Fourier's Law of Conduction Quiz: Test Your Heat Transfer Knowledge

Question 1

What is the best definition of thermal conductivity?

Accepted Answer

The rate of heat transfer per unit area per unit temperature difference

Answer

The heat transfer coefficient per unit length

Answer

The heat capacity per unit volume

Answer

The ratio of heat transfer rate to temperature difference

Question 2

Fourier's Law of Conduction is applicable to which types of heat conduction?

Accepted Answer

Both steady-state and transient heat conduction

Answer

Only steady-state heat conduction

Answer

Only transient heat conduction

Answer

Neither steady-state nor transient heat conduction

Question 3

How is the heat transfer rate through a composite wall determined?

Accepted Answer

By summing the heat transfer rates through each individual layer

Answer

By using the highest heat transfer rate among all layers

Answer

By averaging the heat transfer rates through each layer

Answer

By considering only the layer with the lowest thermal conductivity

Question 4

What is the primary effect of using extended surfaces in heat transfer applications?

Accepted Answer

Increased heat transfer rate

Answer

No change in heat transfer rate

Answer

Reversal of heat transfer direction

Answer

Decreased heat transfer rate

Question 5

What does the Biot number represent in heat transfer?

Accepted Answer

A dimensionless ratio comparing internal resistance to external resistance for heat transfer

Answer

A measure of the temperature difference between two points

Answer

A measure of the thermal conductivity of a material

Answer

A measure of the heat transfer rate through a surface

Question 6

In Fourier's Law of Conduction, the heat flux vector (q) is directly proportional to what factor?

Accepted Answer

Temperature gradient

Answer

Material thickness

Answer

Area of heat transfer

Answer

Thermal conductivity

Question 7

Which of the following is NOT typically considered a boundary condition in heat conduction problems?

Accepted Answer

Specified heat generation rate within the material

Answer

Specified temperature at a surface

Answer

Specified convective heat transfer coefficient at a surface

Answer

Specified heat flux at a surface

Question 8

In a one-dimensional, steady-state heat conduction problem, what is the typical temperature distribution within the material?

Accepted Answer

Linear

Answer

Exponential

Answer

Parabolic

Answer

Logarithmic

Question 9

What does the thermal conductivity of a material primarily indicate?

Accepted Answer

Its ability to conduct heat

Answer

Its thermal expansion coefficient

Answer

Its specific heat capacity

Answer

Its emissivity

Question 10

In a transient heat conduction problem, how does the temperature within the material change over time?

Accepted Answer

It changes over time

Answer

It remains constant

Answer

It exhibits a sinusoidal pattern

Question 11

The Biot number is a dimensionless parameter used to determine whether a transient heat conduction problem can be simplified by assuming a uniform temperature within the object (lumped capacitance method). Which statement is true about the Biot number's application?

Accepted Answer

A small Biot number indicates that the internal resistance to heat transfer is negligible compared to the external resistance, allowing for the lumped capacitance method.

Answer

The Biot number is only relevant for specific geometric shapes.

Answer

The Biot number is only used for steady-state heat conduction problems.

Answer

A large Biot number indicates that the internal resistance to heat transfer is negligible compared to the external resistance, allowing for the lumped capacitance method.

Question 12

Consider a composite wall made of multiple layers of different materials. How is the overall heat transfer rate through the wall determined?

Accepted Answer

The overall heat transfer rate is the same through each layer, as heat flow must be continuous through the composite wall.

Answer

The overall heat transfer rate is less than the heat transfer rate through the layer with the lowest thermal conductivity.

Answer

The overall heat transfer rate is greater than the heat transfer rate through the layer with the highest thermal conductivity.

Answer

The overall heat transfer rate is the sum of the heat transfer rates through each individual layer.

Question 13

A cylindrical rod with uniform heat generation experiences a temperature distribution along its length.  What shape best describes this temperature distribution?

Accepted Answer

Parabolic

Answer

Logarithmic

Answer

Linear

Answer

Exponential

Question 14

Which of these factors does NOT directly affect the rate of heat conduction through a material?

Accepted Answer

Material's color

Answer

Temperature difference across the material

Answer

Material's thermal conductivity

Answer

Material's thickness

Question 15

A cylindrical copper rod (thermal conductivity, k = 400 W/mK) has a diameter of 5 cm and a length of 1 meter. One end is maintained at 100°C, and the other end at 20°C. What is the approximate rate of heat transfer through the rod?

Accepted Answer

1570.8 W

Answer

3141.6 W

Answer

785.4 W

Answer

628.3 W

Question 16

A composite wall is made of two layers: brick (thermal conductivity, k = 0.7 W/mK, thickness = 0.1 m) and concrete (thermal conductivity, k = 1.4 W/mK, thickness = 0.15 m).  What is the approximate equivalent thermal conductivity of this composite wall?

Accepted Answer

0.93 W/mK

Answer

1.21 W/mK

Answer

0.84 W/mK

Answer

1.05 W/mK

Question 17

A sphere with a diameter of 10 cm is heated to 150°C and is surrounded by air at 25°C. What additional information is needed to determine the heat transfer rate from the sphere due to convection?

Accepted Answer

The convection heat transfer coefficient (h) between the sphere's surface and the air.

Answer

The emissivity of the sphere's surface.

Answer

The thermal conductivity of the sphere material.

Answer

The specific heat capacity of the sphere material.

Question 18

Which of the following materials typically exhibits the highest thermal conductivity?

Accepted Answer

Copper

Answer

Air

Answer

Wood

Answer

Polystyrene

Question 19

A metal plate is heated on one side, and the temperature distribution across the plate is measured to be linear. What type of heat conduction is this?

Accepted Answer

Steady-state heat conduction

Answer

Convection heat conduction

Answer

Transient heat conduction

Answer

Radiation heat conduction

Question 20

A large concrete slab is initially at a uniform temperature of 20°C. The slab's surface is suddenly exposed to a hot gas at 500°C. What type of heat conduction occurs within the concrete?

Accepted Answer

Transient heat conduction

Answer

Radiation heat conduction

Answer

Steady-state heat conduction

Answer

Convection heat conduction

Question 21

What is the primary mechanism of heat transfer through a vacuum?

Accepted Answer

Radiation

Answer

Convection

Answer

Conduction

Answer

All of the above

Question 22

A fin is attached to a hot surface to enhance heat transfer. Which of the following factors would increase the effectiveness of the fin?

Accepted Answer

Increasing the fin surface area

Answer

Decreasing the fin length

Answer

Decreasing the fin thermal conductivity

Answer

Increasing the fin thickness