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# Multiple choice question for engineering

## Set 1

1. Which one is true regarding rectangular fin?
a) A C = b δ and P = 2(b + δ)
b) A C = 2 b δ and P = 2(b + δ)
c) A C = 3 b δ and P = 2(b + δ)
d) A C = 4 b δ and P = 2(b + δ)
Where, b = width and δ = thickness

2. Analysis of heat flow from the finned surface is made with the following assumptions
(i) Uniform heat transfer coefficient, h over the entire fin surface
(ii) No heat generation within the fin generation
(iii) Homogenous material
Identify the correct option
a) 1 only
b) 1 and 2 only
c) 1, 2 and 3
d) 2 only

Answer: c [Reason:] The knowledge of temperature distribution is necessary for their optimum design with regard to size and weight.

3. If heat conducted into the element at plane x is Q X = – k A C (d t/d x) X. Then heat conducted out of the element at plane (x + d x) is
a) – 2k A C d/d x (t + d t/d x (d x))
b) – k A C d/d x (t + d t/d x (d x))
c) – 3k A C d/d x (t + d t/d x (d x))
d) – 4k A C d/d x (t + d t/d x (d x))

Answer: b [Reason:] Heat conducted out of the element is – [k A C (d t/d x) X + d x].

4. 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/m2 K. If thermal conductivity of the fin material is 55 W/m K, find the amount of heat transferred from the tube without fin
a) 98.44 W
b) 88.44 W
c) 78.44 W
d) 68.44 W

Answer: a [Reason:] Q = h A d t = h (π d 0 H) (t 0 – t INFINITY).

5. The general solution of linear and homogenous differential equation (second form) is of the form
a) γ = C 1 e 2 m x + C 2 e – m x
b) γ = C 1 e 3m x + C 2 e – m x
c) γ = C 1 e 4 m x + C 2 e – m x
d) γ = C 1 e m x + C 2 e – m x

Answer: d [Reason:] It should contain m x and – m x term.

6. For steady flow of heat along a rod, the general equation is
d2α/dx 2 – m 2 α = 0
The value of constant m is
a) (h P/k A C)
b) (h P/k A C) 3/2
c) (h P/k A C) 1/2
d) (h P/k A C) 2

Answer: c [Reason:] This provides a general form of the energy equation for one dimensional heat flow.

7. In convection from the tip, we introduced a factor known as
a) Fin length
b) Correction length
c) No fin length

Answer: b [Reason:] Just for simplicity we replace fin length by correction length.

8. Find the value of corrected length for rectangular fin?
Where, b is width and t is length of the fin
a) L C = L + b t/2 (b + t)
b) L C = L + b t/ (b + t)
c) L C = L + 2 (b + t)
d) L C = L + b t

Answer: a [Reason:] For rectangle, area = t b.

9. Which one is true for the spine?
a) A C = π d 2/4 and P = 4 π d
b) A C = π d 2/4 and P = 3 π d
c) A C = π d 2/4 and P = π d
d) A C = π d 2/4 and P = 2 π d

Answer: c [Reason:] A spine is a pin fin.

10. In convection from the tip what is the value of correction length?
a) L C = A C/P
b) L C = L + A C
c) L C = L + P
d) L C = L + A C/P

Answer: d [Reason:] It should contain all the three terms i.e. L, A and P.

## Set 2

1. Diagram shows transient heat conduction in an infinite plane wall. Identify the correct boundary condition in transient heat conduction in solids with finite conduction

a) t = t i at T = 0
b) d t /d x = 1 at x = 0
c) d t /d x = infinity at x = 1
d) d t / d x = infinity at x = 0

Answer: a [Reason:] d t / d x = 0 at x = 0. The solution of controlling differential equation in conjunction with initial boundary conditions would give an expression for temperature variation both with time and position.

2. Let there is some conduction resistance, then temperature becomes a function of
(i) Biot number
(ii)Fourier number
(iii) Dimensionless parameter
Identify the correct statement
a) 1 and 2
b) 2 and 3
c) 1 and 3
d) 1, 2 and 3

Answer: d [Reason:] It should be the function of all of the above i.e. Biot number, Fourier number and dimensionless parameters which includes all the dimensionless numbers.

3. “The value of Biot number and Fourier number, as used in the Heisler charts, are evacuated on the basis of a characteristics parameter s which is the thickness in case of plates and the surface radius in case of cylinders and spheres”. Choose the correct option
a) True
b) False

4. A large steel plate 50 mm thick is initially at a uniform temperature of 425 degree Celsius. It is suddenly exposed on both sides to an environment with convective coefficient 285 W/m2 K and temperature 65 degree Celsius. Determine the center line temperature.
For steel, thermal conductivity = 42.5 W/m K and thermal diffusivity = 0.043 m2/hr
a) 261 degree Celsius
b) 271 degree Celsius
c) 281 degree Celsius
d) 291 degree Celsius

Answer: c [Reason:] t 0 – t a/t I – t a = 0.6.

