Master Steady-State Conduction: Heat Transfer Fundamentals for Engineers

Question 1

In a composite wall, the heat flux is:

Accepted Answer

Continuous at the interface

Answer

Discontinuous at the interface

Answer

Zero at the interface

Answer

Equal to the thermal conductivity of the interface material

Question 2

What is the definition of the critical radius of insulation for a cylinder?

Accepted Answer

The radius where heat loss from the bare cylinder equals heat loss from the insulated cylinder

Answer

The radius where the thermal resistance of the insulation equals the thermal resistance of the bare cylinder

Answer

The radius where the outer surface temperature of the insulation equals the ambient temperature

Answer

The radius where the heat flux at the outer surface of the insulation is zero

Question 3

The governing equation for steady-state conduction in rectangular coordinates is:

Accepted Answer

Laplace's equation

Answer

Poisson's equation

Answer

Diffusion equation

Answer

Helmholtz equation

Question 4

For a composite wall with two layers, each having thermal conductivities k1 and k2, and thicknesses L1 and L2, respectively, what is the overall thermal conductivity of the wall?

Accepted Answer

k = (k1L1 + k2L2) / (L1 + L2)

Answer

k = (L1k1 + L2k2) / (L1 + L2)

Answer

k = (k1 + k2) / (L1 + L2)

Answer

k = (k1L1 - k2L2) / (L1 - L2)

Question 5

Which of the following boundary conditions represents a surface subjected to convection?

Accepted Answer

q = h(T - T∞)

Answer

T = T∞

Answer

dT/dx = 0

Answer

k(dT/dx) = q

Question 6

Among the following materials, which has the lowest thermal conductivity?

Accepted Answer

Wood

Answer

Copper

Answer

Aluminum

Answer

Steel

Question 7

For a composite wall with three layers, each having thermal conductivities k1, k2, and k3, and thicknesses L1, L2, and L3, respectively, what is the overall thermal resistance of the wall?

Accepted Answer

R = (L1 / k1) + (L2 / k2) + (L3 / k3)

Answer

R = (k1 / L1) + (k2 / L2) + (k3 / L3)

Answer

R = (L1 / k1) - (L2 / k2) - (L3 / k3)

Answer

R = (k1 / L1) - (k2 / L2) - (k3 / L3)

Question 8

Which concept is NOT fundamental to steady-state conduction?

Accepted Answer

Transient heat transfer

Answer

Energy conservation

Answer

Fourier's law

Answer

Thermal conductivity

Question 9

Which material has the highest thermal conductivity?

Accepted Answer

Copper

Answer

Glass

Answer

Wood

Answer

Aluminum

Question 10

In steady-state conduction through a plane wall of thickness L and thermal conductivity k, the temperature gradient is:

Accepted Answer

- q''/(kL)

Answer

- h(Twall - Tfluid)/kL

Answer

- q''/(hL)

Question 11

For a composite wall consisting of two layers with different thicknesses and thermal conductivities, the overall heat transfer coefficient U is given by:

Accepted Answer

1/(h1*L1/k1 + L2/k2 + 1/h2)

Answer

h1 + h2 + k1/L1 + k2/L2

Answer

1/(h1 + h2 + k1/L1 + k2/L2)

Answer

h1*L1/k1 + L2/k2 + 1/h2

Question 12

A long cylindrical rod of diameter D is initially at a uniform temperature T_i. It is suddenly exposed to a convection environment at T_∞ with a heat transfer coefficient of h. Which of the following equations represents the temperature distribution in the rod at a later time t?

Accepted Answer

T(r, t) = T_i + (T_∞ - T_i) * [1 - (r/D)^2 * Sum(n=1 to ∞)(2/n^2 * exp(-n^2 * pi^2 * alpha * t / D^2))]

Answer

T(r, t) = T_i + (T_∞ - T_i) * [1 - (r/D)^2 * Sum(n=1 to ∞)(2/n * exp(-n^2 * pi^2 * alpha * t / D^2))]

Question 13

A composite wall consists of two layers, each of thickness L and thermal conductivity k. The inner surface is maintained at T_1 while the outer surface is exposed to a convection environment at T_∞ with a heat transfer coefficient of h. Which of the following equations gives the heat transfer rate through the wall?

