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PROBLEM 4.8
KNOWN:
Shape of objects at surface of semiinfinite medium.
F
IND:
Shape factors between object at temperature T
1
and semiinfinite medium at temperature T
2
.
SCHEMATIC:
D
T
2
T
1
D
T
2
T
1
D
T
2
T
1
(a)
(b)
(c)
ASSUMPTIONS:
(1) Steadystate, (2) Medium is semiinfinite, (3) Constant properties, (4) Surface
of semiinfinite medium is adiabatic.
ANALYSIS:
Cases 12 15 of Table 4.1 all pertain to objects buried in an infinite medium.
Since they
all possess symmetry about a horizontal plane that bisects the object, they are equivalent to the cases
given in this problem for which the horizontal plane is adiabatic.
In particular, the heat flux is the
same for the cases of this problem as for the cases of Table 4.1.
Note, that when we use Table 4.1 to
determine the dimensionless conduction heat rate,
, we must be consistent and use the surface area
of the “entire” object of Table 4.1, not the “half” object of this problem.
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This note was uploaded on 12/07/2010 for the course MAE Heat Trans taught by Professor Lee,j.s. during the Spring '10 term at Seoul National.
 Spring '10
 LEE,J.S.
 Heat Transfer

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