ONE DIMENSIONAL UNSTEADY CONDUCTION OBJECTIVE QUESTIONS (GATE, IES,...

5. One Dimensional Unsteady

Conduction

O

BJECTIVE

Q

UESTIONS

(GATE, IES, IAS)

Previous 20-Years GATE Questions Heat Conduction in Solids having Infinite Thermal Conductivity (Negligible internal Resistance-Lumped Parameter Analysis)

GATE-1. The value of Biot number is very small (less than 0.01) when

(a) The convective resistance of the fluid is negligible

[GATE-2002]

(b) The conductive resistance of the fluid is negligible

(c) The conductive resistance of the solid is negligible

(d)

None

of

these

GATE-2. A small copper ball of 5 mm diameter at 500 K is dropped into an oil

bath whose temperature is 300 K. The thermal conductivity of copper is

400 W/mK, its density 9000 kg/m

³

and its specific heat 385 J/kg.K.1f the

heat transfer coefficient is 250 W/m

²

K and lumped analysis is assumed

to be valid, the rate of fall of the temperature of the ball at the

beginning of cooling will be, in K/s.

[GATE-2005]

(a) 8.7

(b) 13.9

(c) 17.3

(d) 27.7

GATE-3. A spherical thermocouple junction of diameter 0.706 mm is to be used

for the measurement of temperature of a gas stream. The convective

heat transfer co-efficient on the bead surface is 400 W/m

²

K.

Thermophysical properties of thermocouple material are k = 20 W/mK,

C =400 J/kg, K and ρ = 8500 kg/m

³

. If the thermocouple initially at 30°C

is placed in a hot stream of 300°C, then time taken by the bead to reach

298°C, is:

[GATE-2004]

(a) 2.35 s

(b) 4.9 s

(c) 14.7 s

(d) 29.4 s

Page 36 of 97

Previous 20-Years IES Questions

IES-1. Assertion (A): Lumped capacity analysis of unsteady heat conduction

assumes a constant uniform temperature throughout a solid body.

Reason (R): The surface convection resistance is very large compared

with the internal conduction resistance.

[IES-2010]

IES-2.

The ratio

Internal conduction resistance

Surface convection resistance

is known as

[IES-1992]

(a) Grashoff number

(b) Biot number

(c) Stanton number

(b) Prandtl number

IES-3.

Which one of the following statements is correct?

[IES-2004]

The curve for unsteady state cooling or heating of bodies

(a) Parabolic curve asymptotic to time axis

(b) Exponential curve asymptotic to time axis

(c) Exponential curve asymptotic both to time and temperature axis

(d) Hyperbolic curve asymptotic both to time and temperature axis

IES-4. Assertion (A): In lumped heat capacity systems the temperature

gradient within the system is negligible

[IES-2004]

Reason (R): In analysis of lumped capacity systems the thermal

conductivity of the system material is considered very high

irrespective of the size of the system

(a) Both A and R are individually true and R is the correct explanation of A

(b) Both A and R are individually true but R is not the correct explanation of A

(c) A is true but R is false

(d) A is false but R is true

IES-5.

A solid copper ball of mass 500 grams, when quenched in a water bath

at 30°C, cools from 530°C to 430°C in 10 seconds. What will be the

temperature of the ball after the next 10 seconds?

[IES-1997]

(a)

300°C

(b)

320°C

(c) 350°C

(d) Not determinable for want of sufficient data

Time Constant and Response of — Temperature Measuring Instruments

IES-6.

A thermocouple in a thermo-well measures the temperature of hot gas

flowing through the pipe. For the most accurate measurement of

temperature, the thermo-well should be made of:

[IES-1997]

(a) Steel

(b) Brass

(c) Copper

(d) Aluminium

Page 37 of 97

Transient Heat Conduction in Semi-infinite Solids (h or Hj 4.5. 30~5 00)

IES-7.

Heisler charts are used to determine transient heat flow rate and

temperature distribution when:

[IES-2005]

(a) Solids possess infinitely large thermal conductivity

(b) Internal conduction resistance is small and convective resistance is large

(c) Internal conduction resistance is large and the convective resistance is small

(d) Both conduction and convention resistance are almost of equal significance

Previous 20-Years IAS Questions

IAS-1.

Assertion (A): During the temperature measurement of hot gas in a

duct that has relatively cool walls, the temperature indicated by the

thermometer will be lower than the true hot gas temperature.

Reason(R): The sensing tip of thermometer receives energy from the

hot gas and loses heat to the duct walls.

[IAS-2000]

(d) A is false but R is true

Page 38 of 97

Answers with Explanation (Objective) Previous 20-Years GATE Answers

GATE-1. Ans. (c)

GATE-2. Ans. (c)

4

0.005 / 2

π

3

V

r

r

Charactaristic length ( )

3

8.3333 10 m

=

=

= =

=

×

4

L

A

r

π

⁻

2

3

3

c

4

s

k

=

=

=

×

−

Thermal

diffusivity,

400

1.1544 10

⁴

ρ

×

α

c

9000 385

p

ατ

=

τ

Fourier number (F

o

) =

₂

166

L

c

×

×

−

−

Biot number (B

i

) =

250 8.3333 10

⁴

5.208 10

⁴

=

=

×

hL

c

400

Then,

300

T T

e

or

T

e

166 5.208 10

4

− ×

−

×

×

−

θ

τ

a

B F

=

=

=

i

o

θ

500 300

T T

i

i

a

τ

−

−

= −

or ln(

300) ln 200

0.08646

T

⎛

⎞

or

1

0.08646 or

0.08646

500 300

17.3K/s

dT

dT

= −

⎜

⎟

= −

×

−

= −

(

)

(

)

τ

τ

T

d

d

−

⎝

⎠

≈

T

K

500

3

0.11767 10 m

=

= =

×

−

GATE-3. Ans. (b) Characteristic length (L

c

) =

A

r

−

Biot number (B

i

) =

400

(

0.11767 10

³

)

3