Mechanical Engineering MCQs – Transient (Unsteady State Heat Conduction) ( Heat Transfer ) MCQs
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Mechanical Engineering MCQs – Transient (Unsteady State Heat Conduction) ( Heat Transfer ) MCQs
The most occurred mcqs of ( ) in past papers. Past papers of Transient (Unsteady State Heat Conduction) ( Heat Transfer ) Mcqs. Past papers of Transient (Unsteady State Heat Conduction) ( Heat Transfer ) Mcqs . Mcqs are the necessary part of any competitive / job related exams. The Mcqs having specific numbers in any written test. It is therefore everyone have to learn / remember the related Transient (Unsteady State Heat Conduction) ( Heat Transfer ) Mcqs. The Important series of Transient (Unsteady State Heat Conduction) ( Heat Transfer ) Mcqs are given below:
Time Constant
1. The time constant of a thermocouple is the time taken to
a) Minimum time taken to record a temperature reading
b) Attain 50% of initial temperature difference
c) Attain the final value to be measured
d) Attain 63.2% of the value of the initial temperature difference
Answer: d
Explanation: The time constant of a thermocouple represents the time required to attain 63.2% value.
2. A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degree Celsius and is placed in a gas stream which is at 200 degree Celsius. Make calculations for junction diameter needed for the thermocouple to have thermal time constant of one second. Assume the thermos-physical properties as given below
k = 20 W/ m K
h = 350 W/m2 K
c = 0.4 k J/kg K
p = 8000 kg/m3
a) 0.556 mm
b) 0.656 mm
c) 0.756 mm
d) 0.856 mm
Answer: b
Explanation: T = p V c/h A = p r c/3h. So, r = 3 h T/p c = 0.000328 m = 0.328 m.
3. A low value of time constant can be achieved for a thermocouple by
(i) Increasing the wire diameter
(ii) Increasing the value heat transfer coefficient
(iii) Use light metals of low density and low specific heat
a) ii and iii
b) i and iii
c) i and ii
d) i, ii and iii
Answer: a
Explanation: Diameter of wire should be less.
4. Which of the following has units of time constant? (Where, P is density, A is area, c is specific heat and V is volume)
a) p V/h A
b) p c/h A
c) p V c/h A
d) V c/h A
Answer: c
Explanation: It has the unit of time and is time constant of the system.
5. “Thermal radiation suffers no attenuation in a vacuum”.
a) True
b) False
Answer: a
Explanation: It is gradual loss of intensity of any kind of flux.
6. How does the body temperature falls or rises with time?
a) Logarithmic
b) Parabolic
c) Linear
d) Exponentially
Answer: d
Explanation: The rate depends on the parameter h A/p V c.
7. The lumped parameter solution for transient conduction can be conveniently stated as
a) t – t a/t I – t a = 2 exponential (- B I F 0)
b) t – t a/t I – t a = exponential (- B I F 0)
c) t – t a/t I – t a = 3 exponential (- B I F 0)
d) t – t a/t I – t a = 6 exponential (- B I F 0)
Answer: b
Explanation: This is the general solution for lumped system parameter.
8. An iron billet (k = 65 W/m K) measuring 20 * 15 * 80 cm is exposed to a convective flow resulting in convection coefficient of 11.5 W/m2 K. Determine the Biot number
a) 0.02376
b) 0.008974
c) 0.004563
d) 0.006846
Answer: d
Explanation: B = h L C/k = 0.006846.
9. A mercury thermometer with bulb idealized as a sphere of 1 mm radius is used for measuring the temperature of fluid whose temperature is varying at a fast rate. For mercury
k = 10 W/m K
α = 0.00005 m2/s
h = 10 W/m2 K
If the time for the temperature change of the fluid is 3 second, what should be the radius of thermocouple to read the temperature of the fluid?
For the thermocouple material
k = 100 W/m K
α = 0.0012 m2/s
h = 18 W/m2 K
a) .864 mm
b) .764 mm
c) .664 mm
d) .564 mm
Answer: a
Explanation: T = k l/h α. So, radius is 0.864 mm.
