Transient Heat Conduction: Master Heat Transfer Over Time

Question 1

Which equation represents Fourier's law for transient heat conduction in one dimension?

Accepted Answer

q = -kA(dT/dx)

Answer

Δx = (kΔt)/(ρc)

Answer

h = Nu * k/L

Answer

Q = mcΔT

Question 2

What is the physical significance of the Biot number?

Accepted Answer

Ratio of the internal thermal resistance to the external thermal resistance

Answer

Ratio of conductivity to thermal diffusivity

Answer

Ratio of surface area to volume

Answer

Ratio of specific heat to density

Question 3

Consider a semi-infinite body with an initial temperature of 20°C exposed to a fluid at 100°C. The Biot number is 0.2. What is the dimensionless temperature at a distance of 2 cm from the surface after 10 minutes, assuming the lumped capacitance method is applicable?

Accepted Answer

0.124

Answer

0.424

Answer

0.324

Answer

0.224

Question 4

Which of the following boundary conditions is represented by the equation T(0, t) = 100°C?

Accepted Answer

Constant surface temperature

Answer

Constant surface heat flux

Answer

Convection boundary condition

Question 5

What is the Fourier number?

Accepted Answer

Ratio of the characteristic time for heat conduction to a characteristic time of interest

Answer

Ratio of thermal diffusivity to specific heat

Answer

Ratio of Biot number to Nusselt number

Answer

Ratio of surface area to volume

Question 6

Which dimensionless number is used to determine if the lumped capacitance method is applicable for analyzing transient heat conduction?

Accepted Answer

Biot Number

Answer

Reynolds Number

Answer

Prandtl Number

Answer

Fourier Number

Question 7

A steel sphere (k = 40 W/mK, α = 10^-5 m^2/s) with a diameter of 5 cm is initially at a uniform temperature of 200°C. It is suddenly exposed to a convective environment at 30°C with h = 50 W/m^2K. What is the Biot number for this scenario?

Accepted Answer

0.125

Answer

0.5

Answer

8

Answer

2

Question 8

What is the significance of the Fourier number (Fo) in transient conduction?

Accepted Answer

It provides a measure of the relative importance of heat conduction and thermal storage within the body.

Answer

It quantifies the ratio of convective to conductive heat transfer.

Answer

It determines the temperature gradient at the center of the body.

Question 9

Which of the following statements about the lumped capacitance method is true?

Accepted Answer

It simplifies the analysis of transient heat conduction problems by assuming a uniform temperature distribution within the body at any given time.

Answer

It is applicable for bodies with high thermal conductivity.

Answer

It accounts for temperature variations within the body.

Question 10

A long cylindrical rod is initially at a uniform temperature and is suddenly exposed to a convective environment. Which coordinate system is most appropriate for analyzing the transient temperature distribution within the rod?

Accepted Answer

Cylindrical coordinates

Answer

The choice of coordinate system does not affect the analysis.

Answer

Cartesian coordinates

Answer

Spherical coordinates

Question 11

In transient heat conduction, what characterizes a 'semi-infinite body'?

Accepted Answer

A body with one dimension significantly larger than the others, where the temperature far from the surface remains constant for a period of time.

Answer

A body where the temperature gradient is uniform throughout.

Answer

A body with an extremely high thermal conductivity.

Answer

A body where the heat transfer is solely through conduction.

Question 12

When using Heisler charts for transient heat conduction in a plane wall, which parameter is determined from the chart to calculate the temperature at a specific location and time?

Accepted Answer

Dimensionless temperature ratio (θ/θi)

Answer

Biot number (Bi)

Answer

Dimensionless heat transfer coefficient (hL/k)

Answer

Fourier number (Fo)

Question 13

Why is the study of transient heat conduction crucial in engineering applications?

Accepted Answer

It helps predict temperature changes and thermal stresses in components undergoing varying thermal conditions.

Answer

It is primarily used for analyzing heat transfer in steady-state systems.

Answer

It is only relevant for systems operating at extremely high temperatures.

Answer

It is only relevant for materials with low thermal conductivity.

Question 14

A small, spherical copper ball heated to 100°C is plunged into a 20°C water bath. Which factor has the **greatest** influence on its cooling time to 50°C?

Accepted Answer

The diameter of the copper ball

Answer

The thermal conductivity of copper

Answer

The specific heat capacity of copper

Answer

The initial temperature of the water bath

Question 15

The Biot number (Bi) is a dimensionless parameter representing the ratio of:

Accepted Answer

Internal thermal resistance to external thermal resistance

Answer

Convective heat transfer coefficient to thermal conductivity

Answer

Heat transfer rate to thermal conductivity

Answer

Thermal diffusivity to the characteristic length

Question 16

A steel plate is exposed to constant heat flux on one side. During transient heat conduction, where is the temperature gradient the **steepest**?

