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# Multiple choice question for engineering

## Set 1

1. In heat dissipation from an infinitely long fin, the boundary conditions are
a) t = t0 at x = infinity and t = ta at x = 0
b) t = t0 at x = 0 and t = ta at x = infinity
c) t = t0 at x = 0 and t = ta at x = 0
d) t = t0 at x = infinity and t = ta at x = infinity

Answer: b [Reason:] These conditions must be approached when ml is greater than 5.

2. The temperature distribution in case of infinitely long fin is
a) t – t a/t 0 – t a = mx
b) t – t a/t 0 – t a = -mx
c) t – t a/t 0 – t a = e-m x
d) t – t a/t 0 – t a = log (m x)

Answer: c [Reason:] Exponential curve should be here.

3. The rate of heat transfer in case of infinitely long fin is given by
a) (h P k A) 1/2 (t 0 – t a)
b) (h P A) 1/2 (t 0 – t a)
c) (P k A) 1/2 (t 0 – t a)
d) (h k A) 1/2 (t 0 – t a)

Answer: a [Reason:] It should contain all the terms i.e. h, p, k and A.

4. Let us say there are two rods having same dimensions, one made of brass (k = 85W/m K) and the other of copper (k = 375W/m K), having one of their ends inserted into a furnace. At a section 10.5 cm away from the furnace, the temperature of brass rod is 120 degree Celsius. Find the distance at which the same temperature would be reached in the copper rod? Both ends are exposed to the same environment
a) 12.54 cm
b) 45.87 cm
c) 12.34 cm
d) 22.05 cm

Explanation: For brass rod, 120 = t a + (t 0 – t a) e –m l and for copper rod, 120 = t a + (t 0 – t a) e –M L So L = L 0 (k 2/k 1) = 22.05 cm.

5. Three rods, one made of silver (l = 420W/m K), second made of aluminum (k = 210W/m K) and the third made of iron (k = 70W/m K) are coated with a uniform layer of wax all around. The rods are placed vertically in a boiling water bath with 250 mm length of each rod projecting outside. If all the rods are having following dimensions i.e. diameter = 15 mm and length = 300 mm and have identical surface coefficient 12.5W/ m2 K, work out the ratio of lengths up to which wax will melt on each rod
a) 2.45:1:1.732
b) 1.732:1:2.45
c) 2.45:1.732:1
d) 1.732:1:2.45

Answer: c [Reason:] k 1/l 12 = k 2/l 22 = k 3/l 32.

6. Let us assume there are two pieces of copper wire 0.1625 cm in diameter with a device that melts it at 195 degree Celsius. The wires are positioned vertically in air at 24 degree Celsius and the heat transfer coefficient of the wire is 17 W/ square m K. Let us say k = 335W/m K i.e. of wire. Find out the energy input?

a) 1.234W
b) 2.652W
c) 4.562W
d) 9.435W

Answer: b [Reason:] A C = π D 2/4 = 2.073 * 10 – 6 square meter. P = π D = 0.0051 m. Q FIN = k A C m (t 2 – t 1) = 1.326W.

7. A rod of 10 mm square section and 160 mm length with thermal conductivity of 50W/m K protrudes from a furnace wall at 200 degree Celsius with convective coefficient 20 W/ square m K. Make calculations for the heat convective up to 80 mm length
a) 6.84W
b) 7.34W
c) 4.54W
d) 5.47W

Answer: a [Reason:] Q = k A C m (t 2 – t 1), m = (P h/k AC) 1/2 = 12.649 /m, so Q = 10.75W. At x = 80 mm, (m x) = 1.01192, so T – 30/200 – 30 = 0.3635. Therefore net heat is 10.75 – k A C m (t 0.08 – t a) = 6.84W.

8. A fin protrudes from a surface which is held at a temperature higher than that of its environment. The heat transferred away from the fin is
a) Heat escaping from the tip of the fin
b) Heat conducted along the fin length
c) Convective heat transfer from the fin surface
d) Sum of heat conducted along the fin length and that convected from the surface

Answer: c [Reason:] As temperature is higher, so it’s convective.