10. A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degree Celsius and is placed in a gas stream which is at 200 degree Celsius. Make calculations for junction diameter needed for the thermocouple to have thermal time constant of one second. Assume the thermos-physical properties as given below
k = 20 W/ m K
h = 350 W/m2 K
c = 0.4 k J/kg K
p = 8000 kg/m3
a) 0.456 mm
b) 0.556 mm
c) 0.656 mm
d) 0.756 mm
Answer: c
Explanation: T = p V c/h A = p r c/3 h.
Response of a Thermocouple
1. “The response of a thermocouple is defined as the time required for the thermocouple to reach the surrounding temperature when it is exposed to it”.
a) True
b) False
Answer: b
Explanation: It is the source temperature.
2. The sensitivity of thermocouple is defined as the time required by thermocouple to reach how much percentage of its steady state values?
a) 43.3
b) 53.2
c) 63.3
d) 73.3
Answer: c
Explanation: The time constant of a thermocouple represents the time required to attain 63.2% value.
3. The response time for different sizes and materials of thermocouple wires usually lie between
a) 0.04 to 2.5 seconds
b) 0.06 to 1.2 seconds
c) 0.02 to 0.04 seconds
d) 2.4 to 9.4 seconds
Answer: a
Explanation: Depending upon the type of fluid used, the response time for different sizes and materials of thermocouple wires usually lie between o.o4 to 2.5 seconds.
4. A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degree Celsius and is placed in a gas stream which is at 200 degree Celsius. Make calculations for time required by the thermocouple to reach 197 degree Celsius temperature. Assume the thermos-physical properties as given below
k = 20 W/ m K
h = 350 W/m2 K
c = 0.4 k J/kg K
p = 8000 kg/m3
a) 1.094 seconds
b) 2.094 seconds
c) 3.094 seconds
d) 4.094 seconds
Answer: d
Explanation: t – t a/t I – t a = exponential (- p V c T/h A).
5. An egg with mean diameter of 4 cm and initially at 25 degree Celsius is placed in an open boiling water container for 4 minutes and found to be boiled at a particular level. For how long should a similar egg boil at the same level, when refrigerator temperature is 5 degree Celsius? Use lumped parameter theory and assume following properties of egg
k = 12 W/m K
h = 125 W/m2 K
c = 2 k J/kg K
p = 1250 kg/m3
a) 251.49 seconds
b) 261.49 seconds
c) 271.49 seconds
d) 281.49 seconds
Answer: c
Explanation: T t – T INFINITY/T i – T INFINITY = e – b T.
6. A person is found dead at 5 pm in a room whose temperature is 20 degree Celsius. The temperature of body is measured to be 25 degree Celsius, when found and heat transfer coefficient is estimated to be 8 W/m2 K. Modeling the body as a 30 cm diameter, 1.7 cm long cylinder. Estimate the time of death of person.
a) 13.55 seconds
b) 12.55 seconds
c) 11.55 seconds
d) 10.55 seconds
Answer: d
Explanation: T t – T INFINITY/T i – T INFINITY = e – b T.
7. The following data pertains to the junction of a thermocouple wire used to measure the temperature of the gas stream.
Density = 8500 kg/m3, specific heat = 325 J/kg K, thermal conductivity = 40 W/m K and the heat transfer coefficient between the junction and gas = 215 W/m2 K.
If thermocouple junction can be approximated as 1 mm diameter sphere, determine how long it will take for the thermocouple to read 99% of the initial temperature difference
a) 9.86 seconds
b) 8.86 seconds
c) 7.86 seconds
d) 6.86 seconds
Answer: a
Explanation: t – t a/t i – t a = exponential (- h A T/p V c).
