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Fig. 8. Effect of the fins crossing

angle on the efficiency criterion

K

Q

at various Biot numbers (

Re

= 10

4

;

ˉ

h

1

= 4 ˉ

h

ˉ

h

;

ˉ

t

p

= 4 ˉ

t

ˉ

t

):

curves

1

— Bi = 0.4; curves

2

Bi = 0.04

Fig. 9. Dependency of the efficiency criterion

K

Q

on the finning pitch at various

angles and Biot numbers (

Re

= 10

4

;

ˉ

h

1

= 4 ˉ

h

ˉ

h

):

curves

1

(Bi = 0.4) —

β

= 20

; —

β

= 30

;

×

β

= 45

; curves

2

(Bi = 0.04) —

β

= 20

; —

β

= 30

;

N

β

= 45

)

3–4-fold; when Bi decreases from 0.4 to 0.04,

K

Q

increases 1.7–2-fold

(Fig. 8). At the same time, when

β

is less than 20. . . 30

the

K

Q

criterion

demonstrates tenuous and inefficient values, even when the Biot number

has favourable values.

When the fins are positioned with small intervals, the efficiency index

K

Q

can reach values from 3 to 10 units. However, as the finning pitch

t

increases, the efficiency index

K

Q

decreases, which is particularly

noticeable at low (favourable) Bi values (Fig. 9).

Both quantitative and qualitative values of

β

angles and Biot numbers

make a significant contribution to the dependency of the efficiency

K

Q

on

the heat releasing fins height

h

1

. For instance, in case of the favourable

(optimistic) value Bi

= 0

.

04

and the fins height

h

1

growing from 1 to 4,

the criterion

K

Q

increases from 1 to 4 and nearly stabilizes afterwards.

In case of the pessimistic values Bi

= 0

.

4

, the efficiency rate does not

exceed 1.5. . . 5.5 units, noteceably decreases as

h

1

grows along the total

range of values, with low sensitivity to the finning pitch ratio (Fig. 10).

This estimation can be used to select finning parameters when designing

cooling channels.

52

ISSN 0236-3941. HERALD of the BMSTU. Series Mechanical Engineering. 2015. No. 2