One end of a stainless steel (AISI 316) rod of diameter 10 mm and length 0.16 m is inserted into a fixture maintained at 200°C. The rod, covered with an insulating sleeve, reaches a uniform temperature throughout its length. When the sleeve is removed the rod is subjected to ambient air at 25°C such that the convection heat transfer coefficient is 30 W/m2 ∙ K.

(a) Using the explicit finite-difference technique with a space increment of ∆x = 0.016 m. estimate the time required for the mid length of the rod to reach 100°C.

(b) With ∆x = 0.016 m and ∆t = 10 s, compute T(x, t) for 0 < t < t1, where t l is the time required for the mid length of the rod to reach 50°C. Plot the temperature distribution for t = 0,200 s, 400 s, and t).