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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:85°C
A
Ar
Ar
AT
55°C
с
Ar
70°C
30°C
B
D
Figure Q3: Distribution of the initial temperatures
25°C
E
Transcribed Image Text:Q3
(b)
DUJA 34103
The heat transfer performance of a new conductor bar of length 20 cm is under inspection.
The material is fully insulated such that the heat transfer is only one dimensional in axial
direction (x-axis). The left end is maintained at temperature of 100°C, while the right end is
maintained at temperature of 20°C, for r>0. The distribution of the initial temperatures is
shown in Figure Q3. The unsteady state heat conduction equation is given by;
0
Where A'is a thermal diffusivity of material and x is the longitudinal coordinate of the bar.
The thermal diffusivity of the material is given as x-10 cm³/s, and Ar=2 second.
By considering numerical differentiation
ST_T(x,1+1)-T(x), deduce that the temperature distribution along the bar at point
Or
A
(x,1+1) in explicit finite-difference form is given by
7(x+1)-27(x,1)+7(x-1,t) and
Ar
T(x,1+1)=0.87(x-1,t)-0.67(x,1)+0.87(x+1,1)
Draw the finite difference grid to predict the temperature of all points up to 4 seconds.
Label all unknown temperatures on the grid.
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