2. [50 points] The problem of transient radial heat flow in a circular rod in nondimensional...

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2. [50 points] The problem of transient radial heat flow in a circular rod in nondimensional form is described by Ju -2 1 = It with boundary conditions u(t, 1) = 1 and (t, 0) = 0 Or u(0,r)=0 0 1) Write down the original equation and the initial/boundary conditions. 2) Write down the general form of the finite difference formulas you are going to use to convert the given analytical PDE to its finite-difference form. 3) Convert the given analytical PDE to its finite difference form (every single step must be shown). 1) Provide the plot of the temperature distribution along the radius of the rod's cross section for different times. 2) Discuss your results (if your plot is consistent with the physics of the problem). 2. [50 points] The problem of transient radial heat flow in a circular rod in nondimensional form is described by Ju -2 1 = It with boundary conditions u(t, 1) = 1 and (t, 0) = 0 Or u(0,r)=0 0 1) Write down the original equation and the initial/boundary conditions. 2) Write down the general form of the finite difference formulas you are going to use to convert the given analytical PDE to its finite-difference form. 3) Convert the given analytical PDE to its finite difference form (every single step must be shown). 1) Provide the plot of the temperature distribution along the radius of the rod's cross section for different times. 2) Discuss your results (if your plot is consistent with the physics of the problem).