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1st Case (IBVP Summary) ut = 1.5uxx, 0≤x≤ 6 ft, t>0 ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0≤ x ≤ 6 ft 2nd Case A 6-ft long rod (laterally insulated) has a thermal diffusivity of 1.5 ft²/hr and initial temperature of f(x) = 80°F. After preparing the initial temperature conditions of the rod, the boundary temperatures are adjusted simultaneously such that the left end of the rod is at 75°F and the right end at 160°F. 1. Identify and obtain the general solution u(x, t) of each case above. 2. From each u(x, t) compare the temperatures of Case 1 and Case 2 if n = 2, x = 3 ft and t = 1.5 hrs.

1st Case (IBVP Summary) ut = 1.5uxx, 0≤x≤ 6 ft, t>0 ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0≤ x ≤ 6 ft 2nd Case A 6-ft long rod (laterally insulated) has a thermal diffusivity of 1.5 ft²/hr and initial temperature of f(x) = 80°F. After preparing the initial temperature conditions of the rod, the boundary temperatures are adjusted simultaneously such that the left end of the rod is at 75°F and the right end at 160°F. 1. Identify and obtain the general solution u(x, t) of each case above. 2. From each u(x, t) compare the temperatures of Case 1 and Case 2 if n = 2, x = 3 ft and t = 1.5 hrs.

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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1st Case (IBVP Summary) ut = 1.5uxx, 0≤x≤ 6 ft, t>0 ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0≤ x ≤ 6 ft 2nd Case A 6-ft long rod (laterally insulated) has a thermal diffusivity of 1.5 ft²/hr and initial temperature of f(x) = 80°F. After preparing the initial temperature conditions of the rod, the boundary temperatures are adjusted simultaneously such that the left end of the rod is at 75°F and the right end at 160°F. 1. Identify and obtain the general solution u(x, t) of each case above. 2. From each u(x, t) compare the temperatures of Case 1 and Case 2 if n = 2, x = 3 ft and t = 1.5 hrs.
Transcribed Image Text:1st Case (IBVP Summary) ut = 1.5uxx, 0≤x≤ 6 ft, t>0 ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0≤ x ≤ 6 ft 2nd Case A 6-ft long rod (laterally insulated) has a thermal diffusivity of 1.5 ft²/hr and initial temperature of f(x) = 80°F. After preparing the initial temperature conditions of the rod, the boundary temperatures are adjusted simultaneously such that the left end of the rod is at 75°F and the right end at 160°F. 1. Identify and obtain the general solution u(x, t) of each case above. 2. From each u(x, t) compare the temperatures of Case 1 and Case 2 if n = 2, x = 3 ft and t = 1.5 hrs.
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