Bahadori Fatemeh, Sima Rezvantalab

35

Journal of Chemical Technology and Metallurgy, 50, 1, 2015, 35-38

VISCOSITY VARIATION EFFECTS ON HEAT TRANSFER AND FLUID FLOW THROUGH TWO-LAYERED POROUS MEDIA

Bahadori Fatemeh, Sima Rezvantalab

Chemical Engineering Department, Urmia University of Technology, Urmia, IranE-mail: f.bahadori@che.uut.ac.ir

ABSTRACT

Temperature dependent viscosity effects on natural convection in a composite cavity, isothermally heated from below and cooled from the opposing surface, are analyzed. The two-layered porous media was composed of two regions with different permeability. It is observed that viscosity reduction, due to temperature rising, affects heat transfer rate and fluid motion at the interface.

Keywords: two layered porous media, viscosity, heat transfer, permeability ratio (Kr), streamline.

Received 10 June 2014Accepted 24 November 2014

INTRODUCTION

Heat transfer in porous media has been extensively studied due to its numerous engineering and environ-mental applications. Oil recovery, underground spread of pollutants, grain storage, geothermal systems, solar power collectors, optimal design of furnaces, compact heat exchangers, packed-bed catalytic reactors and pas-sive thermal control devices are examples of applications of heat transfer in porous media.

Studies concerning natural convection in porous media can be found in the monographs of Ingham and Pop [1], and Nield and Bejan [2]. The case of free convection in a rectangular porous medium, heated on one side and cooled at the opposing side, is also an im-portant problem in thermal convection in porous media. The work of Walker and Homsy [3], Bejan [4], Prasad and Kulacki [5], Manole and Lage [6], Saeid and Pop [7] and others have further contributed some classical results to this problem.

The presence of a free-flow domain adjacent to a porous media, has been studied in literature by Cieszko, Kubik [8], Mharzi et al. [9], Edimilson and de Lemos Marcelo [10] and Baytas et al. [11], and others. Fur-thermore, multilayered cavity has been investigated. Poulikakos and Bejan [12] studied horizontally and vertically layered cavity and approximated a correla-

tion for calculation of the overall Nusselt number for N horizontal sub layers. Lai and Kulacki [13] discussed convection in a vertically divided rectangular cavity, of the right hand side wall which was heated with constant heat flux.

Egorov and Polezhaev [14] investigated a theoretical model and showed that their numerical results are in the line of their experimental data for multilayer insulation. In addition, Merrikh and Mohamad [15], Belghazi et al. [16] and Ordo´n˜ez-Miranda and Alvarado-Gil [17] and others, have investigated multilayered porous media.

It can be seen that composite cavity under natural convection is evaluated extensively in literature, how-ever, the viscosity variation due to temperature rising is considered negligible.

The aim of this paper is the investigation of viscosity variation effects on the natural convection in a saturated enclosure, divided into two different porous layers, with different permeabilities and subjected to a heating from one side and cooling from the other side.

Governing equationsAn incompressible, 2-D, natural convection in a

two-layered cavity, filled with a saturated, isotropic porous medium with temperature dependent viscosity and density variation in the buoyancy term, was studied numerically. It was assumed that the solid matrix and the fluid are in local thermal equilibrium. As suggested

Journal of Chemical Technology and Metallurgy, 50, 1, 2015

36

by Nield and Bejan [2], the equations that govern the conservation of mass, momentum, and energy can be written as follows:

0u∇ = (1)

2f u u Pu v u

x y x Kρ µε

∂ ∂ ∂ + = − ∂ ∂ ∂ (2)

[ ]2 ( )f v v Pu v v g T Tx y x K

ρ µ ρ βε ∞

∂ ∂ ∂ + = − + − ∂ ∂ ∂ (3)

2T Tu v Tx y

α∂ ∂+ = ∇

∂ ∂ (4)

The average Nusselt number is defined by:2

0

L

xNu Nu dx= ∫ (5)

It was assumed that viscosity is varying with tem-perature in the following models:

Cµ = (6a)

0 0( )T T Tµ λ= − − (6b)

0 exp( )T Tµ γ= (6c)

Numerical procedure and grid independenceThe model equations were solved using the commer-

cial flow simulation software FLUENT (version 6.3.26). Fig. 1 shows the geometry of the simulated media. As it can be seen, the rectangular enclosures with different permeability are separated at Y=L/2. The results for Ram=1000 are in line with those in the literature.

RESULTS AND DISCUSSION

The results of simulation are presented in the next sections.

Effect of viscosity variationFig. 2 and Fig. 3 illustrate the streamlines for

Fig. 1. Scheme of the layered porous media and the coor-dinate system.

Fig. 2. Streamlines for horizontally divided porous media, Ra1 = 104, Da = 0.001, Kr = 0.001:(a) constant viscosity, (b) linear variation of viscosity with temperature and (c) exponential variation of viscosity with temperature.

a) b)

c)

Fig. 3. Streamlines for horizontally divided porous media, Ra1 = 104, Da = 0.001, Kr = 1000; (a) constant viscosity, (b) linear variation of viscosity with temperature and (c) exponential variation of viscosity with temperature.

a) b)

c)

Bahadori Fatemeh, Sima Rezvantalab

37

Ra1=104, Da=0.001, Kr= 1000 for a horizontally divided porous media. As it can be seen, viscosity reduction due to temperature raising causes increase of the flow pen-etration rate from one layer to another. In addition, the flow penetration rate for the case, which is modeled by considering exponential variation of viscosity, is higher than the case with linear variation of viscosity.

Heat transferFig. 4 shows Nu numbers obtained by assuming: of

(a) exponential variation of viscosity with temperature, (b) linear variation of viscosity with temperature and (c) constant viscosity. Fig. 4 shows that the mean Nu number obtained when considering exponential variation with temperature (Nuexp) is greater than the Nu number ob-tained with linear variation of viscosity with temperature (Nulin). As it is seen, Nucon is in line with the findings of Poulikakos and Bejan [12].

Velocity profileFig. 5 illustrates the velocity profile in the horizon-

tally divided porous media. As it can be seen, decreas-ing of the velocity due to temperature rising, causes an increase of fluid movement. In addition, comparison of Fig. 5a and Fig. 5b shows that the velocity magnitude in two layered porous media with Kr < 1 is higher than Kr > 1.

CONCLUSIONS

The viscosity variation effect on natural convection in a horizontally layered porous media was investigated numerically using the finite volume method. Results were presented for flow field and heat transfer of enclo-sures subjected to heated from one side, and cooled from the opposite wall, while the other walls were isolated.

Fig. 4. Variation of cavity average Nusselt number for a horizontally divided enclosure(a) Da = 0.01, Kr = 0.1 and (b) Da = 0.01, Kr = 10.

a) b)

a) b)

Fig. 5. Variation of v-velocity at the mid-height of the horizontally divided enclosure for(a) Da = 0.01, Kr = 0.1 and (b) Da = 0.01, Kr = 10.

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