Problem 2 Given the partial differential equation is du(x, t) a u(x, t) - 0.8 for 0

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Problem 2 Given The Partial Differential Equation Is Du X T A U X T 0 8 For 0 X 1 And 0 T 0 04 At A2x With Init 1 (52.18 KiB) Viewed 12 times

Problem 2 Given the partial differential equation is du(x, t) a u(x, t) - 0.8 for 0<x< 1 and 0 <t< 0.04 at a2x with initial condition u(x,0) = f(x) = 5x – x3 for t = 0 and 0<x< 1 = = And boundary conditions u(0,t) = 0 for x = 0 and 0<t<0.04 u(1,t) = 0 for x = 1 and 0<t<0.0.4 Manually, calculate the solution, (x, t), when t = 0.04 by using Ax = h = 0.2 and At = k = 0.02 using Crank Nicholson's method. You have to show all the detail of procedure. And summarize your results in the table format, as shown below. = = x = 0.00 X = 0.20 X = 0.40 x = 0.60 *'s = 0.80 X = 1.00 Times) t = 0.00 ta = 0.02 to = 0.04 Problem 3 For the two dimensional steady state heat transfer problem, the problem is depicted as shown in the below figure. Ax= 0.25 m T,= 500 K Ay = 0.25 m 1 2 7 10 Fire clay brick 11 3 3 4 18 1,- 500K 1.- 300K h = 10 W/ mK 5 on 6 19 12 Air Ts-100 K Write down the system of linear equations which will be used to determine the temperature of point 1 to 12