The Grashof number is:

Summary of Key Equations (Chapter 9 Cheat Sheet)

For students using the solution manual, the following correlations are the most frequently referenced for standard geometries in Çengel Chapter 9: Chapter 9 of Heat and Mass Transfer: Fundamentals

• Similar correlation to vertical plates but uses diameter $D$.
• Laminar: $Nu \approx 0.36 Ra_D^1/4$ (approx) or use the Churchill-Chu cylinder formula provided in Problem 9-2 above.

• Hot surface facing up (or cold facing down): $$ Nu = 0.54 Ra^1/4 \quad (10^4 < Ra < 10^7) $$ $$ Nu = 0.15 Ra^1/3 \quad (10^7 < Ra < 10^11) $$
• Hot surface facing down (or cold facing up): $$ Nu = 0.27 Ra^1/4 \quad (10^5 < Ra < 10^10) $$