9. The value of correction length for equilateral fin is
a) L C = 2 L + a/4(3)1/2
b) L C = L + a/4(3)1/2
c) L C = 3 L + a/4(3)1/2
d) L C = 6 L + a/4(3)1/2

Answer: b [Reason:] Area of triangle i.e. equilateral is (3)1/2/4.

10. The parameter m = (h P/k A C) 1/2 has been stated to increase in a long fin. If all other parameters are constant, then
a) Profile of temperature will remain the same
b) Along the length temperature drop will be less
c) The parameter influences the heat flow only
d) The temperature drop along the length will be steeper

Answer: d [Reason:] For an infinitely long fin t – t a/t 0 – t a = e – m x. Dimensionless temperature falls more with increase in factor m.

## Set 2

1. A very long copper rod 20 mm in diameter extends horizontally from a plane heated wall maintained at 100 degree Celsius. The surface of the rod is exposed to an air environment at 20 degree Celsius with convective heat transfer coefficient of 8.5 W/m2 degree. Workout the heat loss if the thermal conductivity of copper is 400 W/m degree
a) 10.71 W
b) 20.71 W
c) 30.71 W
d) 40.71 W

Answer: b [Reason:] P/A = 4/d and m = (h P/k A) ½ = (4 h/k d) ½ = 2.061.per meter.

2. Common applications of finned surfaces are with
(i) Electrical motors
(ii) Economizers for steam power plant
(iii) Convectors for steam and cold water heating systems
(iv) Cooling coils
Identify the correct option
a) 1, 2 and 4
b) 1, 2 and 3
c) 1, 2, 3 and 4
d) 1 and 2

Answer: a [Reason:] It should be for hot water heating systems.

3. The extended surface used for the enhancement of heat dissipation is
a) Convective coefficient
b) Fourier number
c) Fin
d) No finned surface

Answer: c [Reason:] The surface area exposed to the surroundings is frequently increased by the attachment of protrusions to the surfaces, and the arrangement provides a means by which heat transfer rate can be improved.

4. It is said that fins can take a variety of forms
(i) Longitudinal fins of rectangular cross section attached to a wall
(ii) Cylindrical tubes with radial fins
(iii) Conical rod protruding from a wall
Identify the correct statement
a) 1 only
b) 1 and 2
c) 2 and 3
d) 1, 2 and 3

Answer: d [Reason:] Option b is also known as annular fins.

5. A steel rod (k = 30 W/m degree) 1 cm in diameter and 5 cm long protrudes from a wall which is maintained at 10 degree Celsius. The rod is insulated at its tip and is exposed to an environment with h = 50 W/m2 degree and t a = 30 degree Celsius. Calculate the fin efficiency
a) 56.57%
b) 66.57%
c) 76.57%
d) 86.57%

Answer: b [Reason:] Fin efficiency = tan h ml/ml, where m = (h P/k A) ½ = 25.82 per meter.

6. If fin is sufficiently thin, so heat flows pertains to
a) One dimensional heat conduction
b) Two dimensional heat conduction
c) Three dimensional heat conduction
d) No heat flow is there

Answer: a [Reason:] As, δ is less than b, so one dimensional heat conduction is there.

7. If heat dissipation for one fin is given by 377.45 k J/hour, then what is the heat dissipation for 12 fins?
a) 7529.4 k J/hour
b) 6529.4 k J/hour
c) 5529.4 k J/hour
d) 4529.4 k J/hour

Answer: d [Reason:] For 12 fins, the heat dissipation will be equal to 12 (377.45) = 4529.4 k J/hour.

8. In order to achieve maximum heat dissipation the fin should be designed in such a way that has a
a) Maximum lateral surface towards the tip side of fin
b) Minimum lateral surface near the center line
c) Maximum lateral surface at the root side of fin
d) Maximum lateral surface near the center of fin

Answer: c [Reason:] Fins are so designed that lateral surface at the root side of the fin is maximum. This aspect results into higher heat dissipation.

