Calculate steady-state heat transfer through plane walls and cylindrical pipes. Build thermal resistance networks with multi-layer walls and convection, and compute heat rate, heat flux, and U-values.
Common: fiberglass ~0.04, concrete ~1.0
Choose a single- or multi-layer wall or a cylindrical pipe, enter temperatures, materials, and geometry. We'll build the thermal resistance network and compute heat transfer rate, heat flux, and which layer controls the insulation.
Conduction is the transfer of heat through a solid material due to a temperature difference. Heat flows from hot to cold regions as energy is passed from molecule to molecule. In steady-state conditions, the temperature profile through the material remains constant over time—heat entering one side equals heat leaving the other.
Fourier's law describes one-dimensional conduction: q = -k·A·(dT/dx), where k is thermal conductivity, A is area, and dT/dx is the temperature gradient. For a uniform slab of thickness L, this simplifies to q = k·A·ΔT/L.
Just as electrical resistance relates voltage to current (V = IR), thermal resistance relates temperature difference to heat flow:
For different configurations:
For resistances in series (layers stacked together), they simply add: R_total = R₁ + R₂ + R₃ + ...
For flat walls (building walls, flat insulation panels), heat flows through a constant cross-sectional area. The conduction resistance is R = L/(k·A).
For cylindrical walls (pipes, insulation around pipes), heat flows radially outward through surfaces of increasing area. The resistance formula accounts for this: R = ln(r₂/r₁)/(2πkL). The natural logarithm arises from integrating Fourier's law in cylindrical coordinates.
Real walls often have multiple layers: drywall, insulation, sheathing, and siding, each with different thermal properties. Each layer contributes its own thermal resistance, and they add in series.
The temperature drop across each layer is proportional to its resistance: ΔT_i = q·R_i. By starting from a known boundary temperature and subtracting each temperature drop, you can find the temperature at every interface. This helps identify where condensation might occur or if any material exceeds its temperature limit.
For building applications, the overall heat transfer coefficient (U-value) is often used:
Lower U-value means better insulation. Building codes specify maximum U-values for walls, roofs, and windows to ensure energy efficiency. Typical values range from U = 0.1–0.3 W/m²·K for well-insulated walls to U = 1–5 W/m²·K for uninsulated assemblies.
| Material | k (W/m·K) | Notes |
|---|---|---|
| Copper | ~400 | Excellent conductor |
| Aluminum | ~200 | Good conductor |
| Steel | ~50 | Moderate conductor |
| Concrete | ~1.0 | Building material |
| Wood | ~0.15 | Natural insulator |
| Fiberglass insulation | ~0.04 | Good insulator |
| Still air | ~0.025 | Excellent insulator |
This calculator assumes:
For building envelope design or industrial applications, consult ASHRAE standards, local building codes, and qualified thermal engineers.
Calculate how materials change size with temperature
Heat transfer, phase changes, and ideal gas calculations
Calculate hydrostatic pressure and forces on submerged surfaces
Flow speed, pressure, and head analysis for fluid systems
Determine flow regime and Reynolds number for fluid flow
Calculate log mean temperature difference for heat exchanger design
Calculate power output and thermal efficiency in heat transfer systems