# Heat Transfer Questions and Answers – Time Constant

This set of Heat Transfer Multiple Choice Questions & Answers (MCQs) focuses on “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

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

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

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

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

Explanation: It is gradual loss of intensity of any kind of flux.
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6. How does the body temperature falls or rises with time?
a) Logarithmic
b) Parabolic
c) Linear
d) Exponentially

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)

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

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

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

Explanation: T = p V c/h A = p r c/3 h.

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