HVAC · Heat-Transfer · Problem 15

Problem & Solution

Video Synthesis

Problem: How much heat does a 3-inch horizontal hot water pipe lose to the ambient space per unit length by natural convection?
Given: 32.2 feet per second squared; 3 inches; 12 inches
Approach: A good place to start with any convection problem is Newton's law of cooling and you can actually use that as a search term in ...
Key formula: formula is to find the Rayleigh number
Calc: We're not being asked to find the heat transfer in B2 per hour.
Calc: So we're looking for B2 per hour per foot and that's the answer choice units.
Result: The best answer choice is A.

Office Hours 11

Student questions asked in live office hours about this problem

OH 39: HVAC: Heat Transfer-15

Q: For Heat Transfer 15 (natural convection from a hot pipe), should I use the air temperature or the film temperature to look up properties for the Rayleigh number?

A: Use the film temperature — the average of the surface and ambient temperatures — as the consistent rule for fluid property lookups in convection problems. I know it may appear inconsistent across problems, but film temperature is the physically correct approach.

OH 46: HVAC: Heat Transfer-15

Q: In Heat Transfer 15 you used the surface temperature (100°F) for air property lookups, but in problem 16 you used the film temperature — I thought film temperature was standard for convection?

A: The film temperature approach in problem 16 is the correct one — I made an error in problem 15 by using the surface temperature instead of the film temperature (which should be 85°F). It doesn't change the answer because the properties are close over that range, but you should use film temperature consistently.

OH 53: HVAC: Heat Transfer-15

Q: For Heat Transfer 15, at what temperature should the Prandtl number and kinematic viscosity be looked up — 100°F (pipe surface) or 70°F (ambient)?

A: It should be the film temperature — the average of surface (100°F) and ambient (70°F) — which gives 85°F. I used 100°F in my solution, which is technically incorrect but doesn't shift the answer choice because the property values don't change much over that range.

OH 54: HVAC: Heat Transfer-15

Q: For Heat Transfer 15 with a 100°F pipe in a 70°F room, should I use the film temperature (85°F) or the surface temperature for air property lookups?

A: Use the film temperature — always, for natural convection problems. The 100°F I used in the solution is an oversight; for any similar problem, use the average of the surface and ambient temperatures.

OH 67: HVAC: Heat Transfer-15

Q: Three questions on Heat Transfer 15: (1) Can I use h = 1.2 as a typical convection coefficient value? (2) Why use kinematic viscosity at 100°F rather than 70°F? (3) When can I ignore the pipe outside diameter?

A: The typical h = 1.2 value is a rough estimate only — you wouldn't use it when asked to calculate h from first principles as in this problem. The temperature for property lookup should be the film temperature (85°F), not 100°F — that was an error in my solution — and the pipe's outside diameter is needed for the heat transfer area calculation unless the problem explicitly says to ignore it.

OH 72: HVAC: Heat Transfer-15

Q: In Heat Transfer 15, you used lambda (λ) for thermal conductivity rather than K — should I memorize that thermal conductivity can appear under different variable names in the handbook?

A: Nothing to memorize ahead of time — but having worked through this problem, you won't forget it. Engineering references aren't always consistent with variable naming, so let the units guide you whenever the symbol isn't familiar.

OH 80: HVAC: Heat Transfer-15

Q: I'm confused about which temperature to use for property lookups — in Heat Transfer 15 you used 100°F, but in problem 16 you used the film temperature. Is the difference because one involves air and the other water?

A: The fluid type doesn't change the rule — both problems should use the film temperature, and I made an error in problem 15 by using the surface temperature. Check the office hours archive for previous discussions on this exact question; the consistent answer is always film temperature for convection property lookups.

OH 82: HVAC: Heat Transfer-15

Q: In Heat Transfer 15, how can both the 'Properties of Air at Atmospheric Pressure' table and the 'Properties of Air at Low Pressure' table be used for the same problem — is this common?

A: What's confusing here is that 'low pressure' in the handbook refers to pressures that most engineers would still consider very high — it's a quirk of the handbook's labeling, not a warning that the air is in a vacuum. For this problem at atmospheric conditions, both tables give essentially the same property values, so either works fine.

OH 95: HVAC: Heat Transfer-15

Q: In Heat Transfer 15, why wasn't the film temperature used for the fluid property lookups?

A: I should have used the film temperature (85°F) — this has come up in office hours multiple times. The temperatures 70°F and 100°F are close enough that the property values don't shift the answer choice, which is why the error wasn't immediately obvious.

OH 96: HVAC: Heat Transfer-15

OH 119 · April 28, 2026

Q: For a long horizontal cylinder in a stationary fluid, why is D (not L) used in the Rayleigh number — and where is the Prandtl number equation found?

A: The Rayleigh number subscript indicates the characteristic length for the geometry: Ra_D for cylinders uses diameter, while Ra_L for flat plates uses length — these are two separate equations in the reference handbook, not a substitution. The Prandtl number equation (Pr = C_p·μ/k) is in Section 5.3.1, but in practice it's faster to look Pr up directly from the Properties of Air table at the given temperature since it's essentially a function of temperature alone.

Q: The solution uses 100°F (pipe surface) for property lookups rather than 70°F (ambient) — can you explain why?

A: That's actually incorrect in my solution — the film temperature of 85°F is the right value to use. It doesn't change the answer because the properties at 70°F, 85°F, and 100°F are all close, but technically the film temperature is always what you should use for convection.