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The handle of a newly manufactured skillet pan, which is of length 6 inches, has a perfectly insulated surface. To test its heat resistance, the temperature at both ends of the handle is kept consistently at zero. The initial temperature of the handle throughout follows the room temperature at 26°C. The 1-dimensional heat equation is given as follows: ди 0.5 for all 0

The handle of a newly manufactured skillet pan, which is of length 6 inches, has a perfectly insulated surface. To test its heat resistance, the temperature at both ends of the handle is kept consistently at zero. The initial temperature of the handle throughout follows the room temperature at 26°C. The 1-dimensional heat equation is given as follows: ди 0.5 for all 0

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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The handle of a newly manufactured skillet pan, which is of length 6 inches, has a perfectly insulated surface. To test its heat resistance, the temperature at both ends of the handle is kept consistently at zero. The initial temperature of the handle throughout follows the room temperature at 26°C. The 1-dimensional heat equation is given as follows: = 0.5 for all 0<x<6 and t20 ôx? (a) Describe the initial and boundary conditions of the 1-dimension heat equation in this scenario. (b) Hence, by using the form u(x, t) = (Acos px+ B sin px)(e"), deduce the function modelling the temperature of the handle, subjected to the conditions in (a).
Transcribed Image Text:The handle of a newly manufactured skillet pan, which is of length 6 inches, has a perfectly insulated surface. To test its heat resistance, the temperature at both ends of the handle is kept consistently at zero. The initial temperature of the handle throughout follows the room temperature at 26°C. The 1-dimensional heat equation is given as follows: = 0.5 for all 0<x<6 and t20 ôx? (a) Describe the initial and boundary conditions of the 1-dimension heat equation in this scenario. (b) Hence, by using the form u(x, t) = (Acos px+ B sin px)(e"), deduce the function modelling the temperature of the handle, subjected to the conditions in (a).
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