5. With respect to above problem, determine the temperature inside the plate 12.5 mm from the mid plane after 3 minutes
a) 272.36 degree Celsius
b) 262.36 degree Celsius
c) 252.36 degree Celsius
d) 22.35 degree Celsius

Answer: a [Reason:] x/l = 0.5 and t 0 – t a/t I – t a = 0.96.

6. “When Biot number exceeds 0.1 but is less than 100, use is made of Heislers charts for the solution of transient heat conduction”. Choose the correct answer
a) True
b) False

Answer: a [Reason:] The Heisler charts are extensively used to determine the temperature distribution and heat flow rate when both conduction and convection resistance are of equal importance.

7. In transient heat conduction, the two significant dimensionless parameters are
a) Reynolds number and Fourier number
b) Reynolds number and Biot number
c) Reynolds number and Prandtl number
d) Biot number and Fourier number

Answer: d [Reason:] These two are dimensionless numbers. Biot number is given by ratio of internal conduction resistance to the surface convection resistance whereas Fourier number signifies the degree of penetration of heating or cooling effect through a solid.

8. A 12 cm diameter cylindrical bar, initially at a uniform temperature of 40 degree Celsius, is placed in a medium at 650 degree Celsius with convective coefficient of 22 W/m2 K. Determine the time required for the center to reach 255 degree Celsius. For the material of the bar:
Thermal conductivity = 20 W/m K
Density = 580 kg/m3
Specific heat = 1050 J/kg K
a) 1234.5 seconds
b) 1973.16 seconds
c) 3487.3 seconds
d) 2896.4 seconds

Answer: b [Reason:] 1/B I = k/h R = 0.1515, t – t a/t I – t a = 0.647. X / l = 0 (center of the bar). Therefore, α T/R2 = 0.18.

9. Consider the above problem, calculate the temperature of the surface at this instant
a) 476.4 degree Celsius
b) 453.5 degree Celsius
c) 578.9 degree Celsius
d) 548.6 degree Celsius

Answer: c [Reason:] r/R = 1 and 1/B I = 0.1515. t 0 – t a/t I – t a = 0.18.

10. “A solid which extend itself infinitely in all directions of space is termed as finite solid”. Choose the correct answer
a) True
b) False

Answer: b [Reason:] It is known as infinite solid. This type of solid can extend itself in x-direction, y-direction and z-direction.

## Set 3

1. Consider radiant heat exchange between two non-black parallel surfaces. The surface 1 emits radiant energy E 1 which strikes the surface 2. Identify the correct option

a) The value of B is α E1
b) The value of C is (1 – α1) E 1
c) The value of D is (1 – α1) (1 – α2) 2 E 1
d) The value of E is (1 – α1) 2 (1 – α2) E 1

Answer: c [Reason:] The surface 1 emits radiant energy E 1 which strikes the surface 2. From it a part α2 E 1 is absorbed by the surface 2 and the remainder (1 – α2) E 1 is reflected back to surface 1 and so on.

2. A large plane, perfectly insulated on one face and maintained at a fixed temperature T 1 on the bare face, has an emissivity of 0.84 and loses 250 W/m2 when exposed to surroundings at nearly 0 K. The radiant heat loss from another plane of the same size is 125 W/m2 when bare face having emissivity 0.42 and is maintained at temperature T 2 is exposed to the same surroundings. Subsequently these two planes are brought together so that the parallel bare faces lie only 1 cm apart and the heat supply to each is so regulated that their respective temperatures T 1 and T 2 remains unchanged. Determine he net heat flux between the planes
a) 0
b) 1
c) 2
d) 3

Answer: a [Reason:] Q 12 = F 12 A 1 σ b (T 14 – T 24). Since T 1 = T 2, we get Q 12/A1 = 0.

3. Interchange factor for body 1 completely enclosed by body 2 (body 1 is large) is given by
a) 2/ [1/E 1 + A1/A2 (1/E 2 – 1)].
b) 1/ [1/E 1 + A1/A2 (1/E 2 – 1)].
c) 4/ [1/E 1 + A1/A2 (1/E 2 – 1)].
d) 3/ [1/E 1 + A1/A2 (1/E 2 – 1)].

Answer: b [Reason:] This is the interchange factor for the radiation from surface 1 to surface 2.

