One-Dimensional Steady-State Conduction Quizzes: Test Your Heat Transfer Knowledge

Question 1

A plane wall of thickness L and thermal conductivity k has a temperature difference of ΔT across it. What is the heat transfer rate per unit area through the wall?

Accepted Answer

kΔT/L

Answer

kL/ΔT

Answer

ΔT/(kL)

Answer

LΔT/k

Question 2

What is the thermal resistance of a cylindrical shell of inner radius r1, outer radius r2, length L, and thermal conductivity k?

Accepted Answer

ln(r2/r1) / (2πkL)

Answer

(2πkL) / ln(r2/r1)

Answer

ln(r1/r2) / (2πkL)

Answer

(r2 - r1) / (kL)

Question 3

Which of the following statements is NOT true regarding steady-state conduction?

Accepted Answer

The temperature distribution within the object changes with time.

Answer

The heat transfer rate remains constant over time.

Answer

The temperature gradient within the object is constant.

Question 4

The critical radius of insulation for a cylinder is defined as the ratio of:

Accepted Answer

Thermal conductivity of insulation to convective heat transfer coefficient

Answer

Convective heat transfer coefficient to thermal conductivity of insulation

Answer

Radius of the cylinder to thermal conductivity of insulation

Question 5

For a given temperature difference across a plane wall, what happens to the heat transfer rate if the thermal conductivity of the wall material is doubled and the wall thickness is halved?

Accepted Answer

Increases by four times

Answer

Decreases by two times

Answer

Remains the same

Answer

Increases by two times

Question 6

Which of the following assumptions is NOT made during the derivation of the one-dimensional heat conduction equation for a plane wall?

Accepted Answer

Heat transfer occurs in all three dimensions.

Answer

The material is homogeneous and isotropic.

Answer

Heat transfer is steady-state.

Answer

There is no internal heat generation.

Question 7

A fin is attached to a surface to enhance heat transfer. The effectiveness of the fin is primarily determined by:

Accepted Answer

The ratio of fin surface area to fin base area

Answer

The temperature difference between the fin and the surroundings only

Answer

The convective heat transfer coefficient only

Answer

The thermal conductivity of the fin material only

Question 8

What is the purpose of using thermal contact resistance in heat transfer calculations?

Accepted Answer

To account for the imperfect contact between two surfaces in contact

Answer

To account for the thermal expansion of materials

Answer

To account for the radiative heat transfer between surfaces

Question 9

A long cylindrical rod of diameter D = 0.1 m has a thermal conductivity of k = 50 W/m·K. If the surface temperature is T1 = 200 °C and the center temperature is T2 = 100 °C, what is the heat transfer rate per unit length?

Accepted Answer

251.33 W/m

Answer

125.67 W/m

Answer

377.00 W/m

Answer

502.65 W/m

Question 10

A spherical shell of inner radius 0.1 m and outer radius 0.2 m has a thermal conductivity of 10 W/m·K. If the inner surface temperature is 50 °C and the outer surface temperature is 20 °C, what is the heat transfer rate through the shell?

Accepted Answer

113.09 W

Answer

169.63 W

Answer

226.18 W

Answer

56.55 W

Question 11

A plane wall of thickness 0.1 m is subjected to a constant heat flux of 500 W/m². If the thermal conductivity of the wall is 2 W/m·K, what is the temperature difference across the wall?

Accepted Answer

25 °C

Answer

37.5 °C

Answer

50 °C

Answer

12.5 °C

Question 12

A cylinder of radius 0.05 m is exposed to a convective environment with h = 50 W/m²·K and T∞ = 25 °C. The cylinder has a surface emissivity of ε = 0.8 and is located in a large room with walls at Tsurr = 15 °C. If the cylinder is heated by an internal heat generation rate of q''' = 1000 W/m³, what is the surface temperature of the cylinder?

Accepted Answer

42.88 °C

Answer

64.24 °C

Answer

35.76 °C

Answer

50 °C

Question 13

A plane wall of thickness 0.2 m experiences a temperature gradient of dT/dx = -10 °C/m. If the thermal conductivity of the wall is 2.5 W/m·K, what is the heat flux through the wall?

Accepted Answer

25 W/m²

Answer

37.5 W/m²

Answer

12.5 W/m²

Answer

50 W/m²

Question 14

A plane wall with a thermal conductivity of 20 W/m·K has a temperature difference of 50°C across its thickness of 0.1 m. Determine the heat flux through the wall.

