274
Analytical Heat Transfer
plate is well insulated at the bottom. Let h be the average
convective heat transfer coefficient between the surface and
ambient air. Given h = 10 W/m 2 K, ε 1 = 0.54 = α 1 , σ = 5.67 ×
10 −8 W/m 2 K 4 . Determine the equilibrium plate temperature.
13.7. Consider two very large parallel plates with diffuse, gray surfaces. Determine the irradiation and radiosity for the upper plate
(at T 1 = 1000 ◦ K, ε 1 = 1). What is the radiosity for the lower plate
(at T 2 = 500 ◦ K, ε 2 = 0.8)? What is the net radiation exchange
between the plates per unit area of the plates?
13.8. A 0.25-m-diameter sphere (surface 1) is located inside of a 0.5-mdiameter sphere (surface 2). Surface 1 is 200 ◦ C and surface 2 is
100 ◦ C. Determine all of the view factors and calculate the net heat
transfer rate (W) between the two spherical surfaces. Show all
work and list all assumptions. (Note: = 5.67 × 10 −8 W m 2 K 4
σ
/
)
13.9. For a three-surface enclosure problem as shown in Figure 13.7, do
the following problems by using the matrix method.
a. Given T 1 , T 2 , T 3 , determine q 1 , q 2 , q 3 .
b. Given q 1 , q 2 , q 3 , determine T 1 , T 2 , T 3 .
c. Given T 1 , T 2 , q 3 , determine q 1 , q 2 , T 3 .
d. Given T 1 , q 2 , q 3 , determine q 1 , T 2 , T 3 .
e. Given q 1 , q 2 , T 3 , determine T 1 , T 2 , q 3 .
References
1. W. Rohsenow and H. Choi, Heat, Mass, and Momentum Transfer, Prentice-Hall, Inc.,
Englewood Cliffs, NJ, 1961.
2. A. Mills, Heat Transfer, Richard D. Irwin, Inc., Boston, MA, 1992.
3. F. Incropera and D. Dewitt, Fundamentals of Heat and Mass Transfer, Fifth Edition,
John Wiley & Sons, New York, NY, 2002.
4. R. Siegel and J. Howell, Thermal Radiation Heat Transfer, McGraw-Hill, New York,
NY, 1972.
5. J. Chen, Conduction and Radiation Heat Transfer, Class Notes, Lehigh University,
1973.
Analytical Heat Transfer
plate is well insulated at the bottom. Let h be the average
convective heat transfer coefficient between the surface and
ambient air. Given h = 10 W/m 2 K, ε 1 = 0.54 = α 1 , σ = 5.67 ×
10 −8 W/m 2 K 4 . Determine the equilibrium plate temperature.
13.7. Consider two very large parallel plates with diffuse, gray surfaces. Determine the irradiation and radiosity for the upper plate
(at T 1 = 1000 ◦ K, ε 1 = 1). What is the radiosity for the lower plate
(at T 2 = 500 ◦ K, ε 2 = 0.8)? What is the net radiation exchange
between the plates per unit area of the plates?
13.8. A 0.25-m-diameter sphere (surface 1) is located inside of a 0.5-mdiameter sphere (surface 2). Surface 1 is 200 ◦ C and surface 2 is
100 ◦ C. Determine all of the view factors and calculate the net heat
transfer rate (W) between the two spherical surfaces. Show all
work and list all assumptions. (Note: = 5.67 × 10 −8 W m 2 K 4
σ
/
)
13.9. For a three-surface enclosure problem as shown in Figure 13.7, do
the following problems by using the matrix method.
a. Given T 1 , T 2 , T 3 , determine q 1 , q 2 , q 3 .
b. Given q 1 , q 2 , q 3 , determine T 1 , T 2 , T 3 .
c. Given T 1 , T 2 , q 3 , determine q 1 , q 2 , T 3 .
d. Given T 1 , q 2 , q 3 , determine q 1 , T 2 , T 3 .
e. Given q 1 , q 2 , T 3 , determine T 1 , T 2 , q 3 .
References
1. W. Rohsenow and H. Choi, Heat, Mass, and Momentum Transfer, Prentice-Hall, Inc.,
Englewood Cliffs, NJ, 1961.
2. A. Mills, Heat Transfer, Richard D. Irwin, Inc., Boston, MA, 1992.
3. F. Incropera and D. Dewitt, Fundamentals of Heat and Mass Transfer, Fifth Edition,
John Wiley & Sons, New York, NY, 2002.
4. R. Siegel and J. Howell, Thermal Radiation Heat Transfer, McGraw-Hill, New York,
NY, 1972.
5. J. Chen, Conduction and Radiation Heat Transfer, Class Notes, Lehigh University,
1973.