HVAC · Heat-Transfer · Problem 21PDFSolution in PDF ↓
HVAC · Heat-Transfer · Problem 21
Problem & Solution
Video Synthesis
Problem: An uninsulated 14 inch round duct painted with non-metallic white paint has an average surface temperature of 150 degrees.
Given: 14 inch round duct painted with non-metallic white paint has an average surface temperature of 150 degrees; 14 inches...
Approach: We don't have to concern ourselves too much with what's going on inside the duct because we know the surface temperature.
Key formula: formula for radiation, which we've also used once earlier in this process
Calc: So we got around duct 14 inches, and if we were to draw the side section, it's going through a 20-foot room.
Calc: And this is a round duct, so I'll draw it like this 20 feet long.
Result: Closest answer choice is D.
Office Hours
3
Student questions asked in live office hours about this problem
OH 75: HVAC: Heat Transfer-21
Q: In Heat Transfer 21, should 'the duct goes to a room that's 20 feet' be interpreted as the duct length being 20 feet?
A: Yes — that was my intent, and you read it correctly. Also make sure you're setting up the temperature differences correctly for both the radiation and convection portions of the problem.
OH 82: HVAC: Heat Transfer-21
Q: Heat Transfer 19 uses the Reynolds/Nusselt approach while problem 21 uses the Rayleigh number — is it because problem 19 is forced convection (dedicated system implies fans) and problem 21 is natural convection (no velocity given)?
A: Exactly right — the presence or absence of a specified flow velocity is the tell. Flow velocity given → forced convection → Reynolds number; no velocity given (stationary fluid) → natural convection → Rayleigh number. Good diagnostic reasoning.
OH 87: HVAC: Heat Transfer-21
Q: For Heat Transfer 21 (duct with convection and radiation to the room), wouldn't there also be radiation from the duct to the surrounding air?
A: Technically yes, but in practice radiation between a solid and a gas is negligible — convection dominates heat transfer between solid surfaces and fluids. Radiation is a solid-to-solid (or solid-to-enclosure) mechanism for our purposes; don't account for solid-to-gas radiation in these problems.