbols
Da Darcy number
f Friction coefficient
G Pressure gradient in x - direction
h Convective heat transfer coefficient, W/m
2
K
H Half height of channel
E. Ucar · M. Mobedi
Mechanical Engineering Department, Izmir Institute of Technology, 35430 Urla, Izmir, Turkey
I. Pop (B )
Department of Mathematics, Babe¸ s -Bolyai University, 40084 Cluj-Napoca, Romania
e-mail: popm.ioan@yahoo.co.uk
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