HVAC · Heat-Transfer · Problem 22PDFSolution in PDF ↓
HVAC · Heat-Transfer · Problem 22
Problem & Solution
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Problem: 400 CFM of 50 degree condition supplier enters a 10-inch round uninsulated duct with an outside surface emissivity of .4 and an average surface tem...
Given: 400 CFM of 50 degree condition supplier enters a 10-inch round uninsulated duct with an outside surface emissivity of...
Approach: First, we have to take a look at the temperature of the duct.
Calc: We have air at 50 degrees entering and the volume flow rate is 400 CFM.
Calc: The length of the duct in the room is 30 feet.
Result: So at this point we can write an expression that gives us the total rate of heat transfer for the internal component of this forced convection and ...
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Student questions asked in live office hours about this problem
OH 19: HVAC: Heat Transfer-22
Q: In Heat Transfer 22, you used the exterior film temperature when finding the Reynolds number — but shouldn't the interior air film temperature be used since we're solving for the inside film coefficient?
A: The assumption is that the sheet metal duct wall is thin and highly conductive, so the inside and outside surface temperatures are essentially equal. Given that simplification, the exterior film temperature is a reasonable approximation for interior property lookups.
OH 33: HVAC: Heat Transfer-22
Q: In Heat Transfer 22, why were interior air properties looked up at the exterior film temperature rather than using a separate interior film temperature?
A: This is a hard problem — one of two very hard ones in heat transfer — and I took a shortcut by using the exterior film temperature for both convection regimes. The more rigorous approach would iterate to a separate interior film temperature, but for exam purposes the approximation is acceptable.
OH 41: HVAC: Heat Transfer-22
Q: For Heat Transfer 22, I calculated the external convection and radiation heat gain, then applied Q = 1.08 × CFM × ΔT to find the temperature rise — why doesn't this approach work?
A: I'll be honest — this is probably the hardest problem in the program and I've overcooked it; it should really be three separate problems. Your approach may actually be in the right ballpark, but the issue is that internal forced convection and external heat load need to be set up as a coupled resistance network, not a sequential calculation.
OH 44: HVAC: Heat Transfer-22
Q: For Heat Transfer 22, it's not clear which equation to use for finding h, and why are two different areas used — one for velocity and another for heat transfer rate?
A: Thank you for the specific framing — this is the hardest problem in the bundle and it is genuinely overcooked. The h equation depends on whether you're dealing with internal or external convection, and the two areas are: the duct cross-section (for calculating velocity) and the duct outer surface area (for calculating heat transfer rate).
OH 50: HVAC: Heat Transfer-22
Q: Can Heat Transfer 22 be solved using the same approach as problem 19 — combining convection coefficients into a single U value and using Q = 1.08 × CFM × ΔT?
A: The setups are fundamentally different: in problem 22, the internal forced convection is being driven by external heat gain through the duct wall, creating a coupled problem that doesn't reduce as cleanly as problem 19. In theory you might combine resistances, but the interaction between heat sources makes it more complex.
OH 54: HVAC: Heat Transfer-22
Q: In Heat Transfer 22, using the exterior film temperature for interior air property lookups seems like a stretch — is there a better way?
A: It is a stretch and not ideal — I took that shortcut because this problem is already extremely complex. If I were cleaning it up, I'd either provide the film temperature explicitly or split the problem into parts.
OH 63: HVAC: Heat Transfer-22
Q: Problems 19 and 22 both find the exit temperature of air in a heated duct — in 19 you used Q_total = Q_sensible, but in 22 you used Q_internal = Q_external. How do I know which to use?
A: The two problems have different physical setups: problem 19 has a duct inside a conditioned space where total heat transfer from the surroundings is known, while problem 22 has a duct exposed externally where you need the energy balance across the duct wall. Be flexible — identify the physical setup first, then pick the approach that matches.
OH 71: HVAC: Heat Transfer-22
OH 119 · April 28, 2026
Q: A student solved Heat Transfer 22 with a different approach and got close on convection but their radiation result was roughly 1/100th the expected value — what went wrong?
A: The radiation contribution should be on the same order of magnitude as convection, not negligibly small, so something is missing in the radiation calculation — likely a missing emissivity term or incorrect area. Additionally, the student used a rule-of-thumb shortcut for the internal convection piece rather than the full internal convection method Dan intended, which coincidentally gives a similar answer but skips the key learning objective of the problem.
Q: In Heat Transfer 22, how do you know it's turbulent flow right away without calculating the Reynolds number first — should we always assume turbulent flow in HVAC ducts?
A: Yes — for HVAC duct airflow applications, you can almost always assume turbulent flow. The Reynolds numbers for typical HVAC air velocities are well above the turbulent threshold, so going straight to the turbulent Nusselt correlation is a valid time-saving assumption.