AISI 316 stainless steel billets ($$k = 13.4 \text{ W/m-K}$$, $$\rho = 8238 \text{ kg/m}^3$$, $$c = 468 \text{ J/kg-K}$$, and $$\alpha = 3.48 \times 10^{-6} \text{ m}^2/\text{s}$$) are to be heat-treated to a final temperature of $$100^\circ\text{C}$$. The billets are initially at a temperature of $$500^\circ\text{C}$$ and in order to obtain the required material properties, must be quenched to a temperature of $$325^\circ\text{C}$$ within 220 minutes, and then maintained at this temperature for no more than 275 minutes to ensure that the billet reaches a uniform temperature of $$325^\circ\text{C}$$. The billets are 50 cm in diameter and 1 m long.
There are two choices for the quenching medium: (a) still air at a temperature of $$25^\circ\text{C}$$, or (b) air that flows over the billets at 3 m/s and at a temperature of $$25^\circ\text{C}$$.
Heat Treatment
$$T_i = 275^\circ\text{C}$$
$$h = ? \text{ W/m}^2\text{-K}$$
Stainless Steel
$$D = 25 \text{ cm}$$
Quenching:
$$T_\infty = 25^\circ\text{C}$$
$$h = ? \text{ W/m}^2\text{-K}$$
Option 1: Quenching in Still Air
Heat Treatment
$$T_i = 275^\circ\text{C}$$
$$h = ? \text{ W/m}^2\text{-K}$$
Stainless Steel
$$D = 25 \text{ cm}$$
Quenching:
$$T_\infty = 25^\circ\text{C}$$
$$h = ? \text{ W/m}^2\text{-K}$$
Option 2: Quenching in Forced Air
Required:
Submit a heat transfer analysis for the heat treatment of the steel billet. In your analysis you must present the following:
1. Using the still air quench (Treat the billets as infinitely long horizontal cylinders):
a. Estimate the convection heat transfer coefficient of the air, in W/m2-K. (5 pts)
b. Estimate the actual time required to reach the quench temperature of $$325^\circ\text{C}$$, starting from the initial temperature of $$500^\circ\text{C}$$, in minutes. (5 pts)
c. Estimate the centerline temperature of the steel billet after 25 min, in $$^\circ\text{C}$$. (5 pts)
d. Estimate the heat transfer from a single steel billet, in kJ. (5 pts)
e. Estimate the Biot Number of the steel billets. (5 pts)
2. Repeat using the forced air quench:
3. Select the appropriate quenching medium to complete the heat treatment of the steel billets: