# Multiple choice question for engineering

## Set 1

1. The convective heat transfer coefficient in laminar flow over a flat plate

a) Increases with distance

b) Increases if a higher viscosity fluid is used

c) Increases if a denser fluid is used

d) Decreases with increase in free stream velocity

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2. For laminar flow over a flat plate, the average value of Nusselt number is prescribed by the relation

Nu = 0.664 (Re) ^{0.5 }(Pr)^{ 0.33}

Which of the following is then a false statement?

a) Density has to be increased four times

b) Plate length has to be decreased four times

c) Specific heat has to be increased four times

d) Dynamic viscosity has to be decreased sixteen times

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3. For turbulent flow over a flat plate, the average value of Nusselt number is prescribed by the relation

Nu = 0.664 (Re) ^{0.5 }(Pr)^{ 0.33}

Which of the following is then a false statement?

The average heat transfer coefficient increases as

a) 1/5 power of plate length

b) 2/3 power of thermal conductivity

c) 1/3 power of specific heat

d) 4/5 power of a free stream velocity

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4. A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient is

Nu = 0.13 (Gr Pr) ^{1/3}

a) 143 MW

b) 153 MW

c) 163 MW

d) 173 MV

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5. Consider the above problem, find the value of Grashoff number

a) 101.3 * 10 ^{12}

b) 102.3 * 10 ^{12}

c) 103.3 * 10 ^{12}

d) 104.3 * 10 ^{12}

### View Answer

^{3 }p

^{2 }β g d t/µ

^{2}.

6. A thin walled duct of 0.5 m diameter has been laid in an atmosphere of quiescent air at 15 degree Celsius and conveys a particular gas at 205 degree Celsius. Base your calculations on one meter length of the duct, estimate the convective coefficient of heat transfer

a) 5.086 W/m^{2} K

b) 6.086 W/m^{2} K

c) 7.086 W/m^{2} K

d) 8.086 W/m^{2} K

### View Answer

^{0.25}= 5.086 W/m

^{2}K.

7. Free correction modulus is given by

a) p ^{2} β g c _{P}/µ

b) p ^{2} β g c _{P}/k

c) p ^{2} β g c _{P}/µ k

d) p ^{2} β g c _{P}

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8. The free convection coefficient is given by

h = C _{1} d t ^{m}/l ^{1 – 3m}

The value of exponent for laminar flow is

a) 0.5

b) 0.6

c) 0.7

d) 0.8

### View Answer

_{1}(d t/l)

^{0.25}.

9. For inclined plates we multiply Grashoff number with

a) Cos 2 α

b) Sin 2 α

c) Sin α

d) Cos α

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10. The free convection coefficient is given by

h = C _{1} d t ^{m}/l ^{1 – 3m}

The value of exponent for turbulent flow is

a) 0.43

b) 0.33

c) 0.23

d) 0.13

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## Set 2

1. The following factors need consideration for the optimum design of fins

(i) Cost

(ii) Space considerations

(iii) Weight considerations

Choose the correct option

a) 1 only

b) 1 and 2 only

c) 1, 2 and 3

d) 2 only

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2. A heating unit is made in the form of a vertical tube of 50 mm outside diameter and 1.2 m height. The tube is fitted with 20 steel fins of rectangular section with height 40 mm and thickness 2.5 mm. The temperature at the base of fin is 75 degree Celsius, the surrounding air temperature is 20 degree Celsius and the heat transfer coefficient between the fin as well as the tube surface and the surrounding air is 9.5 W/m^{2} K. If thermal conductivity of the fin material is 55 W/m K, find the amount of heat transferred from the tube with fin

a) 1234 .98 W

b) 1004.84 W

c) 6539.83 W

d) 3829.46 W

### View Answer

_{b }= h A

_{b }(t

_{0 }– t

_{INFINITY}) and heat flow rate convicted from the fins, Q

_{f }= n k A

_{C}m (t

_{0}– t

_{a}).

3. The fins would be effective for heat conduction if the ratio P k/h A _{C} is

a) Greater than 5

b) Less than 5

c) Equal to 5

d) Varies between 2 to 9

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4. Consider the following statements pertaining to heat transfer through fins

(i) They must be arranged at right angles to the direction of flow of working fluid

(ii) The temperature along the fin is variable and accordingly heat transfer rate varies along the fin elements

(iii) Fins are equally effective irrespective whether they are on the hot side or cold side of the fluid

(iv) Fins are made of materials that have thermal conductivity higher than that of wall

Identify the correct statements

a) 3 and 4

b) 1 and 3

c) 2 and 3

d) 1 and 2

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5. An increase in fin effectiveness is caused by high value of

