Thermal Conductivity & Heat Transfer Calculator

Heat Transfer Guide

What do I need to know about Fourier's Law of Conduction?

Q = -kA(dT/dx). For steady-state through a flat wall: Q = kAΔT/L. Where Q = heat flow rate (W), k = thermal conductivity (W/m·K), A = area (m²), ΔT = temperature difference (°C or K), L = thickness (m). Example: brick wall (k=0.72) 100mm thick, 20m² area, 20°C inside vs 5°C outside. Q = 0.72 × 20 × 15 / 0.1 = 2,160 W. That's a 2.16kW heater of heat loss continuously — enormous. This is why uninsulated solid brick walls are so expensive to heat. Adding 100mm mineral wool insulation: total resistance to heat flow increases substantially, cutting heat loss through the wall by a large factor for a relatively modest cost.

What should I know about R-Value and U-Value?

R-value (thermal resistance): R = L/k. Higher R = better insulator. Units: m²·K/W. R-values add for layers in series. Total wall R = R_brick + R_insulation + R_plasterboard + air films. U-value: heat transfer coefficient = 1/R_total. Lower U = better insulator. Building Regs Part L: walls U-value 0.18 W/m²·K or below for new builds. Roofs 0.13. Windows 1.4. Floors 0.18. These targets require modern insulation thicknesses: 100-150mm mineral wool in walls. 270mm+ in lofts. Triple glazing for windows.

What should I know about Insulation Materials Compared?

Common insulation k-values (lower = better): vacuum insulated panel: 0.007 W/m·K (best — expensive). Aerogel: 0.015. PIR/PUR foam: 0.022. Phenolic foam: 0.020. Mineral wool: 0.035-0.040. EPS polystyrene: 0.035. Sheep's wool: 0.039. Cellulose: 0.040. Hemp: 0.040. To achieve U-value 0.18 (Part L target) using each: PIR: 120mm thickness needed. Mineral wool: 200mm. Cellulose: 220mm. PIR is space-efficient (thinner walls) but expensive and embodied carbon higher. Mineral wool: a good balance of performance, cost, and lower embodied carbon, which is why it remains one of the most widely used insulation materials in UK homes.

What should I know about Beyond Conduction?

Total heat transfer through walls involves three mechanisms. Conduction: through solid materials (the dominant mechanism this calculator models). Convection: air movement on both surfaces. Surface heat transfer coefficient ~7-25 W/m²·K. Radiation: longwave IR exchange. Significant especially for low-emissivity surfaces (modern foil-faced insulation, low-E glass coatings). Window U-values: a 'triple glazed' window achieves U-value of approximately 1.0 W/m²·K — mostly due to the multiple air or argon-filled gaps between panes, which resist heat flow far more effectively than the glass itself.

What should I know about Fourier's Law in Detail?

Fourier's law of heat conduction states Q/t = k×A×ΔT/d, where Q/t is heat transfer rate (watts), k is the material's thermal conductivity (W/m·K), A is cross-sectional area, ΔT is temperature difference across the material, and d is thickness. For a glass window (k≈0.96 W/m·K) 4mm thick, 1m² area, with a 15°C indoor-outdoor difference: Q/t = 0.96×1×15/0.004 = 3600W — an enormous heat loss, which is exactly why single-glazed windows are such poor insulators and why double glazing (adding an air gap, k≈0.025 W/m·K for still air) dramatically cuts heat loss despite adding only a few millimetres of material. This formula shows conduction heat loss is directly proportional to area and temperature difference, but inversely proportional to thickness — doubling insulation thickness halves the heat loss rate, all else equal.

What do I need to know about U-Values and Building Regulations?

U-value (W/m²K) is the overall heat transfer coefficient through a complete building element (wall, roof, window), combining all layers' conductivities and thicknesses, plus surface air-film resistances — it's essentially 1/(total thermal resistance), where total resistance is the sum of each layer's d/k plus the inside and outside air film resistances. Lower U-values mean better insulation. UK Building Regulations Part L currently require maximum U-values around 0.18 W/m²K for new-build walls, 0.13 for roofs, and 1.4 for windows (double glazing with low-E coating typically achieves around 1.2-1.6). A cavity wall with 100mm mineral wool insulation (k≈0.035 W/m·K) achieves a far lower U-value than the same wall uninsulated, which is why retrofitting cavity wall insulation is one of the most cost-effective energy efficiency improvements available to older UK housing stock.

