Transient Conduction: Master Heat Transfer in Solids Over Time

Question 1

When applying the lumped capacitance method, which assumption is valid?

Accepted Answer

Negligible temperature gradient within the object

Answer

Uniform heat transfer coefficient over the object's surface

Answer

Perfect insulation from surroundings

Question 2

The governing equation for transient conduction in a semi-infinite solid is:

Accepted Answer

Heat diffusion equation

Answer

Fourier's law

Answer

Poisson's equation

Answer

Laplace equation

Question 3

The Biot number is a dimensionless parameter that characterizes:

Accepted Answer

The ratio of convective heat transfer coefficient to thermal conductivity

Answer

The ratio of surface area to volume

Answer

The ratio of thermal conductivity to heat capacity

Answer

The ratio of temperature difference to thermal conductivity

Question 4

In lumped capacitance analysis, the temperature variation within the solid is assumed to be:

Accepted Answer

Uniform

Answer

Linear

Answer

Parabolic

Answer

Exponential

Question 5

The thermal diffusivity of a material is a measure of its ability to:

Accepted Answer

Transfer heat

Answer

Conduct heat

Answer

Store heat

Answer

Generate heat

Question 6

A Dirichlet boundary condition specifies:

Accepted Answer

The temperature at a surface

Answer

The heat flux at a surface

Answer

The temperature gradient at a surface

Answer

The heat generation rate at a surface

Question 7

The time constant in transient conduction analysis represents:

Accepted Answer

The time required for the temperature to decay to a specified fraction of its initial value

Answer

The time required for the temperature to reach steady state

Answer

The time required for the heat flux to reach steady state

Answer

The time required for the heat flux to decay to a specified fraction of its initial value

Question 8

Which of the following factors does NOT affect the lumped capacitance of a solid?

Accepted Answer

Surface area of the solid

Answer

Volume of the solid

Answer

Specific heat capacity of the solid

Answer

Thermal conductivity of the solid

Question 9

Which of the following dimensionless parameters governs the transient response of a solid to a sudden change in surface temperature?

Accepted Answer

Fourier number

Answer

Biot number

Answer

Nusselt number

Answer

Rayleigh number

Question 10

In a solid cylinder with a uniform initial temperature, the temperature distribution after a sudden change in surface temperature is:

Accepted Answer

One-dimensional radially

Answer

Two-dimensional radially

Answer

Three-dimensional radially

Answer

Depends on the Biot number

Question 11

Which of the following boundary conditions implies that the surface heat flux is proportional to the surface temperature?

Accepted Answer

Third-type boundary condition

Answer

First-type boundary condition

Answer

Second-type boundary condition

Answer

Fourth-type boundary condition

Question 12

In a lumped capacitance analysis, the governing equation is a:

Accepted Answer

Ordinary differential equation

Answer

Partial differential equation

Answer

Algebraic equation

Answer

Integral equation

Question 13

To solve a transient heat transfer problem with complex geometry using the finite element method, which steps should be followed?

Accepted Answer

Discretize the domain into finite elements, apply boundary conditions, and solve the resulting system of equations.

Answer

Employ a lumped capacitance method to approximate the temperature distribution.

Answer

Utilize the method of separation of variables to solve the governing equation.

Question 14

In using commercial CFD software to solve complex transient heat transfer problems, which factor emerges as a primary challenge?

Accepted Answer

High computational expense and prolonged simulation times

Answer

Difficulties in accurately representing intricate geometries

Answer

Limited user control over solution parameters

Answer

Restricted ability to incorporate user-defined subroutines

Question 15

The governing equation for transient conduction heat transfer in a solid is:

Accepted Answer

Fourier's second law (heat diffusion equation)

Answer

Fourier's first law (heat conduction)

Answer

Newton's law of cooling (convection)

Answer

Stefan-Boltzmann law (blackbody radiation)

Question 16

For a semi-infinite solid with a constant surface heat flux, the temperature at a distance 'x' from the surface at time 't' is given by:

Accepted Answer

(q''L) / (2 * sqrt(pi * k * rho * c * t)) * exp(-x^2 / (4 * alpha * t))

Answer

(q'') * t / (rho * c * L)

Answer

(q'') / (h * (1 - erf(x / sqrt(4 * alpha * t)))

Question 17

Which dimensionless parameter represents the ratio of thermal resistance to thermal capacitance in transient conduction?

Accepted Answer

Biot number (Bi)

Answer

Reynolds number (Re)

Answer

Fourier number (Fo)

Answer

Nusselt number (Nu)

Question 18

Which of the following is NOT a commonly encountered transient conduction boundary condition?

Accepted Answer

Periodic boundary condition

Answer

Robin boundary condition (convection)

Answer

Dirichlet boundary condition (specified temperature)

Answer

Neumann boundary condition (specified heat flux)

Question 19

In a lumped capacitance analysis, the temperature within the solid is assumed to be:

Accepted Answer

Spatially uniform

Answer

Parabolically varying

Answer

Exponentially decaying

Answer

Linearly varying

Question 20

A large, thick steel plate is initially at a uniform temperature of 200°C. It is suddenly exposed to a cool air stream at 25°C. Which of the following statements accurately describes the heat transfer process within the plate?

Accepted Answer

The heat transfer is transient, meaning the temperature at any point in the plate changes with time.

Answer

The heat transfer is steady-state, meaning the temperature remains constant over time.

Answer

The heat transfer is primarily by convection, with minimal conduction within the plate.

Question 21

The Biot number (Bi) is a dimensionless parameter used in transient heat transfer analysis. Which of the following statements accurately describes the significance of the Biot number?

Accepted Answer

The Biot number represents the ratio of internal thermal resistance to external thermal resistance.

Answer

The Biot number represents the ratio of heat transfer rate to temperature difference.

Answer

The Biot number represents the ratio of conductive heat transfer to convective heat transfer.

Question 22

A large, flat wall is subjected to a sudden change in surface temperature. The temperature distribution within the wall can be described using the following equation: T(x,t) = T∞ + (T0 - T∞)exp(-αt/L^2)sin(πx/L). What is the physical meaning of the term 'α' in this equation?

Accepted Answer

Thermal diffusivity of the wall material.

Answer

Specific heat capacity of the wall material.

Answer

Heat transfer coefficient at the wall surface.

Answer

Thermal conductivity of the wall material.

Question 23

A spherical object is exposed to a hot environment. The object's temperature increases with time. The temperature profile within the sphere can be represented using the following equation: T(r,t) = T∞ + (T0 - T∞)exp(-αt/R^2)sin(πr/R). Which of the following is the most accurate interpretation of the term 'R' in this equation?

Accepted Answer

The radius of the sphere.

Answer

The surface area of the sphere.

Answer

The volume of the sphere.

Question 24

A thick concrete wall is initially at a uniform temperature. It is suddenly exposed to a hot fire. Which of the following approaches is most suitable for determining the time it takes for the wall's temperature to reach a critical value?

Accepted Answer

Using a numerical method like the finite element method.

Answer

Solving an analytical equation with Bessel functions.

Answer

Applying the lumped capacitance method.