Accepted Answer

Near the surface exposed to the heat flux.

Answer

Near the opposite surface of the plate.

Answer

At the center of the plate.

Answer

Uniformly throughout the plate.

Question 17

A cylindrical rod, initially at 25°C, has one end exposed to hot gas at 100°C. Which action would **reduce** the time it takes to reach a steady-state temperature?

Accepted Answer

Increasing the thermal conductivity of the rod material

Answer

Increasing the diameter of the rod

Answer

Decreasing the heat transfer coefficient between the gas and the rod

Answer

Decreasing the initial temperature of the rod

Question 18

The Fourier number (Fo) is a dimensionless parameter representing the ratio of:

Accepted Answer

Thermal diffusivity to the square of characteristic length

Answer

Temperature difference to thermal diffusivity

Answer

Convective heat transfer coefficient to thermal conductivity

Answer

Heat transfer rate to thermal diffusivity

Question 19

A large concrete block is initially at a uniform temperature. If its surface is suddenly exposed to a cold environment, how will the temperature inside the block change?

Accepted Answer

Decrease gradually, with the center cooling at a slower rate than the surface

Answer

Decrease uniformly throughout the block

Answer

Remain constant throughout the block.

Answer

Increase gradually, with the center warming at a faster rate than the surface

Question 20

Which scenario would **most likely** necessitate the use of the lumped capacitance method for analysis?

Accepted Answer

A small, thin copper wire suddenly exposed to hot air

Answer

A large, steel plate with internal heat generation

Answer

A long, cylindrical rod with varying heat flux along its length

Answer

A thick, concrete wall exposed to a constant heat flux

Question 21

The concept of a 'semi-infinite body' in transient heat conduction refers to a body that is:

Accepted Answer

So large that the temperature at its far end is essentially unaffected by the heat transfer at the surface

Answer

Infinite in size

Question 22

A large, thick slab of aluminum is initially at a uniform temperature of 20°C. One side of the slab is suddenly exposed to a constant heat flux of 1000 W/m². What is the **most appropriate** method to analyze the temperature distribution within the slab as a function of time?

Accepted Answer

Using a numerical method like the finite difference method

Answer

Applying the lumped capacitance method

Answer

Using the analytical solution for a semi-infinite body

Question 23

A small, copper sphere is initially at a uniform temperature of 25°C. It is then placed in a furnace at a constant temperature of 500°C. The temperature of the sphere will:

Accepted Answer

Increase exponentially towards the furnace temperature, asymptotically approaching it

Answer

Increase linearly with time until it reaches the furnace temperature

Answer

Remain constant at 25°C

Question 24

Which of the following methods is used to analyze transient heat transfer in bodies with negligible internal resistance?

Accepted Answer

Lumped capacitance method

Answer

Finite difference method

Answer

Finite element method

Answer

Boundary element method

Question 25

The Biot number is defined as:

Accepted Answer

Ratio of internal resistance to external resistance

Answer

Ratio of heat capacity to thermal conductivity

Answer

Ratio of external resistance to internal resistance

Question 26

A body with a Biot number much less than 0.1 can be considered:

Accepted Answer

Lumped capacitance system

Answer

Semi-infinite system

Answer

Infinite system

Answer

Finite system

Question 27

The Fourier number is defined as:

Accepted Answer

Ratio of conduction time to thermal diffusion time

Answer

Ratio of heat capacity to thermal conductivity

Answer

Ratio of thermal diffusion time to conduction time

Answer

Ratio of surface area to volume

Question 28

For a semi-infinite body, the temperature distribution at a given time is:

Accepted Answer

Gaussian function

Answer

Parabolic function

Answer

Linear function

Answer

Exponential function

Question 29

The heat transfer coefficient in transient heat conduction is typically:

Accepted Answer

Time-dependent

Answer

Constant

Answer

Piecewise constant

Answer

Temperature-dependent

Question 30

The transient temperature response of a body is characterized by:

Accepted Answer

Time-varying temperature distribution

Answer

Constant temperature distribution

Answer

Uniform temperature distribution

Answer

Steady-state temperature distribution

Question 31

Which of the following dimensionless numbers is used to characterize the relative importance of heat conduction and convection in transient heat transfer?

Accepted Answer

Biot number

Answer

Grashof number

Answer

Nusselt number

Answer

Rayleigh number

Question 32

The temperature of a body subjected to sudden immersion in a hot fluid:

Accepted Answer

Increases rapidly at first, then gradually approaches the fluid temperature

Answer

Drops rapidly at first, then gradually approaches the fluid temperature

Answer

Increases steadily until it reaches the fluid temperature