Spherical glass beads coming out of a kiln are allowed to cool in a room temperature of 30...

Spherical glass beads coming out of a kiln are allowed to cool in a room temperature of 30°C. A glass bead with a diameter of 10 mm and an initial temperature of 400°C is allowed to cool for 3 min. If the convection heat transfer coefficient is 28 W/m²·K, determine the temperature at the center of the glass bead using (a) Table 18-2 and (b) the Heisler chart (Fig. 18-16). The glass bead has properties of ρ = 2800 kg/m³, c_p = 750 J/kg·K, and k = 0.7 W/m·K

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 18–16:

Transient temperature and heat transfer charts for a sphere 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.