Question  set 167

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.