Accepted Answer

10,000 W/m²

Answer

500 W/m²

Answer

2,500 W/m²

Question 15

A cylindrical pipe with an inner radius of 0.05 m and an outer radius of 0.1 m has a thermal conductivity of 50 W/m·K. If the inner surface temperature is 100°C and the outer surface temperature is 20°C, calculate the rate of heat transfer per unit length of the pipe.

Accepted Answer

2,356 W/m

Answer

942 W/m

Answer

4,712 W/m

Answer

1,178 W/m

Question 16

A spherical shell with an inner radius of 0.1 m and an outer radius of 0.2 m has a thermal conductivity of 30 W/m·K. The inner surface is maintained at 150°C, and the outer surface is exposed to an environment with a convection heat transfer coefficient of 25 W/m²·K and a temperature of 25°C. Calculate the temperature of the outer surface.

Accepted Answer

116.2°C

Answer

140°C

Answer

100°C

Answer

135°C

Question 17

A composite wall consists of two layers: a 0.1 m thick layer of brick (k = 0.7 W/m·K) and a 0.05 m thick layer of insulation (k = 0.05 W/m·K). Determine the overall heat transfer coefficient (U-value) for this wall.

Accepted Answer

1.25 W/m²·K

Answer

0.375 W/m²·K

Answer

2.5 W/m²·K

Answer

0.625 W/m²·K

Question 18

The thermal resistance of a material is defined as:

Accepted Answer

The ratio of the temperature difference across the material to the heat flux through it.

Answer

The reciprocal of the thermal conductivity.

Answer

The product of the thermal conductivity and the thickness of the material.

Question 19

A fin is primarily used to:

Accepted Answer

Enhance heat transfer by increasing the surface area.

Answer

Reduce the heat transfer rate.

Answer

Insulate the surface.

Question 20

The critical radius of insulation for a cylindrical pipe is defined as the radius at which:

Accepted Answer

The heat transfer rate is maximized.

Answer

The heat transfer rate is minimized.

Answer

The thermal resistance is minimized.

Question 21

Which of the following conditions is NOT a valid assumption for steady-state heat conduction?

Accepted Answer

Temperature varies with time.

Answer

Thermal conductivity is constant.

Answer

Heat transfer is one-dimensional.

Question 22

The Biot number (Bi) is a dimensionless group that represents the ratio of:

Accepted Answer

Internal thermal resistance to external thermal resistance.

Answer

Thermal conductivity to density.

Answer

Heat transfer rate to surface area.

Question 23

A large, flat plate is exposed to a constant heat flux on one side. The temperature distribution within the plate under steady-state conditions is best described by:

Accepted Answer

A linear profile.

Answer

An exponential profile.

Answer

A parabolic profile.

Answer

A sinusoidal profile.

Question 24

A plane wall with a thickness of 0.2 meters experiences a constant heat flux of 1000 W/m² on one side. The other side is exposed to ambient air at 20 °C. If the wall's thermal conductivity is 1.2 W/m·K, what is the temperature at the midpoint of the wall?

Accepted Answer

50 °C

Answer

70 °C

Answer

60 °C

Answer

40 °C

Question 25

A cylinder with a radius of 0.05 meters and a length of 0.3 meters has a constant heat generation rate of 500 W/m³. The cylinder is made of a material with a thermal conductivity of 50 W/m·K. What is the temperature at the center of the cylinder?

Accepted Answer

122.5 °C

Answer

150 °C

Answer

100 °C

Answer

200 °C

Question 26

A sphere with a radius of 0.1 meters experiences a constant surface heat flux of 2000 W/m² on its outer surface and is exposed to ambient air at 25 °C on its inner surface. The sphere's thermal conductivity is 20 W/m·K. What is the temperature at the center of the sphere?

Accepted Answer

120 °C

Answer

140 °C

Answer

100 °C

Answer

160 °C

Question 27

A composite wall consists of three layers: Layer 1 (k = 10 W/m·K, L1 = 0.1 m), Layer 2 (k = 20 W/m·K, L2 = 0.2 m), and Layer 3 (k = 30 W/m·K, L3 = 0.3 m). The temperature at the left surface is 50 °C, and the temperature at the right surface is 20 °C. What is the heat transfer rate through the composite wall?

Accepted Answer

250 W

Answer

200 W

Answer

300 W

Answer

350 W

Question 28

A cylindrical rod with a radius of 0.02 meters and a length of 0.5 meters is subjected to a uniform heat flux of 500 W/m² on its lateral surface. The ends of the rod are exposed to ambient air at 20 °C. The rod's thermal conductivity is 50 W/m·K. What is the heat transfer rate from the rod to the ambient air?

