# A steel rod of diameter D =2 cm, length L =5 cm, and thermal conductivity k = 50W m -I °C -I is…

A steel rod of transection D =2 cm, extension L =5 cm, and thermal
conductivity k = 50W m^{-I} °C^{-I} is defenseless to ambient air
at T_{"}, =20°C delay a excitement remove coefficient β=100 W m^{-2}
°C^{-I}. If the left end of the rod is maintained at air To =
320^{o}C and the other end is insulated (see Fig. P3.19), indicate the
temperatures at distances 25 mm and 50 mm from the left end, and the excitement at
the left end. The governing equation of the example is

where θ = T - T_{~}, T is the air, and
N^{2} is dedicated by

The period provisions are

Use (a) two rectirectilinear parts and (b) one quadratic part to solve the example by the limited part system. The exact answer is

Fig. 3.19