Following Heat Through a Flat Material Layer
Thermal Resistance Across One Layer
Conduction moves thermal energy through a material when its two sides are at different temperatures. Insulation, walls, thermal pads, windows, equipment panels, and furnace linings can often begin with the same flat-layer model. Heat flow rises with conductivity, area, and temperature difference, and falls as thickness increases. The model is deliberately narrow so each physical lever is visible before convection, radiation, and complicated geometry are added.
Fourier's Law with Converted Thickness
The working equation is Heat-transfer rate = conductivity*area*temperature difference/thickness.
A 100 mm insulation layer with conductivity 0.04 W/(m·K), area 10 m², and a 25 K difference passes 0.04×10×25/0.1 = 100 W. Heat flux is 10 W/m². Layer resistance is 0.1/(0.04×10) = 0.25 K/W. If conditions held for 24 hours, the transferred energy would be 2.4 kWh. Multiplying resistance by heat rate returns the 25 K difference.
Model limit: Assumes steady one-dimensional conduction, constant conductivity, uniform thickness, and fixed surface temperatures. Convection and contact resistances are excluded.
A Wall Insulation Example
Ten square metres of insulation is 100 mm thick, has conductivity 0.04 W/(m·K), and separates surfaces differing by 25 K. Thermal resistance is 0.1/(0.04×10) = 0.25 K/W. Heat rate is 25/0.25 = 100 W, heat flux is 10 W/m², and one day transfers 2.4 kWh of heat. Doubling thickness to 200 mm doubles layer resistance and halves heat rate if every other boundary condition stays fixed. Doubling area instead doubles total heat while leaving heat flux unchanged.
A real wall may add inside and outside air films, sheathing, framing, and contact layers. Their series resistances alter the surface-to-surface temperature drops. Wooden or metal studs form parallel paths; averaging conductivity by volume is generally weaker than calculating area-weighted path conductances. The 2.4 kWh is thermal energy, not automatically HVAC electrical consumption. Divide heating demand by equipment efficiency or cooling demand by coefficient of performance with care. For transient warm-up, add heat capacity and time-dependent boundary conditions. Verify the steady estimate with surface-temperature and heat-flux measurements after conditions have settled.
Adding Surface Films and Other Layers
Thermal resistance works much like electrical resistance. Temperature difference plays the role of voltage, heat rate plays the role of current, and thickness divided by conductivity times area is resistance. Layers in series add thermal resistance. Parallel heat paths add conductance. This analogy is useful for assemblies, but it does not mean heat disappears at a resistance; the same steady heat rate crosses every series layer while temperature drops divide among them.
Thermal Bridges Bypass the Nominal Path
Thermal conductivity should match the material, mean temperature, moisture condition, and orientation when those effects matter. Area is normal to the heat-flow direction. Thickness is measured along the heat path and entered in millimetres. A temperature difference in kelvins has the same numerical size as a difference in degrees Celsius. Use surface temperatures for this layer model, not indoor and outdoor air temperatures unless film resistances are handled separately.
Steady Heat Is Not Warm-Up Time
Using air temperatures across a solid while omitting convection resistances can overpredict conduction. Contact gaps, fasteners, framing, and metal edges create thermal bridges that bypass insulation. Another error is assuming conductivity is constant across extreme temperatures. Radiation across cavities and semitransparent materials can also be significant. The calculated steady rate says nothing about warm-up time; thermal mass belongs to a transient energy model.
Heat-transfer rate is total watts crossing the entered area. Heat flux removes area and supports comparisons among sections. Thermal resistance describes the whole layer, whereas an R-value quoted per unit area uses a different convention. Daily kWh converts a thermal leak into energy, but HVAC electrical use depends on equipment coefficient of performance rather than equalling that heat energy directly.
Measurements at the Real Surfaces
Measure surface temperatures on both sides after conditions stabilize, using sensors attached consistently and shielded from radiation where needed. A heat-flux sensor can test the predicted W/m². In buildings, infrared imaging helps locate bypass paths but does not directly measure heat rate without careful boundary data. For multilayer assemblies, list every layer and surface film, add resistances, and isolate repeating bridges such as studs.
Document material source, conductivity condition, true thickness, area, and the temperatures used. State which resistances were omitted. That record makes the first-pass result useful when an assembly model is built later. If safety, condensation, fire performance, or code compliance is involved, use tested material data and the applicable standard. The calculator is best for understanding sensitivity and checking a detailed model's order of magnitude. Moisture can raise insulation conductivity sharply, so dry catalogue data should not silently represent a wet service condition. One-dimensional analysis also needs enough distance from corners and penetrations for lateral heat spreading to be small.