Heat Transfer From Extended Surfaces MCQs
8. A thermocouple junction in the form of 4 mm radius sphere is to be used to measure the temperature of a gas stream. The junction is initially at 35 degree Celsius and is placed in a gas stream which is at 300 degree Celsius. The thermocouple is removed from the hot gas stream after 10 seconds and kept in still air at 25 degree Celsius with convective coefficient 10 W/m2 K. Find out the time constant of the thermocouple. Assume the thermos-physical properties as given below
h = 37.5 W/m2 K
p = 7500 kg/m3
c = 400 J/kg K
a) 6.67 seconds
b) 106.67 seconds
c) 206.67 seconds
d) 306.67 seconds
Answer: b
Explanation: T = p V c/h A = p r c/3 h = 106.67 seconds.
9. What percentage of water an average human body can have?
a) 52%
b) 62%
c) 72%
d) 82%
Answer: c
Explanation: Average human body is 72% water by mass.
10. Heisler charts are valid if
a) Fourier number is equal to 0.2
b) Fourier number is less than 0.2
c) Fourier number is greater than 0.2
d) Fourier number is equal to 0.4
Answer: c
Explanation: The solution to the transient heat flow in infinite flat plates are available in the form of these charts.
Transient Heat Conduction Solids with Infinite Thermal Conductivity
1. A flat wall of fire clay, 50 cm thick and initially at 25 degree Celsius, has one of its faces suddenly exposed to a hot gas at 950 degree Celsius. If the heat transfer coefficient on the hot side is 7.5 W/m2 K and the other face of the wall is insulated so that no heat passes out of that face, determine the time necessary to raise the center of the wall to 350 degree Celsius. For fire clay brick
Thermal conductivity = 1.12 W/m K
Thermal diffusivity = 5.16 * 10 -7 m2/s
a) 43.07 hours
b) 53.07 hours
c) 63.07 hours
d) 73.07 hours
Answer: a
Explanation: t – t a/t 0 – t a = 0.86. Also, α T/l 2 = 0.32.
2. Glass spheres of 2 mm radius and at 500 degree Celsius are to be cooled by exposing them to an air stream at 25 degree Celsius. Find maximum value of convective coefficient that is permissible. Assume the following property values
Density = 2250 kg/m3
Specific heat = 850 J/kg K
Conductivity = 1.5 W/m K
a) 245 W/m2K
b) 235 W/m2K
c) 225 W/m2K
d) 215 W/m2K
Answer: c
Explanation: l = volume/surface area = r/3. So, h = (0.1) (k) (3)/r.
3. The transient response of a solid can be determined by the equation. (Where, P is density, V is volume, c is specific heat and A is area)
a) – 4 p V c = h A (t – t0)
b) – 3 p V c = h A (t – t0)
c) – 2 p V c = h A (t – t0)
d) – p V c = h A (t – t0)
Answer: d
Explanation: It can be determined by relating rate of change of internal energy with conductive heat exchange at the surface.
4. A 2 cm thick steel slab heated to 525 degree Celsius is held in air stream having a mean temperature of 25 degree Celsius. Estimate the time interval when the slab temperature would not depart from the mean value of 25 degree Celsius by more than 0.5 degree Celsius at any point in the slab. The steel plate has the following thermal physical properties
Density = 7950 kg/m3
C P = 455 J/kg K
K = 46 W/m K
a) 6548 s
b) 6941 s
c) 4876 s
d) 8760 s
Answer: b
Explanation: t – t a/t I – t a = exponential (- h A T/p V c). Now A/V = 100 per meter.
5. An average convective heat transfer coefficient for flow of air over a sphere has been measured by observing the temperature-time history of a 12 mm diameter copper sphere (density = 9000 kg/m3 and c = 0.4 k J/kg K) exposed to air at 30 degree Celsius. The temperature of the sphere was measured by two thermocouples one located at the center and the other near the surface. The initial temperature of the ball was 75 degree Celsius and it decreased by 10 degree Celsius in 1.2 minutes. Find the heat transfer coefficient
a) 27.46 W/m2 K
b) 21.76 W/m2 K
c) 29.37 W/m2 K
d) 25.13 W/m2 K
Answer: d
Explanation: t – t a/t I – t a = exponential (- h A T/p V c). So, h = 25.13 W/m2 K.
