Page 108 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

THE FINITE ELEMENT METHOD
100
m (2,3.5) k (4,4)

j (5,2)

i (1,1)
Figure 3.32 Quadrilateral element

(2,7)

(4,3)

(1,1)

Figure 3.33 Triangular element

Exercise 3.7.11 In a double pipe heat exchanger, hot fluid flows inside a pipe and cold fluid
flows outside in the annular space. The heat exchange between the two fluids is given by the
differential equations, (refer to Exercise 2.5.12)

dT h
C 1 =−U(T h − T c )
dA
dT c
C 2 = U(T h − T c ) (3.299)
dA
Develop the stiffness matrix and forcing vector using (a) Sub-domain method (b)
Galerkin method.

Exercise 3.7.12 Calculate (using one, two and four elements) the temperature distribution
and the heat dissipation capacity of a fin of length 4 cm and cross-sectional dimensions of
2◦
6mm × 4 mm with a heat transfer coefficient of 0.1 W/m C and a thermal conductivity of
◦
the material of the fin as 0.5 W/m C. Base temperature is 90 C.
◦
Bibliography

Baker, AJ 1995 Finite Element Computational Fluid Mechanics, Student Edition, McGraw-Hill Book
Company, New York.
Bathe KJ 1982 Finite Element Procedures in Engineering Analysis, Prentice Hall, Englewood
Cliffs, NJ.