A round solid cylinder made of a plastic material (a = 6 x 10^-7 m²/s) is initially at a uniform temperature of 20^oC and is well insulated along its lateral surface and at one end. At time t = 0, heat is applied to the left boundary causing T_o to increase linearly with time at a rate of 1^oC/s.

(a) Using the explicit method with F_o = ½, derive the finite-difference equations for nodes 1, 2, 3, and 4.

(b) Format a table with headings of p, t (s), and the nodal temperatures T _o to T₄. Determine the surface temperature T_o when T4 = 35°C.

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To T2 TA T3 L = 24 mm