heat from a small motorcycle engine. If the average engine surface temperature is 112 C, Exercise 4.6.4 A circular fin of inner diameter 20 cm and outer diameter of 26 cm transfers determine the temperature distribution along the fin surface. The thermal conductivity of the ATE HEAT Cmine the temperature distribution along the fin surface. The thermal conductivity of the Jin material is 21 W/m C and the convective heat transfer coefficient between the fin and the atmosphere is 120 W/m2 C. Assume an atmospheric temperature of 32 C.

Elements Of Electromagnetics
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determine the temperature distribution along the fin surface. The thermal conductivity of the
heat from a small motorcycle engine. If the average engine surface temperature is 112°C,
Exercise 4.6.4 A circular fin of inner diameter 20 cm and outer diameter of 26 cm transfers
124
STEADY STATE HEAT CONDUCTION IN ONE DIMENSION
n material is 21 W/m C and the convective heat transfer coefficient between the fin and
the atmosphere is 120 W/m2 C. Assume an atmospheric temperature of 32 C.
Exercise 4.6.5 Consider a composite wall consisting of four different materials as shown
in Figure 4.16. Assuming a one-dimensional heat flow, determine the heat flow through the
composite slab and the interfacial temperatures. kA = 200 W/m °C, kB = 20 W/m°C and
kc = 40 W/m °C and kp =60 W/m °C. Assume that the areas of the surfaces B anda C are
equal to 0.1 m2.
Exercise 4.6.6 Consider a composite wall, which has one linearly varying cross-sectional
area as shown in Figure 4.17. Determine the heat flow and interfacial temperatures.
Thickness = 10 cm, kA = 200 W/m C, kg = 20 W/m C and kc = 40 W/hm C.
Exercise 4.6.7 A plane wall (k = 20 W/m C) of thickness 40 cm has its outer surfaces
maintained at 30 C. If there is uniform internal heat generation of 0.2 MW/m' in the plane
wall, determine the temperature distribution in the plane wall. Solve this problem using
(a) four linear elements (b) one quadratic element and (c) one modified quadratic element
with only two nodes. Compare the results with analytical solutions.
Exercise 4.6.8 A plane wall (k = 10 W/m C) of thickness 50 cm has its exterior surface
subiected to a convection environment of 30 C with a surface heat transfer coefficient of
600 W/n? C. Determine the temperature distribution in the plane wall using (a) four lin-
ear elements (b) one quadratic element and (c) one modified quadratic element with only
O nodes. Compare the results with the analytical solution. If the heat transfer coefficient
increases to 10,000 W/m C, what happens to the temperature of the exterior surface2
220 °C
Area = 0.2 m2
2 cm
20 °C
5 cm
3 cm
Figure 4.16 A composite wall
Transcribed Image Text:determine the temperature distribution along the fin surface. The thermal conductivity of the heat from a small motorcycle engine. If the average engine surface temperature is 112°C, Exercise 4.6.4 A circular fin of inner diameter 20 cm and outer diameter of 26 cm transfers 124 STEADY STATE HEAT CONDUCTION IN ONE DIMENSION n material is 21 W/m C and the convective heat transfer coefficient between the fin and the atmosphere is 120 W/m2 C. Assume an atmospheric temperature of 32 C. Exercise 4.6.5 Consider a composite wall consisting of four different materials as shown in Figure 4.16. Assuming a one-dimensional heat flow, determine the heat flow through the composite slab and the interfacial temperatures. kA = 200 W/m °C, kB = 20 W/m°C and kc = 40 W/m °C and kp =60 W/m °C. Assume that the areas of the surfaces B anda C are equal to 0.1 m2. Exercise 4.6.6 Consider a composite wall, which has one linearly varying cross-sectional area as shown in Figure 4.17. Determine the heat flow and interfacial temperatures. Thickness = 10 cm, kA = 200 W/m C, kg = 20 W/m C and kc = 40 W/hm C. Exercise 4.6.7 A plane wall (k = 20 W/m C) of thickness 40 cm has its outer surfaces maintained at 30 C. If there is uniform internal heat generation of 0.2 MW/m' in the plane wall, determine the temperature distribution in the plane wall. Solve this problem using (a) four linear elements (b) one quadratic element and (c) one modified quadratic element with only two nodes. Compare the results with analytical solutions. Exercise 4.6.8 A plane wall (k = 10 W/m C) of thickness 50 cm has its exterior surface subiected to a convection environment of 30 C with a surface heat transfer coefficient of 600 W/n? C. Determine the temperature distribution in the plane wall using (a) four lin- ear elements (b) one quadratic element and (c) one modified quadratic element with only O nodes. Compare the results with the analytical solution. If the heat transfer coefficient increases to 10,000 W/m C, what happens to the temperature of the exterior surface2 220 °C Area = 0.2 m2 2 cm 20 °C 5 cm 3 cm Figure 4.16 A composite wall
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