Introduction to Conduction

How is Fourier's law of conduction characterized in its origin?

In the general vector statement of Fourier's law, q'' = -k∇T, what is the relationship between the heat flux vector (q'') and an isothermal surface?

For a material to be considered isotropic in the context of heat conduction, what must be true about its thermal conductivity (k)?

What are the two primary mechanisms for the transport of thermal energy in a solid?

In pure metals, which contribution to conduction heat transfer is typically dominant?

What does thermal diffusivity (alpha) represent?

Calculate the thermal diffusivity (alpha) for paraffin at 300 K, given k = 0.24 W/m·K, rho = 900 kg/m^3, and cp = 2890 J/kg·K.

What is the general form of the heat diffusion equation derived from?

In the one-dimensional, steady-state heat equation with no energy generation, d/dx(k dT/dx) = 0, what is the important implication for the heat flux?

What physical situation is represented by a Dirichlet boundary condition?

A wall has a temperature distribution T(x) = 900 - 300x - 50x^2. The wall has a uniform heat generation (q_dot) of 1000 W/m^3, thermal conductivity (k) of 40 W/m·K, and volumetric heat capacity (rho*cp) of 6.4 x 10^6 J/m^3·K. What is the time rate of temperature change (dT/dt) in the wall?

What is a Neumann boundary condition?

An adiabatic surface is a special case of which type of boundary condition?

What is the general trend for the thermal conductivity of a nonmetallic liquid as temperature increases?

Why is the thermal conductivity of a gas generally much smaller than that of a solid?

What is the physical significance of the energy storage term (E_dot_st) in a control volume energy balance?

In the context of micro- and nanoscale heat transfer in a thin film, what happens to the thermal conductivity as the film thickness (L) becomes very small compared to the mean free path (mfp) of the energy carriers?

For which of the following materials from Table 2.1 is the critical film thickness (L_crit,x), below which microscale effects on conduction become significant, the smallest?

The heat equation for cylindrical coordinates contains the term (1/r) * d/dr(r * dT/dr). Why is the additional 'r' term present inside the derivative compared to the plane wall equation?

What is the primary purpose of solving the heat diffusion equation?

For steady-state conditions in a medium with no heat generation, what must be true about the temperature at a particular location?

What does a material with a large thermal diffusivity (alpha) indicate about its thermal response?

In the derivation of the heat diffusion equation, the conduction heat rate at a surface x+dx is expressed using a Taylor series expansion. What is the assumption made in this step?

How does the thermal conductivity of a gas typically change with increasing temperature and increasing molecular weight?

For a long copper bar described in Example 2.3, initially at a uniform temperature To, what is the initial condition for solving the temperature distribution T(x, t)?

What is the volumetric heat capacity (rho * cp) of a material, and what does it measure?

Why is the minus sign necessary in Fourier's law, q'' = -k(dT/dx)?

In the steady-state heat conduction experiment shown in Figure 2.1, if the cross-sectional area A and temperature difference ΔT are held constant, how does the heat transfer rate qx relate to the rod length Δx?

For a plane wall under steady-state, one-dimensional conduction with constant thermal conductivity and no heat generation, what is the shape of the temperature distribution?

Why might a crystalline, nonmetallic solid like diamond have a higher thermal conductivity than a good metallic conductor like aluminum?

What type of boundary condition is represented by the equation -k(dT/dx)|x=L = h[T(L,t) - T_infinity]?

What is the key feature of heat transfer in an 'effective thermal conductivity' for an insulation system?

Calculate the time rate of change of energy storage, E_dot_st, for a wall with an area of 10 m^2 and length of 1 m, given q_in = 120 kW, q_out = 160 kW, and a uniform heat generation q_dot = 1000 W/m^3.

What is the physical difference between the energy generation term (E_dot_g) and the energy storage term (E_dot_st) in the heat equation?

For a transient conduction problem, how many initial conditions are required to solve the heat equation?

For a three-dimensional conduction problem in Cartesian coordinates, how many boundary conditions must be specified?

What conditions are required for the heat diffusion equation to be valid according to the discussion on microscale effects?

Calculate the thermal diffusivity (alpha) for silicon carbide at 1000 K, given k = 87 W/m·K, rho = 3160 kg/m^3, and cp = 1195 J/kg·K.

The heat flux vector can be resolved into Cartesian components q''_x, q''_y, and q''_z. How is the x-component, q''_x, related to the temperature field T(x,y,z)?

How does the pressure generally affect the thermal conductivity of a gas, according to the text?

What is the general simplified form of the heat equation if the thermal conductivity 'k' is constant?

If heat transfer by conduction through a medium occurs under steady-state conditions, will the temperature at a particular location vary with time?

A plane wall experiences one-dimensional conduction. Under what conditions will the temperature distribution be linear?

What is the primary heat conduction mechanism in a nonconducting solid?

In the general heat diffusion equation, what does the term 'q_dot' represent?

If a material has a very small thermal diffusivity (alpha), how will it behave when subjected to a change in thermal conditions?

What kind of temperature distribution is implied in a solid cylinder under steady-state, one-dimensional radial conduction with no heat generation?

A boundary condition of the 'third kind' involves which physical process at the surface?

A plane wall of thickness 0.25 m and thermal conductivity 50 W/m·K has surface temperatures of T1 = 50 C and T2 = -20 C. What is the heat flux?

In what physical scenario is the alternative approach of directly integrating Fourier's law (qx * integral(dx/A(x)) = - integral(k(T)dT)) a valid method for analysis?