What do I need to know about Thermal Resistance in Series?

A real wall is rarely a single material — it's layers of brick, insulation, and plasterboard, each with its own thermal resistance R = thickness/conductivity. Because heat must pass through each layer in turn, their resistances add just like resistors in a series electrical circuit: R_total = R₁ + R₂ + R₃ + …, and the overall U-value is simply U = 1/R_total. This is exactly why adding even a thin layer of a very low-conductivity insulating material can dramatically cut a wall's overall heat loss — its resistance adds directly onto whatever the brick and plaster were already providing.

What should I know about Metals and the Wiedemann-Franz Law?

Metals are good conductors of both heat and electricity, and this is not a coincidence: both properties stem from the same free electrons moving through the metal's lattice. The Wiedemann-Franz law captures this link quantitatively, stating that the ratio of thermal conductivity k to electrical conductivity σ, divided by absolute temperature T, is approximately the same constant (the Lorenz number, about 2.44 × 10⁻⁸ WΩ/K²) across most metals: k/(σT) ≈ L. This holds because the same free electrons that carry electric current also carry thermal energy as they move and collide within the lattice, so whatever makes a metal a better electrical conductor (more free electrons, fewer scattering collisions) tends to make it a better thermal conductor by a proportional amount. This is why copper and silver, excellent electrical conductors, are also among the best thermal conductors, while poor electrical conductors like most ceramics and plastics are also poor thermal conductors — in those insulating materials, heat is instead carried mainly by lattice vibrations (phonons) rather than free electrons, so the Wiedemann-Franz relationship, which assumes electron-dominated conduction, does not apply to them.

Worked Example: Heat Loss Through a Wall

A brick wall has thermal conductivity k = 0.7 W/m·K, thickness L = 0.25 m, and area A = 12 m². The inside is 20°C and the outside is 5°C, a temperature difference ΔT = 15°C. Using Fourier's law: Q/t = kA(ΔT)/L = 0.7 × 12 × 15 / 0.25 = 126 / 0.25 = 504 W So the wall loses heat at 504 W continuously while that 15°C difference is maintained — over a 24-hour period, that's 504 W × 24 h = 12,096 Wh ≈ 12.1 kWh of heat lost through this one wall alone. Now add 100 mm of mineral wool insulation (k ≈ 0.04 W/m·K) as an extra layer in series. The insulation's own thermal resistance is R_ins = L/k = 0.1/0.04 = 2.5 m²K/W, compared to the brick's R_brick = 0.25/0.7 ≈ 0.357 m²K/W. Total resistance R_total = 0.357 + 2.5 = 2.857 m²K/W, and the new heat loss is Q/t = A·ΔT/R_total = 12 × 15 / 2.857 ≈ 63 W — an 87% reduction, showing why even a relatively thin layer of a genuinely good insulator (low k) can outperform a much thicker layer of a poor one (brick).

Thermal Conductivity Reference Values

The roughly 15,000-fold range between copper and still air explains why double glazing works by trapping a thin layer of still (non-convecting) air or inert gas between panes, rather than trying to make the glass itself a better insulator — air's extremely low conductivity is wasted, however, the moment it's free to circulate, since moving air transfers heat by convection far faster than still air conducts it, which is why insulation materials are engineered specifically to trap air in tiny pockets too small to support convective currents.

Worked Example: Comparing Two Insulation Choices by R-value

A homeowner compares 100mm of mineral wool (k = 0.04 W/m·K) against 50mm of rigid foam board (k = 0.025 W/m·K) for the same wall area. R-value = thickness/k: mineral wool gives R = 0.10/0.04 = 2.5 m²K/W, while the thinner foam board gives R = 0.05/0.025 = 2.0 m²K/W. Despite being half the thickness, the foam board's lower conductivity doesn't quite make up the difference here, so the thicker mineral wool actually provides slightly better insulation (higher R-value) in this comparison — a reminder that comparing insulation products by thickness alone, or by conductivity alone, can be misleading; R-value (thickness divided by conductivity) is the number that actually determines insulating performance.