Accepted Answer

125.66 W

Answer

100 W

Answer

150 W

Answer

200 W

Question 29

A spherical shell with an inner radius of 0.1 meters and an outer radius of 0.2 meters has a constant heat generation rate of 1000 W/m³ within the shell. The shell's thermal conductivity is 25 W/m·K. What is the temperature at the outer surface of the shell?

Accepted Answer

150 °C

Answer

120 °C

Answer

180 °C

Answer

210 °C

Question 30

A plane wall of thickness L = 0.3 m is subjected to a constant heat flux of q = 800 W/m² on one surface and is perfectly insulated on the other surface. The thermal conductivity of the wall material is k = 0.8 W/m·K. Determine the temperature gradient within the wall.

Accepted Answer

2666.67 K/m

Answer

3000 K/m

Answer

4000 K/m

Answer

2000 K/m

Question 31

A cylindrical rod of radius r = 0.05 m and length L = 0.6 m is subjected to a constant heat generation rate of q_gen = 600 W/m³ within the rod. If the thermal conductivity of the rod material is k = 40 W/m·K, determine the heat transfer rate from the rod to the surrounding environment.

Accepted Answer

376.99 W

Answer

450 W

Answer

300 W

Question 32

A spherical shell of inner radius r1 = 0.15 m and outer radius r2 = 0.2 m is subjected to a constant heat flux of q = 1200 W/m² on its outer surface and is insulated on its inner surface. The thermal conductivity of the shell material is k = 30 W/m·K. Determine the temperature difference between the outer and inner surfaces of the shell.

Accepted Answer

36 °C

Answer

30 °C

Answer

48 °C

Answer

42 °C

Question 33

A composite wall consists of three layers: a 10-cm-thick layer of brick with a thermal conductivity of 0.7 W/m·K, a 5-cm-thick layer of insulation with a thermal conductivity of 0.04 W/m·K, and a 2-cm-thick layer of plaster with a thermal conductivity of 0.6 W/m·K. The temperature at the inner surface of the brick layer is 25°C, and the temperature at the outer surface of the plaster layer is 5°C. Calculate the heat transfer rate through the composite wall per unit area.

Accepted Answer

150 W/m²

Answer

200 W/m²

Answer

100 W/m²

Answer

250 W/m²

Question 34

A long cylindrical rod has a diameter of 2 cm and a thermal conductivity of 20 W/m·K. The rod is exposed to a fluid at 100°C with a convective heat transfer coefficient of 50 W/m²·K. If the surface temperature of the rod is measured to be 80°C, determine the heat transfer rate per unit length.

Accepted Answer

31.4 W/m

Answer

25.1 W/m

Answer

40.8 W/m

Answer

15.7 W/m

Question 35

A spherical shell has an inner radius of 10 cm and an outer radius of 15 cm. The thermal conductivity of the shell material is 5 W/m·K. If the inner surface temperature is 120°C and the outer surface temperature is 50°C, determine the heat transfer rate through the shell.

Accepted Answer

113.1 W

Answer

68.8 W

Answer

137.6 W

Answer

88.6 W

Question 36

Which of the following materials has the highest thermal conductivity?

Accepted Answer

Copper

Answer

Rubber

Answer

Glass

Answer

Wood

Question 37

One-dimensional steady-state conduction occurs when:

Accepted Answer

The temperature gradient is constant.

Answer

The heat transfer rate is constant.

Answer

The material is isotropic.

Answer

The heat flux is constant.

Question 38

The thermal resistance of a plane wall is defined as:

Accepted Answer

Thickness divided by thermal conductivity

Answer

Area divided by thermal conductivity

Answer

Thermal conductivity divided by thickness

Answer

Area times thermal conductivity

Question 39

In a one-dimensional steady-state conduction problem involving a composite wall, the heat transfer rate is:

Accepted Answer

The same throughout the wall.

Answer

Proportional to the temperature difference between the layers.

Answer

Inversely proportional to the thermal conductivity of the layers.

Answer

Different in each layer of the wall.

Question 40

The Fourier's law of heat conduction states that:

Accepted Answer

The heat flux is proportional to the temperature gradient.

Answer

The heat transfer rate is proportional to the surface area.

Answer

The thermal conductivity is inversely proportional to the thickness.

Question 41

Which of the following factors does NOT affect the heat transfer rate in steady-state conduction?

Accepted Answer

Time

Answer

Surface area

Answer

Temperature gradient

Answer

Thermal conductivity