(i) Convective coefficient

(ii) Thermal conductivity

(iii) Circumference

(iv) Area

Identify the correct statement

a) 1 and 3

b) 3 and 4

c) 2 and 4

d) 2 and 3

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6. A steel strap is serving as a support for the steam pipe. The strap is welded to the pipe and bolted to the ceiling. The junction between the support strut and the ceiling is adiabatic, and the outside temperature of steam pipe is 105 degree Celsius. The strut AB is 60 cm high and AD = BC = 12.5 cm. It is 0.3 cm thick. Workout the rate at which heat is lost to the surrounding air by the support strut. It may be assumed that thermal conductivity for steel is 45 W/m degree, the total outside surface coefficient is 17 W/m^{2} degree and the surrounding air is at 32 degree Celsius

a) 178 W

b) 168 W

c) 158 W

d) 148 W

### View Answer

_{x}/α

_{0 }= t

_{x }– t

_{a}/t

_{0 }– t

_{a }= cos m (l – x)/cos ml.

7. Choose the correct option regarding fin efficiency and fin effectiveness

a) 2 Fin effectiveness = A_{ FIN}/A _{B} (Efficiency of fin)

b) 3 Fin effectiveness = A_{ FIN}/A _{B} (Efficiency of fin)

c) Fin effectiveness = A_{ FIN}/A _{B} (Efficiency of fin)

d) ½ Fin effectiveness = A_{ FIN}/A _{B} (Efficiency of fin)

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8. The handle of a saucepan, 30 cm long and 2 cm in diameter, is subjected to 100 degree Celsius temperature during a certain cooking operation. The average unit surface conductance over the handle surface is 7.35 W/m^{2} degree in the kitchen air at 24 degree Celsius. The cook is likely to grasp the last 10 cm of the handle and hence the temperature in this region should not exceed 38 degree Celsius. What should be the thermal conductivity of the handle material to accomplish it? The handle may be treated as a fin insulated at the tip

a) 18.36 W/m degree

b) 17.36 W/m degree

c) 16.36 W/m degree

d) 15.36 W/m degree

### View Answer

_{x}/α

_{0 }= t

_{x }– t

_{a}/t

_{0 }– t

_{a }= cos m (l – x)/cos ml. Now, for a circular handle of diameter d, P/A = 4/d.

9. Let us assume a square section fin split longitudinally and used as two fins. This will result in

a) Increase or decrease in heat transfer depending on material of fin

b) Heat flow remains constant

c) Decrease in heat transfer

d) Increase in heat transfer

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10. Mark the false statement regarding effectiveness of fin

a) A high value of film coefficient adversely affects the fin effectiveness

b) Fin effectiveness is improved if fin is made from a material of low conductivity

c) Fin effectiveness is improved by having thin fins

d) It can also be improved by having closely spaced fins

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## Set 3

1. Which one of the following materials are quickly heated by applying high frequency?

a) Textiles

b) Engines

c) Rubber

d) Coal

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2. Generally heat generated depends on some parameters. It is directly proportional to

a) Time

b) Conductivity

c) Voltage

d) Distance between plates

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3. Consider a 1.2 m thick slab of poured concrete (k = 1.148 W/m degree) with both of side surfaces maintained at a temperature of 20 degree Celsius. During its curing, chemical energy is released at the rate of 80 W/m^{3}. Workout the maximum temperature of concrete

a) 30.73 degree celsius

b) 29.73 degree celsius

c) 28.73 degree celsius

d) 27.73 degree celsius

### View Answer

_{g }(δ – x) x/2 k + t

_{w}= 29.73 degree celsius.

4. The insulating material used in dielectric heating is

a) Coal

b) Silver

c) Coin

d) Wool

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5. A composite slab consists of 5 cm thick layer of steel (k = 146 kJ/m hr degree) on the left side and a 6 cm thick layer of brass (k = 276 kJ/m hr degree) on the right hand side. The outer surfaces of the steel and brass are maintained at 100 degree Celsius and 50 degree Celsius. The contact between the two slabs is perfect and heat is generated at the rate of 4.2 * 10 ^{5} k J/m^{2} hr at the plane of contact. The heat thus generated is dissipated from both sides of composite slab for steady state conditions. Calculate the temperature at the interface

a) 115.26 degree celsius

b) 125.26 degree celsius

c) 135.26 degree celsius

d) 145.26 degree celsius

### View Answer

_{1 }+ Q

_{2 }= Q

_{g}. Q

_{1 }= k

_{1}A

_{ 1}t

_{i – }t

_{1})/δ

_{1 }and

_{ }Q

_{2 }= k

_{2}A

_{ 2}t

_{i – }t

_{2})/δ

_{2}.

6. Unit of specific resistance is

a) Ohm mm^{2}/m

b) Ohm mm

c) Ohm/m

d) Ohm mm/m

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7. What maximum thickness of concrete can be poured without causing the temperature gradient to exceed 98.5 degree Celsius per meter anywhere in the slab? Consider a 1.2 m thick slab of poured concrete (k = 1.148 W/m degree) with both of side surfaces maintained at a temperature of 20 degree Celsius. During its curing, chemical energy is released at the rate of 80 W/m^{3}. Workout the maximum temperature of concrete

a) 2.64 m

b) 3.64 m

c) 4.64 m

d) 5.64 m

### View Answer

_{g }(δ – 2 x)/2 k. The temperature is largest at x = 0.

8. Dielectric heating apparatus consists of

a) 4 electrodes

b) Elemental strip

c) No Insulating material

d) 4 plates

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9. The given expression can be used to solve the electrode temperature t _{w1 }and t _{w2}

q _{g }δ = h _{1 }α _{1 }+ h _{2 }α _{2}

Where, α _{1 }= A (t _{w 2 }– t _{a}) and α _{2} = (t _{w1 }– t _{a})

This statement is true or false

a) True

b) False

### View Answer

_{1 }= A (t

_{w 1 }– t

_{a}) and α

_{2}= (t

_{w2 }– t

_{a}).

10. A slab of insulating material of thickness 6 cm and thermal conductivity 1.4kJ/m hr deg is placed between and is in contact with two parallel electrodes, and is then subjected to high frequency dielectric heating at a uniform rate of 140,000kJ/m^{3} hr. At steady state coefficients of combined radiation and convection are 42 and 48 kJ/m^{2 }hr deg. If atmospheric temperature is 25 degree Celsius, find surface temperatures?

a) 144.10 degree Celsius and 134.47 degree Celsius

b) 123.50 degree Celsius and 154.34 degree Celsius

c) 121.60 degree Celsius and 115.45 degree Celsius

d) 165.40 degree Celsius and 165.45 degree Celsius

### View Answer

_{g }x

^{2}/2k + h

_{1}α

_{1}/k + α

_{1}. At x =0.06 m and α = α

_{2}, α

_{2}= -180 + 2.8 α

_{1}.

_{ }Also q

_{g}A δ = h

_{1 }α

_{1 }+ h

_{2 }α

_{2}.

## Set 4

1. How is dimensional homogeneity related with fundamental units of measurements?

a) Independent

b) Dependent

c) Dependent but can vary

d) Twice

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2. What is the time period of oscillation of a simple pendulum of length L and mass m?

a) 2 π (L/g) ^{3/2}

b) 2 π (L/g)

c) 2 π (L/g) ^{2}

d) 2 π (L/g) ^{1/2 }

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3. The principle of dimensional homogeneity serves the following useful concepts

(i) It helps to check whether an equation of any physical phenomenon is dimensionally homogenous or not

(ii) It helps to determine the dimensions of a physical quantity

(iii) It helps to convert the units from one system to another

Identify the correct statements

a) 1 and 2

b) 2 and 3

c) 1, 2 and 3

d) 2 only

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4. The equation of friction loss in a pipe of length l and diameter d through which fluid flows with velocity v is

a) h _{i }= 4 f V ^{2}/d g

b) h _{i }= 4 f V ^{2}/d 2 g

c) h _{i }= 4 f V ^{2}/d 2 g

d) h _{i }= 4 f V ^{2}/2 g

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5. Bernoulli’s equation for fluid flow along a stream line is given as

a) p/w + V ^{2}/2 g + y = 2

b) p/w + V/2 g + y = constant

c) p/w + V ^{2}/2 g + y = 1

d) p/w + V ^{2}/2 g + y = constant

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6. The convective film coefficient in k cal/m^{2} hr degree can be converted to J/m^{2} s degree by multiplying it with a factor

a) 1.1627

b) 1.1527

c) 1.1427

d) 1.1327

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^{2}hr degree and J/m

^{2}s are the units of convective film coefficient.

7. The pressure in kg/cm^{2} can be converted to N/m^{2} by multiplying it with a factor

a) 9.807 * 10 ^{2}

b) 9.807 * 10 ^{3}

c) 9.807 * 10 ^{4}

d) 9.807 * 10 ^{5}

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^{2}and N/m

^{2 }are the units of pressure.

8. How many Newton’s are there in one kg?

a) 9.507

b) 9.607

c) 9.707

d) 9.807

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9. How many Joule are there in 1 k cal?

a) 3186

b) 4186

c) 5186

d) 6186

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10. How many fundamental quantities are there?

a) 1

b) 2

c) 3

d) 4

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## Set 5

1. With variable thermal conductivity, Fourier law of heat conduction through a plane wall can be expressed as

a) Q = -k_{0} (1 + β t) A d t/d x

b) Q = k_{0} (1 + β t) A d t/d x

c) Q = – (1 + β t) A d t/d x

d) Q = (1 + β t) A d t/d x

### View Answer

_{0}is thermal conductivity at zero degree Celsius.

2. The inner and outer surfaces of a furnace wall, 25 cm thick, are at 300 degree Celsius and 30 degree Celsius. Here thermal conductivity is given by the relation

K = (1.45 + 0.5 * 10^{-5} t^{2}) KJ/m hr deg

Where, t is the temperature in degree centigrade. Calculate the heat loss per square meter of the wall surface area?

a) 1355.3 kJ/m^{2} hr

b) 2345.8 kJ/m^{2} hr

c) 1745.8 kJ/m^{2} hr

d) 7895.9 kJ/m^{2} hr

### View Answer

^{-5}t

^{2}) A d t. Integrating over the wall thickness δ, we get Q = 436.45/0.25 = 1745.8 kJ/m

^{2}hr.

3. A plane wall of thickness δ has its surfaces maintained at temperatures T_{1} and T_{2}. The wall is made of a material whose thermal conductivity varies with temperature according to the relation k = k_{0} T^{2}. Find the expression to work out the steady state heat conduction through the wall?

a) Q = 2A k_{0} (T _{1 }^{3} – T _{2 }^{3})/3 δ

b) Q = A k_{0} (T _{1 }^{3} – T _{2 }^{3})/3 δ

c) Q = A k_{0} (T _{1 }^{2} – T _{2 }^{2})/3 δ

d) Q = A k_{0} (T _{1} – T _{2})/3 δ

### View Answer

_{0}T

^{2 }A d t/d x. Separating the variables and integrating within the prescribed boundary conditions, we get Q = A k

_{0}(T

_{1 }

^{3}– T

_{2 }

^{3})/3 δ.

4. The mean thermal conductivity evaluated at the arithmetic mean temperature is represented by

a) k_{m} = k_{0} [1 + β (t_{1} – t_{2})/2].

b) k_{m} = k_{0} [1 + (t_{1} + t_{2})/2].

c) k_{m} = k_{0} [1 + β (t_{1} + t_{2})/3].

d) k_{m} = k_{0} [1 + β (t_{1} + t_{2})/2].

### View Answer

_{1}+ t

_{2})/2.

5. With respect to the equation k = k_{0} (1 +β t) which is true if we put β = 0?

a) Slope of temperature curve is constant

b) Slope of temperature curve does not change

c) Slope of temperature curve increases

d) Slope of temperature curve is decreases

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6. The accompanying sketch shows the schematic arrangement for measuring the thermal conductivity by the guarded hot plate method. Two similar 1 cm thick specimens receive heat from a 6.5 cm by 6.5 cm guard heater. When the power dissipation by the wattmeter was 15 W, the thermocouples inserted at the hot and cold surfaces indicated temperatures as 325 K and 300 K. What is the thermal conductivity of the test specimen material?

a) 0.81 W/m K

b) 0.71 W/m k

c) 0.61 W/m K

d) 0.51 W/m K

### View Answer

_{1}– t

_{2})/δ. So, k = 0.71 W/m K.

7. If β is greater than zero, then choose the correct statement with respect to given relation

k = k_{0} (1 +β t)

a) k doesn’t depends on temperature

b) k depends on temperature

c) k is directly proportional to t

d) Data is insufficient

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8. The unit of thermal conductivity doesn’t contain which parameter?

a) Watt

b) Pascal

c) Meter

d) Kelvin

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9. The temperatures on the two sides of a plane wall are t_{1} and t_{2} and thermal conductivity of the wall material is prescribed by the relation

K = k_{0 }e ^{(-x/δ)}

Where, k_{0} is constant and δ is the wall thickness. Find the relation for temperature distribution in the wall?

a) t _{1} – t _{x }/ t _{1} – t _{2} = x

b) t _{1} – t _{x }/ t _{1} – t _{2} = δ

c) t _{1} – t _{x }/ t _{1} – t _{2} = δ/x

d) t _{1} – t _{x }/ t _{1} – t _{2} = x/δ

### View Answer

_{0 }e

^{(-x/δ)}d t/d x. Separating the variables and upon integration, we get Q/k

_{0 }A = (t

_{1}– t

_{2})/ δ (e – 1). Therefore heat transfer through the wall, Q = k

_{0 }A (t

_{1}– t

_{2})/ δ (e – 1). At x = x and t = t

_{x }we get the answer.

10. “If β is less than zero, then with respect to the relation k = k_{0} (1 + β t), conductivity depends on surface area”. True or false

a) True

b) False