Z. KHEIRANDISH ET AL.

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effect of Reynolds number, block spacing and dimen-

sions and also solid to fluid thermal conductivity ratio.

Their results showed that increasing in Reynolds number

causes more heat removal from the obstacles. Also, it

was revealed that maximum heat removal occurred

around the obstacle corners.

Li et al. [8] carried out an experiment to investigate

the hydrodynamic and thermal behaviors of forced con-

vection flow in rectangular channel with staggered arrays

of elliptic and circular fins. Their results showed that the

rate of cooling by the elliptic fin is more than that of cir-

cular one.

On the other hand, the optimum condition for any

process can be determined by the entropy generation ana-

lysis because one of the primary objectives in the design

of any energy system is to conserve the useful energy

applied to take place a certain process. The ireversibili-

ties associated within the process components destroy the

useful energy. It is clear that using fins in convection

cooling system increases the amount of irreversibilities.

Because of the second law of thermodynamics, irreversi-

bility can not be avoided completely but it can be mini-

mized in order to save the available energy. The present

work also deals with the second law analysis in convec-

tion duct flow with fin to carry out the rate of irreversi-

bilities due to the presence of obstacle.

In the related subject, Bejan [9] obtained a systematic

methodology to calculate irreversibility through fluid

flow and heat transfer in heat exchangers. Chen et al. [10]

studied transverse fin in laminar forced convection chan-

nel flow and analyzed entropy generation. They used

vorticity stream function method to solve the continuity

and momentum equations for fluid flow. They found that

fins increase the rates of irreversibilities, both due to vis-

cous effect and irreversible heat transfer process, al-

though they disturb developing of thermal boundary lay-

er which leads to heat transfer enhancement.

In several researches, entropy generation were studied

in detail for different flow and channel conditions. Ko et

al. [11] carried out a numerical study on wavy channel to

investigate entropy generation of laminar forced convec-

tion flow (Re = 100 up to 400). Their studies showed that

for high Reynolds number convection flows, irreversi-

bilities are minimums when duct width to height ratio is

equal to unity. In another study, they numerically ana-

lyzed entropy generation produced by a forced convec-

tive flow in a curved rectangular duct with external heat-

ing [12]. Three important factors such as Dean number,

external wall heat flux and cross-sectional aspect ratio on

entropy generated from frictional irreversibility and heat

transfer irreversibility were investigated in detail. It was

shown that, at larger Dean number and smaller wall heat

flux, frictional irreversibility is the most impressive

source of entropy generation; whereas and vice versa,

condition for Dean number and wall heat flux, the en-

tropy generation is dominated by heat transfer irreversi-

bility. Also, Ko [13] investigated the effect of longitudi-

nal ribs on laminar forced convection and entropy gen-

eration in a curved rectangular duct. He found that the

number of mounted ribs and their arrangement have in-

fluential effect on flow characteristics and temperature

distributions. Ko et al. [14] did a numerical study on en-

tropy generation by turbulent forced convective flow in a

curved rectangular duct with various aspect ratios. It was

found that the duct aspect ratio has great effect on the

distribution of local entropy generation number through

the flow domain.

Although there are many studies about numerical ana-

lysis of convective cooling in channel and also about the

analysis of such thermal systems by computing the en-

tropy generation, a careful inspection of literatures shows

that the entropy generation analysis in convective cooling

duct flow with obstacles that leads to a conjugate prob-

lem is still not studied. Therefore, the present research

deals with the investigation of entropy generation in a

forced convection flow adjacent to an obstacle in a duct

with conjugate problem for the fist time. Toward this end,

the set of governing equations consists of the continuity,

Navier-Stokes and energy equations for the fluid flow

and conduction equation for the obstacle are solved nu-

merically by the CFD method. Because the Cartesian co-

ordinate system is used for this computation, the block

off method is employed for simulating the obstacle in the

computational domain.

2. Theory

Computational domain of the problem is shown in Fig-

ure 1. Laminar convective flow enters a 2-D channel

which a heated obstacle mounted on bottom wall. Fluid

has uniform temperature Tin and parabolic velocity at the

inlet of channel. The duct walls are kept insulated except

the lower edge of fin which is maintained at constant

temperature Tw which is more than fluid inlet tem-

perature.

The height of the duct is H and the lengths of the duct

upstream and downstream sides of the fin are Li and Le,

respectively. This is made to ensure that the flows at the

inlet and outlet sections are not affected significantly by

the sudden change in the geometry and flow at the exit

section becomes fully developed. The height and width

of the fin are denoted by L and D such that L = D = 0.25

H is considered in all of the subsequent calculations.

3. Basic Equations

The non-dimensional governing equations which are the

conservations of mass, x- and y-momentum and energy

for fluid flow in the Cartesian coordinate can be written