Heat N Mass Tranfer Examples
Some Solutions to Problems (Übungen) to Lecture-1 of Lecture Series “Heat Transfer – 1”
Institut für Energieverfahrenstechnik und Brennstofftechnik, TU Clausthal, SS 2005
1.1 A heat rate of 5 kW is conducted through a cross section area of 20 m2 and thickness of 3 cm. If the inner (hot) surface temperature is 600ºC and the thermal conductivity of the material is 0.5 W/mK, what is the outer surface temperature?
Solution:
Tout = 585 °C
1.2 The heat flux through a wood slab 50 mm thick, whose inner and outer temperatures are 40°C and 20ºC, respectively, has been determined to be 40 W/m2. What is the thermal conductivity of the wood?
Solution:
k = 0.1 W/mK
1.3 A concrete wall, which has a surface area of 20 m2 and is 0.30 m thick, separates conditioned room air from ambient air. The temperature of the inner surface of the wall is maintained at 25ºC, and the thermal conductivity of the concrete is 1 W/mK.
(a) Determine the heat loss in the steady state through the wall for temperatures of the outer side of the wall ranging from -15ºC to 38ºC, which corresponds to winter and summer extremes, respectively. Display your results graphically.
(b) On your graph, also plot the heat loss as a function of ambient temperature for wall materials having thermal conductivity of 0.75 and 1.25 W/mK. Explain the family of curves you have obtained.
Solution:
Heat loss through the wall
heat loss in kW
k=1,
-15
-10
3,50
3,00
2,50
2,00
1,50
1,00
0,50
0,00
-5 -0,50 0
-1,00
-1,50
5
k=0,75,
10
15
k=1,25
20
25
30
35
40
wall temperature at its outer side in °C
1.4 What is the thickness required for a masonry wall having thermal conductivity of
0.75 W/mK if the heat rate is to be 80% of the heat rate through a composite wall having a thermal conductivity of 0.25 W/mK and a thickness of 100 mm? Both walls are subjected to the same surface temperature difference.
Solution:
L = 375 mm.
1.5 A 5-mm thick bottom of a 200-mm diameter pan may be made from aluminum
(k=240 W/mK) or copper
Institut für Energieverfahrenstechnik und Brennstofftechnik, TU Clausthal, SS 2005
1.1 A heat rate of 5 kW is conducted through a cross section area of 20 m2 and thickness of 3 cm. If the inner (hot) surface temperature is 600ºC and the thermal conductivity of the material is 0.5 W/mK, what is the outer surface temperature?
Solution:
Tout = 585 °C
1.2 The heat flux through a wood slab 50 mm thick, whose inner and outer temperatures are 40°C and 20ºC, respectively, has been determined to be 40 W/m2. What is the thermal conductivity of the wood?
Solution:
k = 0.1 W/mK
1.3 A concrete wall, which has a surface area of 20 m2 and is 0.30 m thick, separates conditioned room air from ambient air. The temperature of the inner surface of the wall is maintained at 25ºC, and the thermal conductivity of the concrete is 1 W/mK.
(a) Determine the heat loss in the steady state through the wall for temperatures of the outer side of the wall ranging from -15ºC to 38ºC, which corresponds to winter and summer extremes, respectively. Display your results graphically.
(b) On your graph, also plot the heat loss as a function of ambient temperature for wall materials having thermal conductivity of 0.75 and 1.25 W/mK. Explain the family of curves you have obtained.
Solution:
Heat loss through the wall
heat loss in kW
k=1,
-15
-10
3,50
3,00
2,50
2,00
1,50
1,00
0,50
0,00
-5 -0,50 0
-1,00
-1,50
5
k=0,75,
10
15
k=1,25
20
25
30
35
40
wall temperature at its outer side in °C
1.4 What is the thickness required for a masonry wall having thermal conductivity of
0.75 W/mK if the heat rate is to be 80% of the heat rate through a composite wall having a thermal conductivity of 0.25 W/mK and a thickness of 100 mm? Both walls are subjected to the same surface temperature difference.
Solution:
L = 375 mm.
1.5 A 5-mm thick bottom of a 200-mm diameter pan may be made from aluminum
(k=240 W/mK) or copper