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 %3D (a) Show that c² = 2. (b) By using the method of separation of variable, and applying the boundary condition, prove that 2n²x² 00 u(x,t)=b, sin- плх -e 3 n=1 where b, is an arbitrary constant. (c) By applying the initial condition, find the value of b,.

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 %3D (a) Show that c² = 2. (b) By using the method of separation of variable, and applying the boundary condition, prove that 2n²x² 00 u(x,t)=b, sin- плх -e 3 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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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
%3D
(a) Show that c² = 2.
(b) By using the method of separation of variable, and applying the boundary
condition, prove that
2n²x²
00
u(x,t)=b, sin-
плх
-e
3
n=1
where b, is an arbitrary constant.
(c) By applying the initial condition, find the value of b,.

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