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1st 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. 2nd Case (IBVP Summary) 1.5uxx, 0 < x < 6 ft, t > 0 Ux(0, t) = 0, u(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0< x< 6 ft Ut 1. 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 = 1, x = 2 ft andt = 1 hr.

1st 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. 2nd Case (IBVP Summary) 1.5uxx, 0 < x < 6 ft, t > 0 Ux(0, t) = 0, u(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0< x< 6 ft Ut 1. 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 = 1, x = 2 ft andt = 1 hr.

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 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. 2nd Case (IBVP Summary) 1.5uxx, 0 < x < 6 ft, t > 0 Uz(0, t) = 0, ux(6 ft, t) = 0, t > 0 u(x, 0) = 80°F, 0< x< 6 ft Ut = %3D 1. 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 = 1, x = 2 ft andt = 1 hr.
Transcribed Image Text:1st 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. 2nd Case (IBVP Summary) 1.5uxx, 0 < x < 6 ft, t > 0 Uz(0, t) = 0, ux(6 ft, t) = 0, t > 0 u(x, 0) = 80°F, 0< x< 6 ft Ut = %3D 1. 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 = 1, x = 2 ft andt = 1 hr.
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