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KMM 222E Computational Methods in Chemical Engineering 2022-2023 Spring Homework 5 (Due to: May 18, 2023) Q1- Consider an electrically heated cylindrical wire with radius R. It produces heat with a rate of Se. The surface of the wire is maintained at a temperature To. The temperature of the wire changes in the radial direction. The average temperature rise TTo of the wire can be calculated as, TTo=0R2kSe(1(Rr)2)rdr Determine the average temperature rise in the wire using a) Simpson's 3/8 rule. b) 3 point Gauss-Legendre formula. c) Calculate the relative percentage error for the solutions found in part (a) and (b) knowing that the real value is 8kSeR2. R=0.006m,k=400W/m.K,Se=105W/m3