Thermal resistance networks let engineers predict heat flow through walls, pipes, electronics, insulation, and heat exchangers using an analogy to electric circuits. Instead of current driven by voltage, heat transfer rate is driven by temperature difference. Each material layer, fluid film, or imperfect contact adds a resistance that reduces heat flow.
This method matters because it turns complex thermal paths into organized series and parallel networks that can be solved with algebra.
Key Facts
- Steady heat flow through a network is q = ΔT / Rtotal.
- Plane wall conduction resistance is Rcond = L / (kA).
- Convection resistance is Rconv = 1 / (hA).
- Series resistances add as Rtotal = R1 + R2 + R3 + ...
- Parallel heat paths add by conductance: 1 / Rtotal = 1 / R1 + 1 / R2 + ...
- Thermal contact resistance can be modeled as Rcontact = 1 / (hcA) or given directly in K/W.
Vocabulary
- Thermal resistance
- Thermal resistance is the opposition to heat flow caused by a material layer, fluid film, or interface.
- Composite wall
- A composite wall is a wall made from multiple layers of different materials, each with its own thickness and thermal conductivity.
- Convection coefficient
- The convection coefficient h measures how strongly a moving or still fluid transfers heat to or from a surface.
- Contact resistance
- Contact resistance is the extra thermal resistance at an interface caused by surface roughness, air gaps, or imperfect bonding.
- Thermal circuit
- A thermal circuit is a diagram that represents temperature differences as driving forces and heat flow as a current-like quantity.
Common Mistakes to Avoid
- Adding conductivities instead of resistances for layers in series is wrong because each layer blocks the same heat flow, so the correct sum is Rtotal = Σ L/(kA).
- Forgetting convection resistances at the surfaces is wrong because the hot and cold fluids usually do not have the same temperatures as the wall surfaces.
- Using different areas without checking geometry is wrong because R = L/(kA) and R = 1/(hA) require the heat transfer area for that specific path.
- Treating parallel layers as series layers is wrong because parallel paths have the same temperature difference but split the heat flow, so conductances must be added.
Practice Questions
- 1 A plane wall has two layers in series. Layer 1 has L = 0.05 m, k = 0.20 W/(m K), and A = 2.0 m^2. Layer 2 has L = 0.10 m, k = 0.50 W/(m K), and A = 2.0 m^2. If the surface temperatures are 80°C and 20°C, find Rtotal and the heat transfer rate q.
- 2 A composite wall separates hot air at 120°C from cold air at 25°C. The wall area is 3.0 m^2, the inside convection coefficient is 15 W/(m^2 K), the outside convection coefficient is 30 W/(m^2 K), and the wall conduction resistance is 0.80 K/W. Find the total thermal resistance and steady heat transfer rate.
- 3 A wall contains a metal stud path and an insulation path in parallel between the same indoor and outdoor surfaces. Explain which path carries more heat and why, using the ideas of resistance, conductance, and shared temperature difference.