Consider a thin bar of length 16 with heat distribution T(z, t), where (a) Suppose 7...

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Consider a thin bar of length 16 with heat distribution T(z, t), where (a) Suppose 7 satisfies homogeneous Bs and the IC i. What are un and An (n=1,2,...)? WT An T(z,t) (n*Pi/16 Find T'(x, t) by using a separation solution similar to the one in the course notes. 0 (b) Find the smallest time t when max(7) 0.01. Give your answer to two decimal places. i ko 0 OT Ot iL Apply the initial condition to determine T(z,t). Do not use the notations un and An in your solution. iii. Find 7(z, t) as if 9 lim T(1,t) t> 8T 822 2 (c) Now suppose both ends of the bar are insulated so that 7' satisfies the BCs Number for 0 16 and t> 0. T(0, t) - T(16, t) = 0 for t > 0, T(z,0) = sin Tz (0, t) - Tz (16, t) - 0 for t> 0. Let the eigenvalues of the associated Sturm-Liouville problem be ko, k,k..... where kol Consider a thin bar of length 16 with heat distribution T(z, t), where (a) Suppose 7 satisfies homogeneous Bs and the IC i. What are un and An (n=1,2,...)? WT An T(z,t) (n*Pi/16 Find T'(x, t) by using a separation solution similar to the one in the course notes. 0 (b) Find the smallest time t when max(7) 0.01. Give your answer to two decimal places. i ko 0 OT Ot iL Apply the initial condition to determine T(z,t). Do not use the notations un and An in your solution. iii. Find 7(z, t) as if 9 lim T(1,t) t> 8T 822 2 (c) Now suppose both ends of the bar are insulated so that 7' satisfies the BCs Number for 0 16 and t> 0. T(0, t) - T(16, t) = 0 for t > 0, T(z,0) = sin Tz (0, t) - Tz (16, t) - 0 for t> 0. Let the eigenvalues of the associated Sturm-Liouville problem be ko, k,k..... where kol

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Solution for Heat Equation with Different Boundary Conditions Part a why and 12 w eigenfunctions These represent the spatial modes of vibration or hea... View the full answer