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🧠 What Is the Thermal Resistance Circuit Analogy?
Have you ever solved an electrical circuit with resistors in series and parallel? Now imagine heat flowing through a wall instead of current through a wire. That’s exactly what the thermal resistance analogy is! 🔁
In heat transfer, we often deal with multiple materials and different heat transfer modes (like conduction and convection). Solving this directly can get tricky… but if you map the problem to an electrical circuit, everything becomes way easier!
🧱 The Basic Concept
Just like voltage drives current in electrical circuits, temperature difference drives heat in thermal systems. Here’s the mapping:
| Electrical Concept 🔌 | Heat Transfer Concept ♨️ |
|---|---|
| Voltage (V) | Temperature Difference (ΔT) |
| Current (I) | Heat Transfer Rate (q̇) |
| Resistance (R) | Thermal Resistance (Rth) |
And Ohm’s Law becomes the Heat Transfer Law:
q̇ = ΔT / Rth
🔁 Just like I = V / R
📐 What Is Thermal Resistance?
Thermal Resistance (Rth) tells you how much a material resists heat flow.
It depends on material, geometry, and mode of heat transfer.
🧊 1. Conduction through a Flat Wall:
Where:
- L = thickness of the material (m)
- k = thermal conductivity (W/m·K)
- A = area perpendicular to heat flow (m²)
🔍 This is like a resistor in a wire. A thicker wall or lower conductivity means more resistance to heat.
💨 2. Convection on a Surface:
Where:
- hh = convective heat transfer coefficient (W/m²·K)
- AA = surface area exposed to fluid
🎐 This is like the contact resistance between wire and terminal. Poor convection = high resistance.
🔘 3. Cylindrical Conduction (like pipe insulation):
Where:
- r1, r2 = inner and outer radii of the cylinder (m)
- L = length of the cylinder (m)
- k = thermal conductivity
📌 [Insert ASHRAE diagram from Chapter 4 on concentric cylinder heat flow here.]
🧱 Heat Transfer Through Building Materials – Instant Quiz
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What is the dominant mode of heat transfer in walls?
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What does the symbol
krepresent in Fourier’s Law?
-
A higher R-value means:
-
Which material has the highest thermal conductivity?
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Which part of the formula is affected by wall thickness?
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Emissivity describes how much a surface:
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Which surface emits more radiation?
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If you double insulation thickness, heat transfer will:
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Which unit is used for thermal conductivity?
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Which formula gives thermal resistance?
🧠 Composite Wall Example (Series)
Say we have multiple layers in a wall:
🧱 Brick → 🧊 Insulation → 💨 Outside Air
Each layer has its own resistance. Total resistance in series:
Then, total heat flow:
🔀 Parallel Path Example (Walls with Studs)
Imagine a wall with wooden studs and fiberglass insulation side-by-side.
Two paths = parallel thermal resistances:
Where:
- R1 = resistance through fiberglass
- R2 = resistance through wood
Then again,
📌 [Insert ASHRAE table of material thermal conductivities for insulation and wood]
⚙️ Real-World Applications
- ✅ HVAC Ducting: Estimating how much heat is lost along duct walls
- ✅ Pipe Insulation: Designing multi-layer insulation for steam or chilled water pipes
- ✅ Building Envelope: Calculating U-values and R-values for walls and roofs
🧮 Bonus: Thermal Circuit for a Wall with Outside Air
So the full resistance:
Then,
🔍 Key Takeaways
✨ Using the thermal resistance analogy:
- Simplifies complex heat transfer problems
- Lets us use electrical circuit logic 🧠
- Helps in sizing insulation, estimating losses, and optimizing energy efficiency!
🧱 Composite Wall Thermal Resistance Calculator
| Location | Description | h Value (W/m²·K) |
|---|---|---|
| Indoor Air (Natural) | Still air inside room | 8.3 |
| Indoor Air (Forced) | Air movement due to fan/AC | 25 |
| Outdoor Air (Still) | No wind | 10 |
| Outdoor Air (Windy) | Breezy or windy conditions | 25–60 |
