Heat conduction is the transfer of thermal energy through matter by microscopic collisions and interactions. It matters in buildings, electronics, cookware, engines, and clothing because it controls how quickly heat moves from hot regions to cold regions. A layered wall, window, or heat shield can be designed by choosing materials and thicknesses that reduce unwanted heat flow.
The central idea is that heat flows more easily through high-conductivity materials and more slowly through insulating materials.
Key Facts
- Fourier's law for a flat slab: q = kA(Th - Tc)/L
- Thermal resistance of one layer: R = L/(kA)
- Heat flow through one layer: q = Delta T/R
- Series thermal resistances add: Rtotal = R1 + R2 + R3 + ...
- For layers in series: q = (Th - Tc)/Rtotal
- Thermal conductivity k has units W/(m·K), while thermal resistance R has units K/W
Vocabulary
- Heat conduction
- Heat conduction is the transfer of thermal energy through a material from higher temperature to lower temperature without bulk motion of the material.
- Thermal conductivity
- Thermal conductivity is a material property that measures how easily heat conducts through a substance.
- Thermal resistance
- Thermal resistance is the opposition a layer or object provides to heat flow for a given temperature difference.
- Steady state
- Steady state is the condition in which temperatures at each location stay constant over time even though heat is flowing.
- Temperature gradient
- A temperature gradient is the rate at which temperature changes with position inside a material.
Common Mistakes to Avoid
- Using Celsius values instead of temperature differences, which is wrong because conduction equations need Delta T and a difference of 1 °C equals a difference of 1 K.
- Adding thermal conductivities for layers, which is wrong because layers in series are combined by adding thermal resistances, not k values.
- Forgetting the area A in R = L/(kA), which is wrong because a larger cross-sectional area gives more pathways for heat to flow and reduces resistance.
- Assuming thicker material always conducts more heat, which is wrong because increasing thickness L increases thermal resistance and lowers heat flow when other factors are fixed.
Practice Questions
- 1 A 0.20 m thick brick wall has area 12 m² and thermal conductivity k = 0.72 W/(m·K). If the inside is 22 °C and the outside is 2 °C, find the steady heat flow rate through the wall.
- 2 A wall has two layers in series: insulation with L = 0.08 m, k = 0.040 W/(m·K), and plywood with L = 0.015 m, k = 0.12 W/(m·K). The area is 10 m² and the temperature difference is 25 K. Find the total thermal resistance and the heat flow rate.
- 3 Two walls have the same area and the same temperature difference. Wall A is a thin layer of metal, while Wall B is a thick layer of foam insulation. Explain which wall has the larger thermal resistance and why heat flow is smaller through that wall.