6. Transient condition means
a) Conduction when temperature at a point varies with time
b) Very little heat transfer
c) Heat transfer with a very little temperature difference
d) Heat transfer for a short time
Answer: a
Explanation: The term transient or unsteady state designates a phenomenon which is time dependent.
7. Which of the following is not correct in a transient flow process?
a) The state of matter inside the control volume varies with time
b) There can be work and heat interactions across the control volume
c) There is no accumulation of energy inside the control volume
d) The rate of inflow and outflow of mass are different
Answer: c
Explanation: In transient heat conduction there is accumulation of energy inside the control volume.
8. A cylindrical stainless steel (k = 25 W/m K) ingot, 10 cm in diameter and 25 cm long, passes through a heat treatment furnace which is 5 meter in length. The initial ingot temperature is 90 degree Celsius, the furnace gas is at 1260 degree Celsius and the combined radiant and convective surface coefficient is 100 W/m2 K. Determine the maximum speed with which the ingot moves through the furnace if it must attain 830 degree Celsius temperature. Take thermal diffusivity as 0.45 * 10 -5 m2/s
a) . 000116 m/s
b) .000216 m/s
c) . 000316 m/s
d) . 000416 m/s
Answer: b
Explanation: t – t a/t I – t a = exponential (- h A T/p V c). Now, A/V = 2(r + L)/r L = 0.48 per cm. Also, T = 1158.53 second so required velocity is 0.25/1158.53.
9. The curve for unsteady state cooling or heating of bodies is
a) Hyperbolic curve asymptotic both to time and temperature axis
b) Exponential curve asymptotic both to time and temperature axis
c) Parabolic curve asymptotic to time axis
d) Exponential curve asymptotic to time axis
Answer: d
Explanation: α/α 0 = exponential [- h A T/p c V], which represents an exponential curve.
10. What is the wavelength band for TV rays?
a) 1 * 10 3 to 34 * 10 10 micron meter
b) 1 * 10 3 to 2 * 10 10 micron meter
c) 1 * 10 3 to 3 * 10 10 micron meter
d) 1 * 10 3 to 56 * 10 10 micron meter
Answer: b
Explanation: This is the maximum and minimum wavelength for TV rays.
Transient Heat Conduction in Solids with Finite Conduction
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
Explanation: 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
a) i and ii
b) ii and iii
c) i and iii
d) i, ii and iii
Answer: d
Explanation: 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.
a) True
b) False
Answer: b
Explanation: It must be semi thickness instead of thickness.
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
Explanation: 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
Explanation: 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.
a) True
b) False
Answer: a
Explanation: 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
Explanation: These two are dimensionless numbers. Biot number is given by the 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
Explanation: 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
Explanation: 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.
a) True
b) False
Answer: b
Explanation: It is known as infinite solid. This type of solid can extend itself in x-direction, y-direction and z-direction.
Biot Number
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
Explanation: 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
Explanation: 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
Explanation: 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
Answer: a
Explanation: 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
Explanation: 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
Explanation: 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
Explanation: 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
Explanation: 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
Answer: a
Explanation: It signifies the degree of penetration of heating or cooling effect through a solid. Where, α is thermal diffusivity, T is time constant and L C is characteristics length
10. Identify the correct relation between Biot number and Fourier number
a) 4 b T = B I F 0
b) 2 b T = B I F 0
c) 3 b T = B I F 0
d) b T = B I F 0
Answer: d
Explanation: B I = h L C/k and F 0 = α T/LC2.
Lump System Analysis
1. According to lumped system analysis, solid possesses thermal conductivity that is
a) Infinitely large
b) Infinitely small
c) Moderate
d) 50% small
Answer: a
Explanation: Solutions to the many of the transient heat flow problems are obtained by the lumped system parameter analysis.
