2 A 3 cm length silver bar with a constant cross section area 1 cm² (density 10 g/cm³, thermal conductivity 3 cal/(cm sec °C), specific heat 0.15 cal/(g °C)), is perfectly insulated laterally, with ends kept at temperature 0 °C and initial uniform temperature f(x) =25 °C. The heat equation is: 1 ди ax c? at (a) Show that c? = 2. (b) By using the method of separation of variable, and applying the boundary condition, prove that 2nx³t u(x,t) -Σ, sin: NTX -e 3 9 n=1 where b, is an arbitrary constant. (c) By applying the initial condition, find the value of b,.
2 A 3 cm length silver bar with a constant cross section area 1 cm² (density 10 g/cm³, thermal conductivity 3 cal/(cm sec °C), specific heat 0.15 cal/(g °C)), is perfectly insulated laterally, with ends kept at temperature 0 °C and initial uniform temperature f(x) =25 °C. The heat equation is: 1 ди ax c? at (a) Show that c? = 2. (b) By using the method of separation of variable, and applying the boundary condition, prove that 2nx³t u(x,t) -Σ, sin: NTX -e 3 9 n=1 where b, is an arbitrary constant. (c) By applying the initial condition, find the value of b,.
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:A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm,
thermal conductivity 3 cal/(cm sec °C), specific heat 0.15 cal/(g °C)), is perfectly
insulated laterally, with ends kept at temperature 0 °C and initial uniform
temperature f(x) = 25 °C.
Q1
The heat equation is:
1 ди
c2 at
(a) Show that c2 = 2.
(b) By using the method of separation of variable, and applying the boundary
condition, prove that
2nx?t
NTX
u(x,t) Σb, sin
3
9
n=1
where b, is an arbitrary constant.
(c) By applying the initial condition, find the value of b,.
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