Consider a 2-m-long wire of thermal diffusivity a=1 subjected to initial temperature 3x(2-x) and boundary temperature...

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Consider a 2-m-long wire of thermal diffusivity a=1 subjected to initial temperature 3x(2-x) and boundary temperature 1 and t. The governing equation is: = a at subject to T(0,t) = 1,T(2,t) =t and T(x, 0) = 3x(2–- x) a) Write the system of equations to determine the temperature at t=0.125 d according to the Crank-Nicolson method with At=0.125d and Ax=0.5m. b) Solve the problem using the Thomas method. Consider a 2-m-long wire of thermal diffusivity a=1 subjected to initial temperature 3x(2-x) and boundary temperature 1 and t. The governing equation is: = a at subject to T(0,t) = 1,T(2,t) =t and T(x, 0) = 3x(2–- x) a) Write the system of equations to determine the temperature at t=0.125 d according to the Crank-Nicolson method with At=0.125d and Ax=0.5m. b) Solve the problem using the Thomas method.