2. The temperature and rate of heat conduction are undoubtedly dependent on
a) Time coordinates
b) Space coordinates
c) Mass coordinates
d) Both time and space coordinates
Answer: d
Explanation: It should depend on both time coordinates and space coordinates.
3. Glass spheres of 2 mm radius and at 500 degree Celsius are to be cooled by exposing them to an air stream at 25 degree Celsius. Find the minimum time required for cooling to a temperature of 60 degree Celsius. Assume the following property values
Density = 2250 kg/m3
Specific heat = 850 J/kg K
Conductivity = 1.5 W/m K
a) 13.78 seconds
b) 14.78 seconds
c) 15.78 seconds
d) 16.78 seconds
Answer: b
Explanation: t – t a/t I – t a = exponential (- h A T/p V c).
Conduction With Heat Generation MCQs
4. Which is true regarding lumped system analysis?
(i) Conductive resistance = 0
(ii) Convective resistance = 0
(iii) Thermal conductivity = 0
(iv) Thermal conductivity = infinity
Identify the correct statements
a) i and ii
b) i, ii and iv
c) i and iv
d) ii and iv
Answer: c
Explanation: Solids have infinite thermal conductivities. It implies that internal conductance resistance is very low.
5. Which of the following is an example of lump system analysis?
a) Heating or cooling of fine thermocouple wire due to change in ambient temperature
b) Heating of an ingot in an furnace
c) Cooling of bars
d) Cooling of metal billets in steel works
Answer: a
Explanation: Others are the examples of non-periodic variation.
6. What is the criterion for the applicability of lump system analysis?
a) Mean length
b) Normal length
c) Characteristics length
d) Mass no
Answer: c
Explanation: The first set in establishing criteria for the applicability of lump system analysis is to define a characteristics length.
7. What is the value of characteristics length for cylinder?
a) R/5
b) R/4
c) R/3
d) R/2
Answer: d
Explanation: π R2 L/2 π R L = R/2.
8. 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. Find the value of biot number if thermal conductivity is 40 W/m degree
a) 0.0082
b) 0.0072
c) 0.0062
d) 0.0052
Answer: a
Explanation: For a cylindrical piece, the characteristic linear dimension is, l = volume/surface area = .00441 m. So, biot number = hl/k = -.00882.
9. What is the value of characteristics length for sphere?
a) R/2
b) R/3
c) R/4
d) R/5
Answer: b
Explanation: 4/3 π R3/4 π R2 = R/3.
10. What is the value of characteristics length for cube?
a) L/3
b) L/4
c) L/5
d) L/6
Answer: d
Explanation: L3/6 L2 = L/6.
Transient Heat Conduction in Infinite Thick Solids
1. “An infinite solid is one which extends itself infinitely in all directions of space”. Identify the correct option
a) True
b) False
Answer: a
Explanation: If the infinite solid is split in the middle by the plane, each half is known as semi-infinite solid.
2. The boundary conditions in case of transient heat conduction in infinite thick solids are
(i) t (x = 0) = t i
(ii) t (0, T) = t a for T greater than zero
(iii) t (infinity, T) = t i for T greater than zero
Identify the correct statements
a) i and ii
b) i and iii
c) ii and iii
d) i, ii and iii
Answer: d
Explanation: Boundary conditions are those by which we could find out the values of constant.
3. The perturbation time varies as
a) d 2/α
b) 2 d 2/α
c) 3 d 2/α
d) 4 d 2/α
Answer: a
Explanation: At penetration depth d, there will be 1% perturbation.
4. The temperature perturbation at all the surface has penetrated to the depth
a) 1.6 (α T) 1/2
b) 2.6 (α T) 1/2
c) 3.6 (α T) 1/2
d) 4.6 (α T) ½
Answer: c
Explanation: At penetration depth d, there will be 1% perturbation at a time t.