9. A steel rod (k = 30 W/m degree) 1 cm in diameter and 5 cm long protrudes from a wall which is maintained at 10 degree Celsius. The rod is insulated at its tip and is exposed to an environment with h = 50 W/m2 degree and t a = 30 degree Celsius. Calculate the rate of heat dissipation
a) 2.658 W
b) 3.658 W
c) 4.658 W
d) 5.658 W

Answer: b [Reason:] Q = k A m tan h ml (t 0 – t a) = 3.658 W.

10. On a heat transfer surface, fins are provided to
a) Increase turbulence in flow for enhancing heat transfer
b) Increase temperature gradient so as to enhance heat transfer
c) Pressure drop of the fluid should be minimized
d) Surface area is maximum to promote the rate of heat transfer

Answer: d [Reason:] Fins are provided to a heat exchanger surface to augment the heat transfer by increasing the surface area exposed to the surroundings.

## Set 3

1. Which one is having highest value of fouling factor?
a) Sea water
b) Distilled water
c) Liquid gasoline
d) Clean river

Answer: c [Reason:] Fouling factor for liquid gasoline is 0.0008 while that of clean river, sea water and distilled water are 0.0002, 0.0001 and 0.0001 respectively. Fouling factor = 1/hS.

2. What is the value of fouling factor for sea water?
a) 0.0001-0.0002 m2 K/W
b) 0.0002-0.0003 m2 K/W
c) 0.0003-0.0004 m2 K/W
d) 0.0004-0.0005 m2 K/W

Answer: a [Reason:] There are strong hydrogen bonding between its molecules.

3. What is the value of fouling factor for clean river?
a) 0.0014-0.0018 m2 K/W
b) 0.0010-0.0014 m2 K/W
c) 0.0006-0.0010 m2 K/W
d) 0.0002-0.0006 m2 K/W

Answer: d [Reason:] It has low electrical conductivity but this increases with the dissolution of small amount of ionic materials.

4. Which one is having lowest value of fouling factor?
a) Lake river
b) Distilled water
c) Transformers
d) Lubricating oil

Answer: b [Reason:] Fouling factor for distilled water is 0.0001 while that of Lake River, transformer and lubricating oil are 0.0002, 0.0002 and 0.0002 respectively.

5. What is the value of fouling factor for treated boiler feed water?
a) 0.0001-0.0002 m2 K/W
b) 0.0002-0.0003 m2 K/W
c) 0.0003-0.0004 m2 K/W
d) 0.0004-0.0005 m2 K/W

Answer: a [Reason:] It is a good polar solvent and is referred to as the universal solvent. Fouling factor = 1/hS.

6. Which one is having highest value of fouling factor?
a) Industrial liquids
b) Fuel oil
c) Turbine exhaust
d) Engine exhaust

Answer: d [Reason:] Fouling factor for engine exhaust is 0.002 while that of industrial liquids, fuel oil and turbine exhaust are 0.0002, 0.0010 and 0.0002 respectively.

7. What is the value of fouling factor for fuel oil?
a) 0.0009 m2 K/W
b) 0.0010 m2 K/W
c) 0.0011 m2 K/W
d) 0.0012 m2 K/W

Answer: b [Reason:] It is a neutral, non-polar chemical substance that is viscous liquid at ambient temperature.

8. Which one is having lowest value of fouling factor?
a) Fuel gases
b) Oil bearing system
c) Non-oil bearing system
d) Engine exhaust

Answer: c [Reason:] Fouling factor for non-oil bearing system is 0.0001 while that of fuel gases, oil bearing system and engine exhaust are 0.0010, 0.0002 and 0.002 respectively.

9. What is the value of fouling factor for oil bearing steam?
a) 0.0002 m2 K/W
b) 0.0003 m2 K/W
c) 0.0004 m2 K/W
d) 0.0005 m2 K/W

Answer: a [Reason:] Fouling factor = 1/hS.