4. A thermos flask has a double walled bottle and the space between the walls is evacuated so as to reduce the heat flow. The bottle surfaces are silver plated and the emissivity of each surface is 0.025. If the contents of the bottle are at 375 K, find the rate of heat loss from the thermos bottle to the ambient air at 300 K
a) 5.38 W
b) 6.38 W
c) 7.38 W
d) 8.38 W

Answer: d [Reason:] Q 12 = F 12 A 1 σ b (T 14 – T 24). F 12 = 1/ (1/E 1 + 1/E2 – 1) = 0.01266.

5. A 250 mm by 250 mm ingot casting, 1.5 m high and at 1225 K temperature, is stripped from its mold. The casting is made to stand on end on the floor of a large foundry whose wall, floor and roof can be assumed to be at 300 K temperature. Make calculation for the rate of radiant heat interchange between the casting and the room. The casting material has an emissivity of 0.85
a) 161120 W
b) 171120 W
c) 181120 W
d) 191120 W

Answer: b [Reason:] Q 12 = F 12 A 1 σ b (T 14 – T 24). F 12 = 0.85 and A 1 = (0.25)2 + 4(1.5) (0.25) = 1.5625 m2.

6. Interchange factor for infinitely long concentric cylinders is given by
a) 1/ [A1/A2 (1/E 2 – 1)].
b) [1/E 1 + A1/A2 (1/E 2 – 1)].
c) 2/ [1/E 1 + A1/A2 (1/E 2 – 1)].
d) 1/ [1/E 1 + A1/A2 (1/E 2 – 1)].

Answer: d [Reason:] This is the interchange factor for the radiation from surface 1 to surface 2.

7. What is the geometric factor for infinitely long concentric cylinders?
a) 1
b) 0.5
c) 0.33
d) 0.75

Answer: a [Reason:] The inner cylinder is completely enclosed by the outer cylinder and as such the entire heat radiations emitted by the emitted by the inner cylinder are intercepted by the outer cylinder.

8. What is the geometric factor for concentric spheres?
a) 0.85
b) 0.33
c) 1
d) 0.95

Answer: c [Reason:] The inner sphere is completely enclosed by the outer sphere and as such the entire heat radiations emitted by the emitted by the inner sphere are intercepted by the outer cylinder.

9. The net heat interchange between non-black bodies at temperature T 1 and T 2 is given by
a) f 12 F 12 σ (T 14 – T 24)
b) f 12 F 12 A 1 σ (T 14 – T 24)
c) f 12 A 1 σ (T 14 – T 24)
d) F 12 A 1 σ (T 14 – T 24)

Answer: b [Reason:] The factor f 12 is called the interchanging factor from surface 1 to surface 2.

10. A thermos flask has a double walled bottle and the space between the walls is evacuated so as to reduce the heat flow. The bottle surfaces are silver plated and the emissivity of each surface is 0.025. If the contents of the bottle are at 375 K and temperature of ambient air is 300 K. What thickness of cork (k = 0.03 W/m degree) would be required if the same insulating effect is to be achieved by the use of cork?
a) 26.8 cm
b) 25.8 cm
c) 24.8 cm
d) 23.8 cm

Answer: a [Reason:] Q = k A (t 1 – t 2)/δ. So, δ = 0.268 m = 26.8 cm.

## Set 4

1. Energy strikes a vertical hemispherical plate with an intensity of 640 W/m2. The absorptivity is thrice the transmissivity and twice the reflectivity. Determine the rate of transmission
a) 236.74 W/m2
b) 116.37 W/m2
c) 187.87 W/m2
d) 456.09 W/m2

Answer: b [Reason:] Rate os transmission = (0.5455) (640)/3 = 116.37 W/m2.

2. The absorptivity of a surface depends upon
(ii) Temperature of the surface
(iii) Composition
Identify the correct statements
a) 1, 2 and 3
b) 1 and 3
c) 2 only
d) 2 and 3

Answer: d [Reason:] It depend upon the direction of incident radiation. Absorptivity is the fraction of total energy absorbed by the body.

3. What is the absorptivity of gray body?
a) Below unity
b) Unity
c) 2
d) 2.5

Answer: a [Reason:] Gray body absorbs a certain fixed percentage of impinging radiations.

4. A body that reflects all the incident thermal radiations is called a
a) Opaque body
b) Gases
c) Black body
d) Specular body

Answer: d [Reason:] In this case reflection is regular. For such bodies reflectivity is unity and transmissivity is equal to zero.

