An infinite cylindrical rod (radius a ) is initially at temperature T=T0 and its surface temperature is reduced to T=0. Determine the time required for the cylinder to cool. To do this: (a) Write down the defining equations and scale the problem to reduce it to the form: r1(rTr)r=Tt with T(r,0)=1, and T(1,t)=0,T(0,t) finite. (b) Proceed as in lectures to obtain a Bessel function expansion of the solution and evaluate the coefficients so that the initial condition is satisfied. 1 (c) Plot out the solution as a function of r at t=0 to see how many terms are required for a good answer. (d) Plot out the temperature at r=0 and thus determine the cooling time in unscaled terms as a function of radius etc