Consider the thick slab of copper in Example 5.12, which is initially at a uniform temperature of 20°C and is suddenly exposed to a net radiant flux of 3 × 10 5 W / m 2 . Use the Finite-Difference Equations/One-Dimensional/Transient conduction model builder of IHT to obtain the implicit form of the finite-difference equations for the interior nodes. In your analysis, use a space increment of Δ x = 37.5 m m with a total of 17 nodes 00 − 16 , and a time increment of Δ t = 1.2 s . For the surface node 00, use the finite-difference equation derived in Section 2 of the Example. (a) Calculate the 00 and 04 nodal temperatures at t = 120 s , that is, T 0 , 120 s and T 0.15 m , 120 s , and compare the results with those given in Comment 1 for the exact solution. Will a time increment of 0.1 2 s provide more accurate results? (b) Plot temperature histories for x = 0 , 150, and 600 mm, and explain key features of your results.
Consider the thick slab of copper in Example 5.12, which is initially at a uniform temperature of 20°C and is suddenly exposed to a net radiant flux of 3 × 10 5 W / m 2 . Use the Finite-Difference Equations/One-Dimensional/Transient conduction model builder of IHT to obtain the implicit form of the finite-difference equations for the interior nodes. In your analysis, use a space increment of Δ x = 37.5 m m with a total of 17 nodes 00 − 16 , and a time increment of Δ t = 1.2 s . For the surface node 00, use the finite-difference equation derived in Section 2 of the Example. (a) Calculate the 00 and 04 nodal temperatures at t = 120 s , that is, T 0 , 120 s and T 0.15 m , 120 s , and compare the results with those given in Comment 1 for the exact solution. Will a time increment of 0.1 2 s provide more accurate results? (b) Plot temperature histories for x = 0 , 150, and 600 mm, and explain key features of your results.
Solution Summary: The author calculates the rod temperature when the brass rod of length left extends horizontally from casting.
Consider the thick slab of copper in Example 5.12, which is initially at a uniform temperature of 20°C and is suddenly exposed to a net radiant flux of
3
×
10
5
W
/
m
2
. Use the Finite-Difference Equations/One-Dimensional/Transient conduction model builder of IHT to obtain the implicit form of the finite-difference equations for the interior nodes. In your analysis, use a space increment of
Δ
x
=
37.5
m
m
with a total of 17 nodes
00
−
16
, and a time increment of
Δ
t
=
1.2
s
. For the surface node 00, use the finite-difference equation derived in Section 2 of the Example.
(a) Calculate the 00 and 04 nodal temperatures at
t
=
120
s
, that is,
T
0
,
120
s
and
T
0.15
m
,
120
s
, and compare the results with those given in Comment 1 for the exact solution. Will a time increment of 0.1 2 s provide more accurate results?
(b) Plot temperature histories for
x
=
0
, 150, and 600 mm, and explain key features of your results.
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