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1st Case (IBVP Summary) 1.3uxx, 0 < x < 5 ft, t > 0 u(0, t) = 70°F, u(5ft, t) = 150°F, t > 0 u(x,0) = 60°F, 0 < x < 5 ft и (х,0) 2nd Case A 5-ft long bar (laterally insulated) has a thermal diffusivity of 1.3 ft? /hr and initial temperature of f(x) = 60°F . After preparing the initial temperature conditions of the bar, the left and right ends of the bar are simultaneously insulated. 1. Obtain the general solution u(x, t) of each case above. 2. Substituten= 1,x = 2 ft and t = 1 hr into each of u(x,t) of the 2 cases and compare their temperatures.

1st Case (IBVP Summary) 1.3uxx, 0 < x < 5 ft, t > 0 u(0, t) = 70°F, u(5ft, t) = 150°F, t > 0 u(x,0) = 60°F, 0 < x < 5 ft и (х,0) 2nd Case A 5-ft long bar (laterally insulated) has a thermal diffusivity of 1.3 ft? /hr and initial temperature of f(x) = 60°F . After preparing the initial temperature conditions of the bar, the left and right ends of the bar are simultaneously insulated. 1. Obtain the general solution u(x, t) of each case above. 2. Substituten= 1,x = 2 ft and t = 1 hr into each of u(x,t) of the 2 cases and compare their temperatures.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 32EQ
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1st Case (IBVP Summary) 1.3uxx, 0 < x < 5 ft, t > 0 u(0, t) = 70°F, u(5ft, t) = 150°F, t > 0 u(x,0) = 60°F, 0 < x < 5 ft Ut 2nd Case A 5-ft long bar (laterally insulated) has a thermal diffusivity of 1.3 ft2 /hr and initial temperature of f(x) = 60°F . After preparing the initial temperature conditions of the bar, the left and right ends of the bar are simultaneously insulated. 1. Obtain the general solution u(x, t) of each case above. 2. Substitute n = 1,x = 2 ft and t = 1 hr into each of u(x, t) of the 2 cases and compare their temperatures.
Transcribed Image Text:1st Case (IBVP Summary) 1.3uxx, 0 < x < 5 ft, t > 0 u(0, t) = 70°F, u(5ft, t) = 150°F, t > 0 u(x,0) = 60°F, 0 < x < 5 ft Ut 2nd Case A 5-ft long bar (laterally insulated) has a thermal diffusivity of 1.3 ft2 /hr and initial temperature of f(x) = 60°F . After preparing the initial temperature conditions of the bar, the left and right ends of the bar are simultaneously insulated. 1. Obtain the general solution u(x, t) of each case above. 2. Substitute n = 1,x = 2 ft and t = 1 hr into each of u(x, t) of the 2 cases and compare their temperatures.
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