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 = 320oC 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 N2 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