(Question 11) (16 points) (Short Answer) Consider a uniform iron (thermal diffusivity a? 0.23 ) rod of length 3 with an initial temperature uniformly 0. Assume that the temperature of the left end x = 0 is held at 0 and the temperature of the right end x = 3 is held at 21 until a steady-state result, answer the following questions. (a) (8 points) Set up a boundary value problem for the heat conduction in the rod, solve for the temperature distribution in the rod at any time t > 0. that is, u(x, t) . No need to elaborate your work for applying method of separation of variables except derivations for finding undetermined coefficients Cs in your series 1 solution. (b) (7 points) Now, in a new scenario, let t O correspond to some time after the stead-state of part(a) has been reached. Assume that at this instant both ends are insulated and maintained that way thereafter, set up a boundary value problem for the heat conduction in the rod and solve for the temperature distribution in the rod at any time t > 0, that is, u(x, t). No need to elaborate your work for applying method of separation of variables except derivations for finding undetermined coefficients cns in your series solution. (c) (1 point) What is the steady-state temperature distribution of part(b)? (Question 11) (16 points) (Short Answer) Consider a uniform iron (thermal diffusivity a? 0.23 ) rod of length 3 with an initial temperature uniformly 0. Assume that the temperature of the left end x = 0 is held at 0 and the temperature of the right end x = 3 is held at 21 until a steady-state result, answer the following questions. (a) (8 points) Set up a boundary value problem for the heat conduction in the rod, solve for the temperature distribution in the rod at any time t > 0. that is, u(x, t) . No need to elaborate your work for applying method of separation of variables except derivations for finding undetermined coefficients Cs in your series 1 solution. (b) (7 points) Now, in a new scenario, let t O correspond to some time after the stead-state of part(a) has been reached. Assume that at this instant both ends are insulated and maintained that way thereafter, set up a boundary value problem for the heat conduction in the rod and solve for the temperature distribution in the rod at any time t > 0, that is, u(x, t). No need to elaborate your work for applying method of separation of variables except derivations for finding undetermined coefficients cns in your series solution. (c) (1 point) What is the steady-state temperature distribution of part(b)