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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,.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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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 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,.
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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