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Consider the heat distribution u (x, t) in a semi-infinite rod. Assume that the finite end is kept in contact with ice at 0°C and if initially the rod is submerged in hot water at 100°C. ..n the choice e Fourier (a) Uth ppropriate Fourier transform to show that form) 2 (b) Establish that QUESTION 2 Then derive that solution u TO 00ac² ppropriate ourier trans.orm of u(x, t) = 100- û (a‚t) – 100 √ √²/ (1 – e-c³a²t). Writt 200 dc is the spec heat of the rod. -c²a²t opoda ㅠ /0 sin arda.

Consider the heat distribution u (x, t) in a semi-infinite rod. Assume that the finite end is kept in contact with ice at 0°C and if initially the rod is submerged in hot water at 100°C. ..n the choice e Fourier (a) Uth ppropriate Fourier transform to show that form) 2 (b) Establish that QUESTION 2 Then derive that solution u TO 00ac² ppropriate ourier trans.orm of u(x, t) = 100- û (a‚t) – 100 √ √²/ (1 – e-c³a²t). Writt 200 dc is the spec heat of the rod. -c²a²t opoda ㅠ /0 sin arda.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Consider the heat distribution u(x, t) in a semi-infinite rod. Assume that the finite end is kept in contact with ice at 0°C and if initially the rod is submerged in hot water at 100°C. the choice e Fourier (a) U the ppropriate Fourier transform to show the form) (b) Establish that QUESTION 2 Then derive that solution u ppropriate ourier trans.orm of û (a, t) u (x, t): 100 = 100- J0ac²2 a 200 π /0 With (1 – e-c³²a²t). a dc is the spec heat of the rod. ²a²t 100) sin arda.
Transcribed Image Text:Consider the heat distribution u(x, t) in a semi-infinite rod. Assume that the finite end is kept in contact with ice at 0°C and if initially the rod is submerged in hot water at 100°C. the choice e Fourier (a) U the ppropriate Fourier transform to show the form) (b) Establish that QUESTION 2 Then derive that solution u ppropriate ourier trans.orm of û (a, t) u (x, t): 100 = 100- J0ac²2 a 200 π /0 With (1 – e-c³²a²t). a dc is the spec heat of the rod. ²a²t 100) sin arda.
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