Accepted Answer

Q = (T_1 - T_∞) * k * A / (L/k + L/k + 1/h)

Answer

Q = (T_1 - T_∞) * k * A / (2*L/k + 1/h)

Answer

Q = (T_1 - T_∞) * k * A / (L/k + 2*L/k + 1/h)

Answer

Q = (T_1 - T_∞) * k * A / (L/k + L/k - 1/h)

Question 14

A plane wall of thickness L has a constant heat generation rate of q". Which of the following expressions gives the temperature distribution in the wall?

Accepted Answer

T(x) = (q * L^2) / (2 * k) + (T_s - q * L^2 / (2 * k)) * x / L

Answer

T(x) = (q * L^2) / (k) + (T_s - q * L^2 / (k)) * x / L

Answer

T(x) = (q * L^2) / (2 * k) - (T_s + q * L^2 / (2 * k)) * x / L

Question 15

A composite sphere consists of two concentric spheres with radii r_i and r_o. The inner sphere is maintained at T_i while the outer sphere is exposed to a convection environment at T_∞ with a heat transfer coefficient of h. Which of the following expressions gives the thermal resistance of the composite sphere?

Accepted Answer

R_th = (r_o - r_i) / (4 * pi * k) + 1 / (h * 4 * pi * r_o)

Answer

R_th = (r_o - r_i) / (4 * pi * k) - 1 / (h * 4 * pi * r_o)

Answer

R_th = (r_o + r_i) / (4 * pi * k) + 1 / (h * 4 * pi * r_o)

Question 16

Which of the following is the governing equation for steady-state conduction?

Accepted Answer

Fourier's Law

Answer

Ohm's Law

Answer

Newton's Law of Cooling

Answer

Kirchhoff's Law

Question 17

A plane wall of thickness L and thermal conductivity k has a constant heat flux applied to one surface. Which of the following expressions represents the temperature gradient through the wall?

Accepted Answer

q''/k

Answer

-q/kL

Answer

k/q'L

Answer

q'L/k

Question 18

A composite wall consists of three layers of different materials with thicknesses L1, L2, and L3 and thermal conductivities k1, k2, and k3, respectively. What is the thermal resistance of the composite wall?

Accepted Answer

(L1/k1) + (L2/k2) + (L3/k3)

Answer

(L1 + L2 + L3)/(k1 + k2 + k3)

Answer

(k1 + k2 + k3)/(L1 + L2 + L3)

Answer

k1L1 + k2L2 + k3L3

Question 19

Which of the following shapes has the highest critical radius for insulation?

Accepted Answer

Sphere

Answer

Cone

Answer

Plane Wall

Answer

Cylinder

Question 20

A hollow cylinder has inner and outer radii r1 and r2, respectively, and a thermal conductivity k. If the inner surface is maintained at a constant temperature T1 and the outer surface is maintained at a constant temperature T2, what is the rate of heat transfer through the cylinder?

Accepted Answer

(2πkL(T1 - T2))/(ln(r2/r1))

Answer

(2πkL(T1 - T2))/(r2 - r1)

Answer

(πkL(T1 - T2))/(2ln(r2/r1))

Question 21

A spherical shell has an inner radius r1 and an outer radius r2. The thermal conductivity of the material is k. If the inner surface is maintained at a constant temperature T1 and the outer surface is maintained at a constant temperature T2, what is the thermal resistance of the shell?

Accepted Answer

ln(r2/r1)/(4πk)

Answer

(4πk)/ln(r2/r1)

Answer

ln(r2/r1)/(2πk)

Question 22

Which of the following boundary conditions represents a constant heat flux applied to a surface?

Accepted Answer

q'' = constant

Answer

dT/dx = 0

Answer

T = constant

Answer

h(T - T∞) = constant

Question 23

A plane wall is subjected to convection on both sides. The convection heat transfer coefficients are h1 and h2 on the left and right surfaces, respectively. What is the overall heat transfer coefficient for the wall?

Accepted Answer

1/(1/h1 + L/k + 1/h2)

Answer

h1h2/(h1 + h2)

Answer

h1 + h2

Answer

h1 - h2

Question 24

Which of the following materials has the highest thermal diffusivity?

Accepted Answer

Copper

Answer

Glass

Answer

Plastic

Answer

Wood

Question 25

A long rod of length L and thermal conductivity k is subjected to a constant heat flux q'' at one end, while the other end is insulated. What is the temperature at a distance x from the heated end?

Accepted Answer

q''x^2/(2k)

Answer

q''L/(k)

Answer

q''x/(kL)

Answer

q''L^2/(2kx)