A long Pyroceram rod (ρ = 2600 kg/m3, cp = 808 J/kg·K, k = 3.98 W/m·K, and α = 1.89 × 10−6...

A long Pyroceram rod (ρ = 2600 kg/m³, c_p = 808 J/kg·K, k = 3.98 W/m·K, and α = 1.89 × 10⁻⁶ m²/s) with diameter of 10 mm has an initial uniform temperature of 1000°C. The Pyroceram rod is allowed to cool in ambient temperature of 25°C and convection heat transfer coefficient of 80 W/m²·K. If the Pyroceram rod is allowed to cool for 3 min, determine the temperature at the center of the rod using (a) Table 18-2 and (b) the Heisler chart (Fig. 18-15).

Table 18-2:

Coefficients used in the one-term approximate solution of transient one-dimensional heat conduction in plane walls, cylinders, and spheres (Bi = hL/k for a plane wall of thickness 2L, and Bi = hr_o/k for a cylinder or sphere of radius r_o

FIGURE 18–15:

Transient temperature and heat transfer charts for a long cylinder of radius r_o initially at a uniform temperature T_i subjected to convection from all sides to an environment at temperature T_∞ with a convection coefficient of h.