Chapter 9, Problem 9.83P

A natural convection air healer consists of an array of parallel, equally spaced vertical plates, which may be maintained at a fixed temperature $T_s$ by embedded electrical heaters. The plates are of length and width $L=W=300\text{mm}$ and are in quiescent, atmospheric air at $T_{\infty }=20°C$ . The total width of the array cannot exceed a value of $W_{\text{ar}}=150\text{mm}$ .

For $T_s=75°C$ , what is the plate spacing S that maximizes heat transfer from the array? For this spacing, how many plates comprise the array and what is the corresponding rate of heat transfer from the array?