5. Energy strikes a vertical hemispherical plate with an intensity of 640 W/m2. The absorptivity is thrice the transmissivity and twice the reflectivity. Determine the rate of absorption
a) 449.12 W/m2
b) 349.12 W/m2
c) 249.12 W/m2
d) 149.12 W/m2

Answer: b [Reason:] Rate of absorption = (0.5455) (640) = 349.12 W/m2.

6. Let 220 W/m2 of radiant energy is absorbed by a convex surface, 90 W/m2 is reflected and 40 W/m2 is transmitted through it. What is the value of absorptivity?
a) 0.72
b) 0.62
c) 0.52
d) 0.42

Answer: b [Reason:] It is the ratio of incident energy flow to that of absorbed radiations. Absorptivity = 220/(220 + 90 + 40) = 0.62.

7. For a grey surface
a) Reflectivity equals emissivity
b) Emissivity equals transmissivity
c) Absorptivity equals reflectivity
d) Emissivity is constant

Answer: d [Reason:] Emissivity is constant only for grey surfaces because grey surface radiates much more than any of the other surface.

8. Which quantity can be neglected for gases?
a) Transmissivity
b) Reflectivity
c) Absorptivity
d) None can be neglected

Answer: b [Reason:] Gases are known to reflect very little of the radiation incident on their surface.

9. Absorptivity of a body is equal to its emissivity
a) Under thermal equilibrium conditions
b) For a polished surface
c) At one particular temperature
d) At shorter wavelengths

Answer: a [Reason:] In most case absorptivity of a body is equal to its emissivity under thermal equilibrium conditions.

10. Electromagnetic waves strikes a hot body maintained at 900 degree Celsius which has a reflectivity of 0.66 and a transmissivity of 0.022. Let the absorbed flux be 60 W/m2. Determine the rate of incident flux
a) 168.67 W/m2
b) 178.67 W/m2
c) 188.67 W/m2
d) 198.67 W/m2

Answer: c [Reason:] Absorptivity + Reflectivity + Transmissivity = 1. So, incident flux = 60/0.318 = 188.67 W/m2.

## Set 5

1. A gold ring (k = 65 W/m K) measuring 15 * 10 * 60 cm is exposed to a surface where h = 11.5 W/m2 K. Find the value of biot number
a) 0.68
b) 0.58
c) 0.48
d) 0.38

Answer: c [Reason:] Biot number = h l/k = 0.48.

2. In the lumped system parameter model, the variation of temperature with time is
a) Linear
b) Exponential
c) Sinusoidal
d) Cube

Answer: b [Reason:] t – t a/t I – t a = exponential [-h A T/p V c].

3. Which of the following dimensionless number gives an indication of the ratio of internal (conduction) resistance to the surface (convective) resistance?
a) Biot number
b) Fourier number
c) Stanton number
d) Nusselt number

Answer: a [Reason:] It is the ratio of conduction resistance to that of convective resistance.

4. Lumped parameter analysis for transient heat conduction is essentially valid for
a) B I < 0.1
b) 1 < B I < 10
c) 0.1 < B I < 0.5
d) It tends to infinity
Where, B I is the non-dimensional Biot number

Answer: a [Reason:] It is generally accepted that lump system analysis is applicable if Biot number is less than 0.1.

5. In the non-dimensional Biot number, the characteristics length is the ratio of
a) Perimeter to surface area of solid
b) Surface area to perimeter of solid
c) Surface area to volume of solid
d) Volume of solid to its surface area

Answer: d [Reason:] We introduced characteristics length for lump system analysis.

6. During heat treatment, cylindrical pieces of 25 mm diameter, 30 mm height and at 30 degree Celsius are placed in a furnace at 750 degree Celsius with convective coefficient 80 W/m2 degree. Calculate the time required to heat the pieces to 600 degree Celsius. Assume the following property values
Density = 7850 kg /m3
Specific heat = 480 J/kg K
Conductivity = 40 W/m degree
a) 226 sec
b) 326 sec
c) 426 sec
d) 526 sec

Answer: b [Reason:] t – t a/t I – t a = exponential (- h A T/p V c).

7. The quantity h L C/k is known as
a) Biot number
b) Fourier number
c) Stanton number
d) Nusselt number

Answer: a [Reason:] Biot number = conduction resistance/convection resistance.

8. For a plat plate (thickness δ, breadth b and height h) the heat exchange occurs from both the sides. The characteristics length is equal to
a) δ/4
b) δ/3
c) δ/2
d) δ

Answer: c [Reason:] l = δ b h/2 b h = δ/2.

9. Fourier number is given by
a) α T/LC2
b) 2 α T/LC2
c) 3 α T/LC2
d) 4 α T/LC2
Where,
α is thermal diffusivity, T is time constant and L C is characteristics length