10. Which one is having highest value of fouling factor?
a) Clean water
b) Sea water
c) Liquid gasoline
d) Distilled water

Answer: c [Reason:] Fouling factor for liquid gasoline is 0.0008 while that of clean water, sea water and distilled water are 0.0002, 0.0001 and 0.0001 respectively.

## Set 4

1. The famous Fourier series is named after
a) Diller and Ryan
b) J.B. Joseph Fourier
c) Stefan- Boltzmann
d) Wein’s

Answer: b [Reason:] He gave this theory in 1824.

2. Fourier law of heat conduction is best represented by
a) Q = -k A d t /d x
b) Q = k A d x/d t
c) Q = -k A
d) Q = k d t/d x

Answer: a [Reason:] According to Fourier law of heat conduction, Q = -k A d t /d x.

3. Here are some assumptions that are made for Fourier law. Identify the wrong one
a) No internal heat generation
c) Non- linear temperature profile
d) Isotropic and homogenous material

Answer: c [Reason:] It has constant temperature gradient and a linear temperature profile.

4. Consider the following statements:
The Fourier heat conduction equation
Q = -k A d t /d x
Presumes
ii) Constant value of thermal conductivity
iii) Uniform temperature at the wall surface
iv) One dimensional heat flow
Which of these statements are correct?
a) 1, 2 and 3
b) 1, 2 and 4
c) 2, 3 and 4
d) 1, 3 and 4

Answer: d [Reason:] Thermal conductivity is different for different materials.

5. The diagram shows heat conduction through a plane wall. The surface temperature is 475 K and it radiates heat to the surroundings at 335 K. If thermal conductivity of the material is 12.5 W/m degree, find the temperature gradient. Let convective coefficient be 80 W/m2 degree and radiation factor is 0.9

a) – 1052.4 degree celsius
b) – 2052.4 degree celsius
c) – 3052.4 degree celsius
d) – 4052.4 degree celsius

Answer: a [Reason:] Heat conducted through the plate = convection heat losses + radiation heat losses. So, d t /d x = – 13155/12.5 = – 1052.4 degree Celsius.

a) Heat always flow is in the direction of positive temperature gradient
b) Heat always flow in the direction of negative temperature gradient
c) No heat flow is there
d) Data is insufficient

Answer: b [Reason:] The ratio d t/d x represents the change in temperature per unit thickness i.e. the temperature gradient. So it represents heat flow in the direction of negative temperature gradient.

7. Transmission of heat i.e. molecular is smallest in case of
a) Gases
b) Liquids
c) Alloys
d) Solids

Answer: a [Reason:] In gases atoms are arranged loosely, there is less molecular transmission of heat as compared to solids, liquids and alloys.

8. Which one is not the unit of thermal conductivity?
a) kcal/m hr K
b) KJ/m hr K
c) W/m s K
d) Cal/cm s K

Answer: c [Reason:] The unit kcal/m hr K could also be specified as J/m s K or W/m s K and this is actually done while quoting the numerical values of thermal conductivity.

9. “Thermal conductivity represents the amount of heat conducted across unit area when a temperature difference of one kelvin”. True or false
a) True
b) False

Answer: b [Reason:] It is across unit area and through unit distance.

10. Which of the following is the unit of thermal resistance?
a) degree/kcal
b) hour degree
c) s degree/kcal
d) degree/W

Answer: d [Reason:] Thermal resistance is expressed in the unit’s hr degree/kcal, degree/W and s degree/J.

## Set 5

1. When evaporation takes place at the liquid-vapor interface, the heat transfer is solely due to free convection and the film coefficient follows the relation
a) Nu = f 1 (G r) f 2 (P r)
b) Nu = 2 f 1 (G r) f 2 (P r)
c) Nu = 3 f 1 (G r) f 2 (P r)
d) Nu = 4 f 1 (G r) f 2 (P r)

Answer: a [Reason:] The functions f 1 and f 2 depend upon the geometry of the heating surface.