5. A water line is buried underground in dry soil that has an assumed initial temperature of 4.5 degree Celsius. The pipe may have no flow through it for long period of time, yet it will not be drained in order that no freezing occurs, the pipe must be kept at a temperature not lower than 0 degree Celsius. The pipe is to be designed for a 30 hour period at the beginning of which the soil surface temperature suddenly drops to – 17 degree Celsius. Workout the minimum earth covering needed above the water pipe so as to prevent the possibility of freezing during 36 hour cold spell. The soil in which the pipe is buried has the following properties
Density = 640 kg/m3
Specific heat = 1843J/kg degree
Thermal conductivity = 0.345 W/m degree
a) 0.25 m
b) 0.35 m
c) 0.45 m
d) 0.55 m
Answer: b
Explanation: t – t a/t i – t a = erf [x/2 (α T) ½].
6. At the penetration depth d, there will be 1% perturbation at a time given by
a) 4 d 2/13 α
b) 3 d 2/13 α
c) 2 d 2/13 α
d) d 2/13 α
Answer: d
Explanation: d/2 (α t) ½ = 1.8.
7. A large steel ingot, which has been uniformly heated to 750 degree Celsius, is hardened by quenching it in an oil bath that is maintained at 25 degree Celsius. What length of time is required for the temperature to reach 600 degree Celsius at a depth of 1 cm? Thermal diffusivity for the steel ingot is 1.21 * 10 -5 m2/s. The ingot may be approximated as a flat plate
a) 4.55 seconds
b) 3.55 seconds
c) 2.55 seconds
d) 1.55 seconds
Answer: c
Explanation: t – t a/t I – t a = erf [x/2 (α T) ½].
8. A mild steel plate 5 cm thick and initially at 40 degree Celsius temperature is suddenly exposed on one side to a fluid which causes the surface temperature to increase to and remain at 90 degree Celsius. Calculate maximum time that the slab be treated as a semi-infinitely body
For steel, thermal diffusivity = 1.25 * 10 –5 m2/s
a) 100 seconds
b) 200 seconds
c) 300 seconds
d) 400 seconds
Answer: b
Explanation: T MAX = δ 2/4 α (0.5)2 = 200 seconds.
9. Consider the above problem, find the temperature at the center of the slab one minute after the change in surface temperature
a) 66 degree Celsius
b) 76 degree Celsius
c) 86 degree Celsius
d) 96 degree Celsius
Answer: a
Explanation: t – t a/t I – t a = erf [x/2 (α T) ½]. Therefore, temperature at the center of the slab is t a + 0.48 (t I – t a).
10. Water pipes are to be buried underground in a wet soil (thermal diffusivity = 2.78 * 10 -3 m2/s) which is initially at 4.5 degree Celsius. The soil surface temperature suddenly drops to -5 degree Celsius and remains at this value for 10 hours. Calculate the minimum depth at which the pipe be laid if the surrounding soil temperature is to remain above 0 degree Celsius. The soil may be considered as semi-infinite solid
a) 0.467 m
b) 0.367 m
c) 0.267 m
d) 0.167 m
Answer: d
Explanation: t – t a/t I – t a = erf [x/2 (α T) ½]. Thus x = 2 (0.50) (α T) ½ = 0.167 m.
Periodic Variation
1. When the surface temperature variation inside a solid are periodic in nature, the profile of temperature variation with time may assume
a) Triangular
b) Linear
c) Parabolic
d) Hyperbolic
Answer: a
Explanation: Any type of waveform can be analyzed and resolved into an infinite number of sine and cosine waves.
2. The surface temperature oscillates about the mean temperature level in accordance with the relation
a) α S,T – α S,A = 2 sin (2 π n T)
b) α S,T – α S,A = 5 sin (2 π n T)
c) α S,T – α S,A = sin (2 π n T)
d) α S,T – α S,A = 3 sin (2 π n T)
Answer: c
Explanation: α S,T = t S,T – t M.
3. The temperature variation of a thick brick wall during periodic heating or cooling follows a sinusoidal waveform. During a period of 24 hours, the surface temperature ranges from 25 degree Celsius to 75 degree Celsius. Workout the time lag of the temperature wave corresponding to a point located at 25 cm from the wall surface. Thermo-physical properties of the wall material are; thermal conductivity = 0.62 W/m K; specific heat = 450 J/kg K and density = 1620 kg/m3
a) 3.980 hour
b) 6.245 hour
c) 2.648 hour
d) 3.850 hour
Answer: b
Explanation: d T = x/2 (1/α π n) ½ where x = 0.25 m and n = frequency.
4. A single cylinder 2-stroke engine operates at 1500 rpm. Calculate the depth where the temperature wave due to variation in cylinder is damped to 1% of its surface value. For the cylinder material, thermal diffusivity = 0.042 m2/hr
a) 0.1996 cm
b) 0.3887 cm
c) 0.2774 cm
d) 0.1775 cm
Answer: d
Explanation: α X,A = α S,A exponential [-x (π n/α) ½] where frequency = 1500 * 60.
5. The temperature distribution at a certain time instant through a 50 cm thick wall is prescribed by the relation
T = 300 – 500 x – 100 x2 + 140 x3
Where temperature t is in degree Celsius and the distance x in meters has been measured from the hot surface. If thermal conductivity of the wall material is 20 k J/m hr degree, calculate the heat energy stored per unit area of the wall
a) 4100 k J/hr
b) 4200 k J/hr
c) 4300 k J/hr
d) 4400 k J/hr
Answer: a
Explanation: d t/d x = -500 + 200 x + 420 x2. Now heat storage rate = Q IN – Q OUT = 10000 – 5900 = 4100 k J/hr.
6. A large plane wall, 40 cm thick and 8 m2 area, is heated from one side and temperature distribution at a certain time instant is approximately prescribed by the relation
T = 80 – 60 x +12 x2 + 25 x3 – 20 x4
Where temperature t is in degree Celsius and the distance x in meters. Make calculations for heat energy stored in the wall in unit time.
For wall material:
Thermal conductivity = 6 W/m K and thermal diffusivity = 0.02 m2/hr.
a) 870.4 W
b) 345.6 W
c) 791.04 W
d) 238.5 W
Answer: c
Explanation: Q IN = – k A (d t/d x)X = 0 = 2880 W and Q OUT = – k A (d t/d x)X = 0.4 = 2088.96 W.
7. Consider the above problem, calculate rate of temperature change at 20 cm distance from the side being heated
a) 0.777 degree Celsius/hour
b) 0.888 degree Celsius/hour
c) 0.999 degree Celsius/hour
d) 0.666 degree Celsius/hour
Answer: b
Explanation: d t/d T = α d 2t/d x 2 = 0.888 degree Celsius/hour.
8. At a certain time instant, the temperature distribution in a long cylindrical fire tube can be represented approximately by the relation
T = 650 + 800 r – 4250 r2
Where temperature t is in degree Celsius and radius r is in meter. Find the rate of heat flow such that the tube measures: inside radius 25 cm, outside radius 40 cm and length 1.5 m.
For the tube material
K = 5.5 W/m K
α = 0.004 m2/hr
a) 3.672 * 10 8 W
b) 3.672 * 10 2 W
c) 3.672 * 10 5 W
d) – 3.672 * 10 5 W
Answer: d
Explanation: Q = – k A (d t/d r), Rate of heat storage = Q IN – Q OUT = – 3.672 * 10 5 W.
9. Consider he above problem, find the rate of change of temperature at the inside surface of the tube
a) – 35 degree Celsius/hour
b) – 45 degree Celsius/hour
c) – 55 degree Celsius/hour
d) – 65 degree Celsius/hour
Answer: c
Explanation: d t/d T = α [d 2t/d r2 + d t/r d r] = – 55 degree Celsius/hour.
10. Time lag is given by the formula
a) x/2 [1/ (α π n) ½].
b) x/3 [1/ (α π n) ½].
c) x/4 [1/ (α π n) ½].
d) x/5 [1/ (α π n) ½].
Answer: a
Explanation: The time interval between the two instants is called the time lag.