HVAC · Heat-Transfer · Problem 10PDFSolution in PDF ↓
HVAC · Heat-Transfer · Problem 10
Problem & Solution
Video Synthesis
Problem: An exterior wall is made up of 4 inch brick cladding with thermal conductivity 3.5 inch mineral fiber bat insulation with a conductance or conducti...
Given: 4 inch brick cladding with thermal conductivity 3; 5 inch mineral fiber bat insulation with a conductance or conducti...
Approach: The external surface of the brick is zero degrees and the inside surface of the gypsum board is maintained at 70 degrees.
Calc: It actually states that the surface of the gypsum board is maintained at 70 and the surface of the brick is maintained at zero.
Calc: So let's draw the 4 inch brick, 3.5 inch insulation and the 5.8 gypsum board.
Result: Best answer choice is a and that jives with our earlier intuition.
Office Hours
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Student questions asked in live office hours about this problem
OH 16: HVAC: Heat Transfer #10
Q: Why do we exclude interior and exterior film coefficients when calculating R and U—is there a quick way to tell whether to include or exclude them?
A: If the problem gives you the film coefficients, include them—it doesn't take much extra effort and they're there for a reason. If they're not given, you'd have to assume values, which is rarely required on the PE exam. The quick rule: use what the problem gives you, and don't assume additional resistance unless you have a value to put there.
OH 19: HVAC: Heat Transfer #10
Q: I found k by multiplying C·L (since C = k/L), then computed L/k to get resistance—is this method correct even though I got a slightly different value?
A: Yes, the method is correct—C = k/L rearranges to k = C·L, and then R = L/k is the standard expression for thermal resistance. A slight numerical difference likely comes from rounding at an intermediate step. Check that you're using the same units for L throughout, and the answer should reconcile.
OH 64: HVAC: Heat Transfer #10
Q: Is there a reason you didn't include film coefficients in the U-factor calculation, and if I add them, does it still lead to the correct answer?
A: If you have values for the film coefficients from the handbook and you included them, that's more rigorous and still valid—the fact that you still got answer A confirms the film coefficients are small relative to the wall resistance. Including them is technically more correct; excluding them is a common simplification when the dominant resistance is clearly in the wall itself. On the exam, include them if the problem provides values or if the answer choices are close.
OH 82: HVAC: Heat Transfer #10
Q: I solved this problem by setting Q_total = Q_brick + Q_insulation + Q_gypsum and using algebra to find the interface temperature—is this the longer way?
A: That approach is perfectly valid—it leverages the fact that heat flux is constant across all layers in steady state, which is exactly what allows you to solve for interface temperatures. The shortcut in the solution sets total heat flux equal to partial heat flux (Q_total = Q_brick) since flux is constant, which is algebraically the same thing and arrives faster. Both get you 3.93°F at the brick/insulation interface.
OH 86: HVAC: Heat Transfer #10
Q: Wouldn't the heat transfer rate Q through the brick be different (higher) than through the insulation, since brick has higher conductivity?
A: No—in steady state, the heat flux (Q per unit area) must be the same through every layer, regardless of material. If the flux were different in adjacent layers, energy would pile up or disappear at the interface, which violates energy conservation. What changes between layers is the temperature gradient, not the flux; a more insulating layer has a larger delta T across it for the same flux.
OH 104: HVAC: Heat Transfer #10
Q: Can I solve this using the R_x/R_total proportion equation from the handbook, and how does that relate to the approach in the solution?
A: Yes—the T_x = T_i − (R_x/R_total)·(T_i − T_o) equation from the handbook is equivalent to equating partial and total heat flux, just rearranged algebraically. If you used it and got the right answer (4.5°F or 3.93°F depending on which interface), great. Know both approaches so you can verify your answer if one method feels uncertain.