Transient, Unsteady State Heat Conduction

This quiz contains multiple-choice problems on thermocouple response, time constant, heat conduction in solids using various mechanisms like infinite thermal conductivity, finite conduction and infinite thick solids, Biot number and periodic variation.

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A thermocouple junction of spherical form is used to measure the temperature of the gas stream. The junction is at 20 °C and is placed in a gas stream at 200 °C. What junction diameter is needed for the thermocouple to have a thermal time constant of one second? Assume the thermophysical quantities as given below
k = 20 W/m K
h = 350 W/m^2 K
c = 0.4 k J/kg K
p = 8000 kg/m^3

0.556 mm

0.656 mm

0.756 mm

0.856 mm

A low value of the 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

Which statements are correct?

ii and iii

i and iii

i and ii

i, ii and iii

Which of the following has units of time constant (where P is density, A is area, c is specific heat, and V is volume)?

p V/h A

p c/h A

p V c/h A

V c/h A

Thermal radiation suffers no attenuation in a vacuum. True or false?

True

False

How does body temperature fall or rise with time?

Logarithmic

Parabolic

Linear

Exponentially

The lumped parameter solution for transient conduction can be conveniently expressed as

(t – t{a})/(t{I} – t{a}) = 2*exponential (- B{I}F{0})

(t – t{a})/(t{I} – t{a}) = exponential (- B{I}F{0})

(t – t{a})/(t{I} – t{a}) = 3*exponential (- B{I}F{0})

(t – t{a})/(t{I} – t{a}) = 6*exponential (- B{I}F{0})

An iron billet (k = 65 W/m K) measuring 20 * 15 * 80 cm is exposed to a convective flow resulting in a convection coefficient of 11.5 W/m^2 K. Determine the Biot number.

0.02376

0.008974

0.004563

0.006846

The sensitivity of a thermocouple is defined as the time required to reach what percentage of its steady-state values?

43.3

53.2

63.3

73.3

The response time for different sizes and materials of thermocouple wires usually lies between

0.04 to 2.5 s

0.06 to 1.2 s

0.02 to 0.04 s

2.4 to 9.4 s

A thermocouple junction of spherical form is used to measure the temperature of the gas stream. The junction is at 20 °C and placed in a gas stream at 200 °C. What is the time required by the thermocouple to reach 197 °C? Assume the thermophysical properties as given below
k = 20 W/m K
h = 350 W/m^2 K
c = 0.4 kJ/kg K
p = 8000 kg/m^3

1.094 s

2.094 s

3.094 s

4.094 s

An egg with a mean diameter of 4 cm, whose initial temperature is 25 °C, is placed in boiling water for 4 minutes and boils itself at a particular level. How long should a separate but similar egg boil at the same level when the refrigerator temperature is 5 °C? Use lumped parameter theory and assume the following properties of the egg:
k = 12 W/m K
h = 125 W/m^2 K
c = 2 kJ/kg K
p = 1250 kg/m^3

251.49 s

261.49 s

271.49 s

281.49 s

A person is found dead at 5 p.m in a room whose temperature is 20 °C. The body temperature is measured as 25 °C when found. The heat transfer coefficient is 8 W/m^2 K. Modeling the body to have a 30 cm diameter and 1.7 cm long cylinder, estimate the person’s time of death.

13.55 s

12.55 s

11.55 s

10.55 s

The following data pertains to a thermocouple wire’s junction used to measure the temperature of the gas stream:

Density = 8500 kg/m^3

Specific heat = 325 J/kg K

Thermal conductivity = 40 W/m K

Heat transfer coefficient between the junction and gas = 215 W/m^2 K

If the thermocouple junction is approximated as a 1 mm diameter sphere, determine how long it will take for the thermocouple to read 99% of the initial temperature difference.

9.86 s

8.86 s

7.86 s

6.86 s

A thermocouple’s response is defined as the time required to reach the surrounding temperature when exposed to it. True or false?

True

False

The time constant of a thermocouple is

The minimum time taken to record a temperature reading

The time taken to attain 50% of initial temperature difference

The time taken to attain the final value to be measured

The time taken to attain 63.2% of the initial temperature difference’s value