Fins and Transient Heat Conduction
Exam Duration: 45 Mins Total Questions : 25
A plate of asbestos material having thickness 5 cm is maintained at 300°C. It is suddenly put in surrounding at 30°C. Assume p = 2000 kg/m3, c = 100 J/kg-K, K = 10 W/m-K and convection heat transfer coefficient h = 90 W/m-K. What will be the temperature of slab after 100 s.
- (a)
140.20°C
- (b)
278.93°C
- (c)
110.20°C
- (d)
Data is insufficient
Match List I (Parameter) with List II (Definition) and select the correct answer using the codes given below the lists.
| List I | List II |
|---|---|
| P. Time constant of a thermometer of radius r0 | \(\frac { h{ r }_{ 0 } }{ { K }_{ fluid } } \) |
| Q. Biot number for sphere of radius r0 | \(\frac { K }{ h } \) |
| R. Critical thickness of insulation for a wire of radius r0 | \(\frac { h{ r }_{ 0 } }{ { K }_{ solid } } \) |
| S. Nusselt number for a sphere of radius r0 | \(\frac { h\pi { r }_{ 0 }l }{ \rho CV } \) |
- (a)
P Q R S 4 3 2 1 - (b)
P Q R S 1 2 3 4 - (c)
P Q R S 2 3 4 1 - (d)
P Q R S 4 1 2 3
In order to achieve maximum heat dissipation, the fin should be designed in such a way that
- (a)
it should have maximum lateral surface at the root side of the fin
- (b)
it should have maximum lateral surface towards the tip side of the fin
- (c)
it should have maximum lateral surface near the centre of the fin
- (d)
it should have minimum lateral surface near the centre of the fin
Consider the following statements:
Assertion (A) Lumped capacity analysis of unsteady heat conduction assumes a constant uniform temperature througout a solid body.
Reason (R) The surface convection resistance is very large compared with the internal conduction resistance. Of these statements
- (a)
both A and R are true and R is the correct explanation of A
- (b)
both A and R are true but R is not a correct explanation of A
- (c)
A is true but R is false
- (d)
A is false but R is true
A fin of length l protrudes from a surface held at temperature To; it being higher than the ambient temperature Ta. The heat dissipation from the free end of the fin is stated to be negligibly small. What is the temperature gradient \(\left( \frac { dT }{ dx } \right) _{ x=l }\) at the tip of the fin?
- (a)
Zero
- (b)
\(\frac { { T }_{ o }-{ T }_{ l } }{ l } \)
- (c)
h(To - Ta)
- (d)
\(\frac { { T }_{ l }-{ T }_{ a } }{ { T }_{ o }-{ T }_{ a } } \)
The value of m for this pin fin is
- (a)
\(\sqrt { \frac { h }{ kl } } \)
- (b)
\(2\sqrt { \frac { h }{ Kd } } \)
- (c)
\(2\sqrt { \frac { hl }{ Kd } } \)
- (d)
\(\sqrt { \frac { 4Kd }{ h } } \)
If a = 5 mm and K = 54 W/m-°C, h = 90 W/m2-°C, then
- (a)
m = 50
- (b)
m = 48.06
- (c)
m = 42.07
- (d)
m = 60.73
Select the condition at which heat transfer from insulated tip can be considered the case of fin of infinite length.
- (a)
m = 0.75, L = 3
- (b)
m = 1, L = 3
- (c)
m = 3, L = 0.72
- (d)
m = 2, L = 1.2
Two identical long rods are attached to base of heat source having (T0 = 100 °C). If K1 = 43 W/m-K, then K2 (in W/m-K) is
- (a)
400
- (b)
376.43
- (c)
339.56
- (d)
471.26
In the given long fin, T1 = 120°C, T2 = 90°C and d0 = 1.5 cm and surrounding temperature T\(\infty \) = 30°C then, K (in W/m-K) is (approximate) (h = 15 W/m2-K)
- (a)
300
- (b)
400
- (c)
350
- (d)
275
A fin has 5 mm diameter and 100 mm length. The thermal conductivity of fin material is 400 W/m-K. One end of the fin is maintained at 130°C and its remaining surface is exposed to ambient air at 30°C. If the convective heat transfer coefficient is 40 W/m2 -K, the heat loss (in watt) from the fin is
- (a)
0.08
- (b)
5.0
- (c)
7.0
- (d)
7.8
The cylindrical rod is being used as a fin. Given, To = 500 °C, T\(\infty \) = 30°C, h = 40 W/m2-K, K = 300 WIm-K and do = 0.5 cm.
If l0 = 50 cm, then heat transfer from fin is,
- (a)
28.58 W
- (b)
30.92 W
- (c)
27.02 W
- (d)
26.72 W
The cylindrical rod is being used as a fin. Given, To = 500 °C, T\(\infty \) = 30°C, h = 40 W/m2-K, K = 300 WIm-K and do = 0.5 cm.
