Check conduction through two flat layers with prescribed surface temperatures. Remove all default layers and add exactly two conduction layers, ordered from side A to side B.
1. Calculator Inputs
Select units before entering values.
| Calculator field | Value / setting |
|---|---|
| Solve for | Heat transfer |
| Boundary A / B | 200 / 70 °F |
| Area | 100 ft² |
| Interface temperature unit | °F |
| Layer 1: thickness / conductivity | 1 in / 0.025 Btu/(h·ft·°F) |
| Layer 2: thickness / conductivity | 0.5 in / 0.1 Btu/(h·ft·°F) |
| Other layers | None; remove convection and contact layers |
2. Step-by-step Math
Resistance per unit area
R1 = (1/12)/0.025 = 3.333333333 h·ft²·°F/Btu R2 = (0.5/12)/0.1 = 0.416666667 h·ft²·°F/Btu Rtotal = 3.75 h·ft²·°F/Btu
Divide inches by 12 before using conductivity stated per foot.
Heat flux and total rate
U = 1/Rtotal = 0.266666667 Btu/(h·ft²·°F) q″ = (200−70)/3.75 = 34.666666667 Btu/(h·ft²) Q = q″ A = 34.666666667 × 100 = 3466.666666667 Btu/h
Area multiplies heat flux to give total heat-transfer rate.
Interface temperature
Tinterface = 200 − q″ R1 Tinterface = 200−34.666666667×3.333333333 ≈ 84.4°F TB = 84.444444444−34.666666667×0.416666667 = 70°F
Each layer has the same heat flux at steady state.
3. Compare Your Answers
Keep full precision until the final result. Display rounding may differ; compare answers rounded to three significant figures; retain unrounded intermediate values.
| Result | Expected answer | Your answer |
|---|---|---|
| Total resistance per area | 3.75 h·ft²·°F/Btu | __________ |
| Heat flux | 34.7 Btu/(h·ft²) | __________ |
| Heat-transfer rate | 3,470 Btu/h | __________ |
| Interface temperature | 84.4°F | __________ |
Second check
Double the area to 200 ft². Total heat transfer doubles to 6,930 Btu/h; heat flux and interface temperature stay the same.
4. Assumptions and Method
One-dimensional steady flat-wall conduction with constant, hypothetical conductivities. With no convection layers, the boundary values are surface temperatures; no fluid-film temperature drop is represented. Radiation and contact resistance are excluded.
Equation definitions and implementation: open calculator. See also calculation methodology.