1) To estimate the thermal conductivity of a material it is proposed to run an experiment as shown. Two very long rods of the same diameter, one made of brass with thermal conductivity k=110 W/m°C and the other whose conductivity is to be determined, are attached to a plate. The steady state temperatures at two points in the rods are measured as shown. For the measurements indicated, determine the unknown thermal conductivity. The value of the convective heat transfer coefficient for both rods may be assumed to be the same.

2) Radioactive wastes (krw=20 W/m°C) are stored in a spherical stainless steel (kss=15 W/m°C) container of inner radius ri=0.5 m and outer radius ro=0.6 m. Heat is generated volumetrically within the wastes at a uniform rate of g=105 W/m3, and the outer surface of the container is exposed to water at a temperature T =25°C and for which h=100 W/m2°C. a) Evaluate the steady state inner surface temperature (Ts,i) b) Evaluate the steady state outer surface temperature (Ts,o) c) Obtain an expression for the temperature distribution T(r) in the radioactive wastes. Express your result in terms of ri, Ts,i, krw, and g. Evaluate the temperature at r=0.

3) Water at T∞,1=5°C with a convective heat transfer coefficient of h1=80 W/m2°C flows inside a long stainless steel pipe (kss = 15 W/m°C). The pipe is covered with a 1.25-cm-thick insulation to reduce heat transfer and eliminate condensation on the outer surface. The cross section of the pipe is shown. It is desired to maintain the outer surface temperature of the insulation at 15°C to prevent the condensation. The pipe is located in a room whose temperature is T∞,2=30°C. The walls of the room are also at Tsurr=30°C. The outer surface of the insulation has an emissivity of ε=0.9. Heat transfer from the outer surface of the insulation to the surroundings is by radiation and natural convection with a convective heat transfer coefficient of h2=10 W/m2°C. Under steady conditions: (a) Sketch the equivalent thermal circuit,

labeling all resistances and temperatures. (b) Determine the rate of heat transfer per unit

length of the pipe. (c) Determine the conductivity of the

insulation.

8 cm

5.5 cm

5 cm

T∞,1 h1

Water

Stainless steel pipe kss=15 W/m°C

Insulation kins=?

h2

T∞,2

Tsurr = T∞,2

ε =0.9

1 

   

 

 

3 

 

 

Q4. With solution, solve only (a) and (b)

Question 5: Example 4-8, page 251, the course textbook Question 6: Problem 3-123, page 204, the course textbook. It is also in assignment no. 3. “solutions”.