2. Fritz criterion is given by
a) h = 1.973 (Q/A) 0.45
b) h = 1.973 (Q/A) 0.55
c) h = 1.973 (Q/A) 0.65
d) h = 1.973 (Q/A) 0.75

Answer: d [Reason:] Fritz formulated the following formula for water boiling at atmospheric pressure in free convection in a vertical tube headed from outside.

3. A 0.10 cm diameter and 15 cm long wire has been laid horizontally and submerged in water at atmospheric pressure. The wire has a steady state voltage drop of 14.5 V and a current of 42.5 A. Determine the heat flux of the wire.
The following equation applies for water boiling on a horizontal submerged surface
H = 1.54 (Q/A) 0.75 = 5.58 (d t) 3 W/m2 K where Q/A is the heat flux rate in W/m2 and d t is the temperature difference between surface and saturation
a) 1.308 * 10 8 W/m2
b) 1.308 * 10 7 W/m2
c) 1.308 * 10 6 W/m2
d) 1.308 * 10 5 W/m2

Answer: c [Reason:] Q = E I = 616.25 W and A = 4.71 * 10 -4 m2.

4. Consider the above problem, find the excess temperature of the wire
a) 18.01 degree Celsius
b) 19.01 degree Celsius
c) 20.01 degree Celsius
d) 21.01 degree Celsius

Answer: b [Reason:] 1.54 (1.308 * 10 6) 2 = 5.58 (d t) 3.

5. Natural convection heat transfer coefficients over surface of a vertical pipe and a vertical flat plate for same height. What is/are the possible reasons for this?
(i) Same height
(ii) Both vertical
(iii) Same fluid
(iv) Same fluid flow pattern
a) 4
b) 1 and 2
c) 1
d) 3 and 4

Answer: d [Reason:] The fluids must be same so their flow pattern.

6. The heat flux in nucleate boiling varies in accordance with
a) h f g
b) (h f g) 0.5
c) 1/(h f g) 2
d) (h f g) 3

Answer: c [Reason:] Q/A = δ f h f g [(p f – p g) g/σ] 0.5 [C f d t/h f g p C s f] 3.

7. In nucleate pool boiling, the heat flux depends on
a) Liquid properties, material and condition of the surface
b) Material of the surface only
c) Material and roughness of the surface
d) Liquid properties and material of the surface

Answer: a [Reason:] The heat flux must depends on liquid properties material and condition of the surface.

8. Identify the wrong statement with respect to boiling heat transfer?
a) The steam boilers employing natural convection have steam raised through pool boiling
b) Boiling occurs when a heated surface is exposed to a liquid and maintained at a temperature lower than the saturation temperature of the liquid
c) Leiden-frost effect refers to the phenomenon of stable film boiling
d) The nucleation boiling is characterized by the formation of bubbles at the nucleation sites and the resulting liquid agitation

Answer: b [Reason:] For boiling to occur, the heated surface must be exposed to a liquid and maintained at a temperature higher than the saturation temperature of the liquid.

9. Estimate the peak heat flux for water boiling at normal atmospheric pressure. The relevant thermo-physical properties are
p f (liquid) = 958.45 kg/m3
p g (vapor) = 0.61 kg/m3
h f g = 2.25 * 10 6 J/kg
σ = 0.0585 N/m
a) 1.53 * 10 8 W/m2
b) 1.53 * 10 7 W/m2
c) 1.53 * 10 6 W/m2
d) 1.53 * 10 5 W/m2

Answer: c [Reason:] (Q/A) = 0.18 p g h f g [σ (p f – p g)/p g 2] 0.25.

10. A 1.0 mm diameter and 300 mm long nickel wire is submerged horizontal in water at atmospheric pressure. At burnout, the wire has a current of 195 A. Calculate the voltage at burnout. The relevant thermos-physical properties are
p f (fluid) = 959.52 kg/m3
p g (vapor) = 0.597 kg/m3
h f g = 2257000 J/kg
σ = 0.0533 N/m
a) 6.15 V
b) 7.15 V
c) 8.15 V
d) 9.15 V