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A 3 cm length silver bar with a constant cross section area 1 cm (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: a²u 1 ôu ax c? ôt %3D (a) Show that c? = 2. (b) By using the method of separation of variable, and applying the boundary condition, prove that 2nx?t плх u(x,t)=Eb, sin- 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/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: a²u 1 ôu ax c? ôt %3D (a) Show that c? = 2. (b) By using the method of separation of variable, and applying the boundary condition, prove that 2nx?t плх u(x,t)=Eb, sin- 3 n=1 where b is an arbitrary constant. (c) By applying the initial condition, find the value of b,.

Advanced Engineering Mathematics
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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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 ôt (a) Show that c? = 2. (b) By using the method of separation of variable, and applying the boundary condition, prove that 2n²x?t u(x,t)=b, sin- плх e 3 n=1 where b, is an arbitrary constant. Answer: -50/n.pi(cosn"pi-1) (c) By applying the initial condition, find the value of b,.
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 ôt (a) Show that c? = 2. (b) By using the method of separation of variable, and applying the boundary condition, prove that 2n²x?t u(x,t)=b, sin- плх e 3 n=1 where b, is an arbitrary constant. Answer: -50/n.pi(cosn"pi-1) (c) By applying the initial condition, find the value of b,.
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