All 14 Chapters Covered
SOLUTION MANUAL
,Table of Contents
1. Introduction
2. Introduction to Conduction
3. One-Dimensional, Steady-State Conduction
4. Two-Dimensional, Steady-State Conduction
5. Transient Conduction
6. Introduction to Convection
7. External Flow
8. Internal Flow
9. Free Convection
10. Boiling and Condensation
11. Heat Exchangers
12. Radiation: Processes and Properties
13. Radiation Exchange Between Surfaces
14. Diffusion Mass Transfer
Appendices
, PROBLEM 1.1
KNOWN: Thermal conductivity, thickness and temperature difference across a sheet of rigid
extruded insulation.
FIND: (a) The heat flux through a 2 m × 2 m sheet of the insulation, and (b) The heat rate
through the sheet.
SCHEMATIC:
A = 4 m2
W
k = 0.029
m ⋅K qcond
T1 – T2 = 10˚C
T1 T2
L = 20 mm
x
ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (2) Steady-state
conditions, (3) Constant properties.
ANALYSIS: From Equation 1.2 the heat flux is
dT T -T
q′′x = -k =k 1 2
dx L
Solving,
W 10 K
q"x = 0.029 ×
m⋅K 0.02 m
W
q′′x = 14.5 <
m2
The heat rate is
W
q x = q′′x ⋅ A = 14.5 2
× 4 m 2 = 58 W <
m
COMMENTS: (1) Be sure to keep in mind the important distinction between the heat flux
(W/m2) and the heat rate (W). (2) The direction of heat flow is from hot to cold. (3) Note that
a temperature difference may be expressed in kelvins or degrees Celsius.
, PROBLEM 1.2
KNOWN: Thickness and thermal conductivity of a wall. Heat flux applied to one face and
temperatures of both surfaces.
FIND: Whether steady-state conditions exist.
SCHEMATIC:
L = 10 mm
T2 = 30°C
q” = 20 W/m2
q″cond
T1 = 50°C k = 12 W/m·K
ASSUMPTIONS: (1) One-dimensional conduction, (2) Constant properties, (3) No internal energy
generation.
ANALYSIS: Under steady-state conditions an energy balance on the control volume shown is
′′ = qout
qin ′′ = qcond
′′ = k (T1 − T2 ) / L = 12 W/m ⋅ K(50°C − 30°C) / 0.01 m = 24,000 W/m 2
Since the heat flux in at the left face is only 20 W/m2, the conditions are not steady state. <
COMMENTS: If the same heat flux is maintained until steady-state conditions are reached, the
steady-state temperature difference across the wall will be
ΔT = q′′L / k = 20 W/m 2 × 0.01 m /12 W/m ⋅ K = 0.0167 K
which is much smaller than the specified temperature difference of 20°C.
SOLUTION MANUAL
,Table of Contents
1. Introduction
2. Introduction to Conduction
3. One-Dimensional, Steady-State Conduction
4. Two-Dimensional, Steady-State Conduction
5. Transient Conduction
6. Introduction to Convection
7. External Flow
8. Internal Flow
9. Free Convection
10. Boiling and Condensation
11. Heat Exchangers
12. Radiation: Processes and Properties
13. Radiation Exchange Between Surfaces
14. Diffusion Mass Transfer
Appendices
, PROBLEM 1.1
KNOWN: Thermal conductivity, thickness and temperature difference across a sheet of rigid
extruded insulation.
FIND: (a) The heat flux through a 2 m × 2 m sheet of the insulation, and (b) The heat rate
through the sheet.
SCHEMATIC:
A = 4 m2
W
k = 0.029
m ⋅K qcond
T1 – T2 = 10˚C
T1 T2
L = 20 mm
x
ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (2) Steady-state
conditions, (3) Constant properties.
ANALYSIS: From Equation 1.2 the heat flux is
dT T -T
q′′x = -k =k 1 2
dx L
Solving,
W 10 K
q"x = 0.029 ×
m⋅K 0.02 m
W
q′′x = 14.5 <
m2
The heat rate is
W
q x = q′′x ⋅ A = 14.5 2
× 4 m 2 = 58 W <
m
COMMENTS: (1) Be sure to keep in mind the important distinction between the heat flux
(W/m2) and the heat rate (W). (2) The direction of heat flow is from hot to cold. (3) Note that
a temperature difference may be expressed in kelvins or degrees Celsius.
, PROBLEM 1.2
KNOWN: Thickness and thermal conductivity of a wall. Heat flux applied to one face and
temperatures of both surfaces.
FIND: Whether steady-state conditions exist.
SCHEMATIC:
L = 10 mm
T2 = 30°C
q” = 20 W/m2
q″cond
T1 = 50°C k = 12 W/m·K
ASSUMPTIONS: (1) One-dimensional conduction, (2) Constant properties, (3) No internal energy
generation.
ANALYSIS: Under steady-state conditions an energy balance on the control volume shown is
′′ = qout
qin ′′ = qcond
′′ = k (T1 − T2 ) / L = 12 W/m ⋅ K(50°C − 30°C) / 0.01 m = 24,000 W/m 2
Since the heat flux in at the left face is only 20 W/m2, the conditions are not steady state. <
COMMENTS: If the same heat flux is maintained until steady-state conditions are reached, the
steady-state temperature difference across the wall will be
ΔT = q′′L / k = 20 W/m 2 × 0.01 m /12 W/m ⋅ K = 0.0167 K
which is much smaller than the specified temperature difference of 20°C.
