Page 133 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

STEADY STATE HEAT CONDUCTION IN ONE DIMENSION
A B C 125
120 °C

5 cm 10 cm

20 °C

5 cm
1 cm 1 cm

Figure 4.17 A composite wall

Exercise 4.6.9 Calculate the outer wall surface temperature and the temperature distribu-
◦
tion in a thick-walled hollow cylinder when the inner wall temperature is 120 C and the
◦
outer wall is exposed to a convection environment of 25 C with a surface heat transfer coef-
ficient of 20 W/m 2 ◦ C. The inner and outer radii of the hollow cylinder are 30 cm and 60 cm
◦
respectively. The thermal conductivity of the material of the hollow cylinder is 20 W/m C.
Use one linear element and two linear elements for the solution. Compare the results with
the analytical solution.

Exercise 4.6.10 Calculate the surface temperature in a circular solid cylinder (k =
3
20 W/m 2 ◦ C) of radius 30 mm with a volumetric heat generation of 25 MW/m . The exter-
nal surface of the cylinder is exposed to a liquid at 25 C with a heat transfer coefficient of
◦
5000 W/m 2 ◦ C. Use (a) four linear elements and (b) two quadratic elements. Compare the
solution with the analytical solution.
Exercise 4.6.11 Consider a tapered fin of length 5 cm dissipating heat to an ambient at
◦
30 C. The heat transfer coefficient on the surface and the tip is 100 W/m 2 ◦ C. The fin tapers
from a thickness of 5 mm to a thickness of 2 mm at the tip. The thermal conductivity of the
◦
material of the fin is 100 W/m C. The width of the fin is constant along the length and equal
to 2 mm. Determine the heat dissipation from the fin for a base temperature of 100 C. Use
◦
(a) two linear elements and (b) one quadratic element. Also, calculate the fin efficiency.

Bibliography

Bejan A 1993 Heat Transfer, John Wiley & Sons, New York.
Holman JP 1989 Heat Transfer, McGraw-Hill, Singapore.
Incropera FP and Dewitt DP 1990 Fundamentals of Heat and Mass Transfer, John Wiley & Sons,
New York.
Ozisik MN 1968 Boundary Value Problems of Heat Conduction, International Text Book Company,
Scranton, PA.