STEADY-STATE WITH HEAT GENERATION SELECT THE CORRECT ANSWER USING T...

3. Steady-state with heat generation

Select the correct answer using the codes given below:

[IES-1998]

Codes: (a) 2 alone

(b) 1 and 2

(c) 1 and 3 (d) 1, 2 and 3

IES-18. In a long cylindrical rod of radius R and a surface heat flux of q

o

the

uniform internal heat generation rate is:

[IES-1998]

(a)

2q

⁰

R

(b)

2q

₀

(c)

q

⁰

R

(d)

q

⁰

₂

R

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IAS-1.

In order to substantially reduce leakage of heat from atmosphere into

cold refrigerant flowing in small diameter copper tubes in a refrigerant

system, the radial thickness of insulation, cylindrically wrapped

around the tubes, must be:

[IAS-2007]

(a) Higher than critical radius of insulation

(b) Slightly lower than critical radius of insulation

(c) Equal to the critical radius of insulation

(d) Considerably higher than critical radius of insulation

IAS-2.

A copper pipe carrying refrigerant at – 200 C is covered by cylindrical

insulation of thermal conductivity 0.5 W/m K. The surface heat transfer

coefficient over the insulation is 50 W/m

²

K. The critical thickness of

the insulation would be:

[IAS-2001]

(a) 0.01 m

(b) 0.02 m

(c) 0.1 m

(d) 0.15 m

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k

GATE-1. Ans. (c) Critical radius of insulation (r

c

) =

1

m 12.5cm

8

h

=

=

GATE-2. Ans. (b) Critical radius of insulation (r

c

) =

0.1

m 1 mm

100

Critical thickness of enamel point

1

1

0.5 mm

∴

= − = − =

r

r

c

i

2

GATE-3. Ans. (b) Maximum heat dissipation occurs when thickness of insulation is

critical.

r

k

Critical radius of insulation

( )

^0.5

^{m 25 mm}

c

20

=

h

=

=

Therefore thickness of insulation =

25

20

15 mm

r

− =

r

−

=

GATE-4. Ans. (c)

IES-1. Ans. (a)

IES-2. Ans. (c) The thickness upto which heat flow increases and after which heat flow

decreases is termed as Critical thickness. In case of cylinders and spheres it is

called 'Critical radius'.

IES-3. Ans. (a) Minimum

q at r

o

=

(k/h) = r

cr

(critical radius)

IES-4. Ans. (c) Critical radius of insulation (r

c

)

1

0.2m 20 cm

5

=

h

= =

=

∴

Critical thickness of insulation

( )

Δ

r

_C

= − =

r

_c

r

1

20 0.5 19.5cm

−

=

r

K

IES-5. Ans. (a)

Critical radius of insulation ( )

0.1

0.02m 2cm

c

5

=

h

=

=

=

Critical thickness of insulation ( )

t

= − = − =

r

_c

r

1

2 1 1cm

IES-6. Ans. (a)

IES-7. Ans. (b)

IES-8. Ans. (b) The critical radius of insulation for ensuring maximum heat transfer by

=

×

=

Therefore diameter should be 16 mm.

conduction (r) =

2

2 0.04

m 8mm.

10

h

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IES-9. Ans. (b) Critical radius of insulation for sphere in

^2k

h

and for cylinder is k/h

IES-10. Ans. (a) A and R are correct. R is right reason for A.

IES-11. Ans. (a)

IES-12. Ans. (a)

IES-13. Ans. (c)

IES-14. Ans. (a) For minimum heat transfer, the better insulation must be put inside.

IES-15. Ans. (a)

IES-16. Ans. (a)

IES-17. Ans. (a)

IES-18. Ans. (a)

IAS-1. Ans. (d) At critical radius of insulation heat leakage is maximum if we add more

insulation then heat leakage will reduce.

IAS-2. Ans. (a) Critical radius of insulation

( )

c

^0.5

₅₀

^{m 0.01m}

Page 29 of 97