Temperature of rod at point P, if distance from wall is 20 cm, is
- (a)
89.6°C
- (b)
91.2°C
- (c)
86.43°C
- (d)
99.3°C
The temperature distribution in a fin along its length is as \(\theta\) = \(\theta\)0 (ae-x - bx2). Here, \(\theta\) = T - Ta. If thermal conductivity of fin is K and length is L, then total heat transfer from fin (in W/m2) is
- (a)
Ka\(\theta\)0
- (b)
K(aeL - 2bL) \(\theta\)0
- (c)
2 b\(\theta\)0 K
- (d)
None of these
One end of a rectangular fin (L = 20 cm) is at constant base temperature of T0= 127°C, it is kept in surrounding having temperature T\(\infty \) = 25°C. If Kfin = 200 W/m-K and h = 80 W/m2-K and temperature at any point of fin varies as T = T0 (a - bx2).
The temperature of end point TL is (if b = 0.75)
- (a)
25° C
- (b)
52°C
- (c)
49.02°C
- (d)
0°C
One end of a rectangular fin (L = 20 cm) is at constant base temperature of T0= 127°C, it is kept in surrounding having temperature T\(\infty \) = 25°C. If Kfin = 200 W/m-K and h = 80 W/m2-K and temperature at any point of fin varies as T = T0 (a - bx2).
Heat transfer QL from cross-sectional area is
- (a)
24 kW/m2
- (b)
2.16 W/m2
- (c)
20 kW/m2
- (d)
2.00 W/m2
One end of a rectangular fin (L = 20 cm) is at constant base temperature of T0= 127°C, it is kept in surrounding having temperature T\(\infty \) = 25°C. If Kfin = 200 W/m-K and h = 80 W/m2-K and temperature at any point of fin varies as T = T0 (a - bx2).
If cross-section is perfectly insulated, then heat transfer rate from this is
- (a)
2.16 kW/m2
- (b)
zero
- (c)
2.16 W/m2
- (d)
None of these
There is shown an internal fin (a pocket is created radially into the pipe) as shown in figure. An air is flowing inside the pipe (Ta = 200°C). Length of pocket is L = 5 cm and wall temperature is Ta = 140°C, \(\delta \) = 1 mm and Kfin = 112 W/m-K. Heat transfer coefficient for air and fin material is 400 W / m2-K. (Assume insulated end)
Temperature of point P is
- (a)
199°C
- (b)
194°C
- (c)
201°C
- (d)
189°C
There is shown an internal fin (a pocket is created radially into the pipe) as shown in figure. An air is flowing inside the pipe (Ta = 200°C). Length of pocket is L = 5 cm and wall temperature is Ta = 140°C, \(\delta \) = 1 mm and Kfin = 112 W/m-K. Heat transfer coefficient for air and fin material is 400 W / m2-K. (Assume insulated end)
If temperature of point P is not equal to air temperature then, percentage change in temperature is
- (a)
2.5%
- (b)
3.2%
- (c)
2.8%
- (d)
3%
A longitudinal copper fin (K = 380 W/m-°C) 600 mm long and 5 mm diameter is exposed to air stream at 20°C. If h = 20 W/m2- °C, then efficiency of fin at insulated tip is
- (a)
22%
- (b)
43%
- (c)
25.66%
- (d)
41.26%
A solid copper ball of mass 500 g, when quenched in a water bath at 30 °C, cools from 530°C to 430° in 10 s. What will be the temperature of the ball after the next 10 s?
- (a)
300°C
- (b)
320°C
- (c)
350°C
- (d)
Not determinable for want of sufficient data
A finned surface consists of root or base area of 1 m2 and fin surface area of 2 m2. The average heat transfer coefficient for finned surface is 20 W/m2-K, effectiveness of fins provided is 0.75. If finned surface with root or base temperature of 50°C is transferring heat to a fluid at 30°C, then rate of heat transfer is
- (a)
400 W
- (b)
800 W
- (c)
1000 W
- (d)
1200 W
A solid sphere of 1 cm radius made up of copper is initially at 300°C temperature. For Cu, K = 60 W/m-K, p = 7800 kg/m3, C = 434 J/kg-K. The time required for cooling it upto 50°C when it is kept in air at 25°C with h = 20 W/m2-K, is
- (a)
1296 s
- (b)
1353 s
- (c)
2016 s
- (d)
1491 s
A body is exposed to cooling airflow at 20°C. If Bi = 0.007143 and Fo = 7200 \(\tau \) Here, \(\tau \) is time (in hour) required to cool the body from 550°C to 90°C. The value of \(\tau \) is
- (a)
171 s
- (b)
141.7 s
- (c)
161.7 s
- (d)
181 s
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 coefficient on bend surface is 400 W/m2-K. Thermophysical properties of thermocouple material are K = 20 W/m2-K, C = 400 J/kg-K and p = 8500 kg/m3. If the thermocouple initially at 30°C is placed in a hot stream of 300°C, the time taken by the bead to reach 298°C, is
- (a)
2.35 s
- (b)
4.9 s
- (c)
14.7 s
- (d)
29.4 s
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