Question  set 142

Fourier Equation

1.     The famous Fourier series is named after
a) Diller and Ryan
b) J.B. Joseph Fourier
c) Stefan- Boltzmann
d) Wein’s
Answer: b
Explanation: He gave this theory in 1824.

2.     Fourier law of heat conduction is best represented by
a) Q = -k A d t /d x
b) Q = k A d x/d t
c) Q = -k A
d) Q = k d t/d x
Answer: a
Explanation: According to Fourier law of heat conduction, Q = -k A d t /d x.

3.     Here are some assumptions that are made for Fourier law. Identify the wrong one
a) No internal heat generation
b) Steady state heat conduction
c) Non- linear temperature profile
d) Isotropic and homogenous material
Answer: c
Explanation: It has constant temperature gradient and a linear temperature profile.

4.     Consider the following statements:
The Fourier heat conduction equation
Q = -k A d t /d x
Presumes
i) Steady state conditions
ii) Constant value of thermal conductivity
iii) Uniform temperature at the wall surface
iv) One dimensional heat flow
Which of these statements are correct?
a) i, ii and iii
b) i, ii and iv
c) i, iii and iv
d) i, iii and iv
Answer: d
Explanation: Thermal conductivity is different for different materials.

5.     The diagram shows heat conduction through a plane wall. The surface temperature is 475 K and it radiates heat to the surroundings at 335 K. If thermal conductivity of the material is 12.5 W/m degree, find the temperature gradient. Let convective coefficient be 80 W/m² degree and radiation factor is 0.9

a) – 1052.4 degree celsius
b) – 2052.4 degree celsius
c) – 3052.4 degree celsius
d) – 4052.4 degree celsius
Answer: a
Explanation: Heat conducted through the plate = convection heat losses + radiation heat losses. So, d t /d x = – 13155/12.5 = – 1052.4 degree Celsius.

6.     Negative sign in Fourier heat conduction equation indicates
a) Heat always flow is in the direction of positive temperature gradient
b) Heat always flow in the direction of negative temperature gradient
c) No heat flow is there
d) Data is insufficient
Answer: b
Explanation: The ratio d t/d x represents the change in temperature per unit thickness i.e. the temperature gradient. So it represents heat flow in the direction of negative temperature gradient.

7.     Transmission of heat i.e. molecular is smallest in case of
a) Gases
b) Liquids
c) Alloys
d) Solids
Answer: a
Explanation: In gases, atoms are arranged loosely, there is less molecular transmission of heat as compared to solids, liquids and alloys.

8.     Which one is not the unit of thermal conductivity?
a) kcal/m hr K
b) KJ/m hr K
c) W/m s K
d) Cal/cm s K
Answer: c
Explanation: The unit kcal/m hr K could also be specified as J/m s K or W/m s K and this is actually done while quoting the numerical values of thermal conductivity.

9.     “Thermal conductivity represents the amount of heat conducted across the unit area when a temperature difference of one kelvin”.
a) True
b) False
Answer: b
Explanation: It is across unit area and through unit distance.

10.Which of the following is the unit of thermal resistance?
a) degree/kcal
b) hour degree
c) s degree/kcal
d) degree/W
Answer: d
Explanation: Thermal resistance is expressed in the unit’s hr degree/kcal, degree/W and s degree/J.