Let a silver rod 20 cm longinitially has a uniform temperature of 100°𝐶throughout.Suppose that at 𝑡=0the ends of the bar are plunged into an ice bath at 0°𝐶and thereafter maintained at this temperature, but that no heat is allowed to escape through the lateral surface. The thermal diffusivityof silver is𝛼2=1.71𝑐𝑚2/𝑠𝑒𝑐a) State the boundary value problem and use the method for separation of variables to find the expression for the temperature at any point 𝑥in the rod at any time𝑡. Explain why the method for separation of variables can beapplied.
b) Determine the temperature at the center of the rod at time 𝑡=30sec (Use the firstterm ofthe solution)
c) Find/estimate the time that will elapse before the center of the rodcools to a temperature of 5°𝐶. (Use the firstterm ofthe solution)
