Thermal Conduction Calculator
Enter conductivity k, area A, temp difference ΔT, time t and thickness d to compute conducted heat Q=k·A·ΔT·t/d. k=0.8, A=2, ΔT=20, t=3600, d=0.1 → 1.15 MJ.
Input Data
Results
At a glance:Thermal conduction is heat transfer through a material by microscopic particle collisions and vibrations, flowing from hot to cold; it is the dominant mechanism in solids. The steady-state rate follows Fourier's law of heat conduction. Over a time t, the total heat through a slab is Q=k·A·ΔT·t/d, where k is thermal conductivity (W/(m·K), an intrinsic property), A is the cross-sectional area (m²), ΔT is the temperature difference (K or °C), d is the thickness along heat flow (m), and t is time (s); Q is in joules. Influencing factors: (1) material — higher k (metals) conducts faster, lower k (foam, air) insulates; (2) area — larger A conducts more (proportional); (3) temperature difference — larger ΔT drives stronger flow (proportional); (4) thickness — thicker d raises thermal resistance and reduces flow (inversely). That is why thick walls, double glazing and thick blankets insulate. Example: glass k=0.8 W/(m·K), A=2 m², d=0.1 m, ΔT=20 K, t=3600 s → Q=0.8×2×20×3600/0.1=1,152,000 J (~1.15 MJ). Common k (W/(m·K), room temp): copper ~400, aluminum ~235 (excellent); glass ~0.8, concrete ~1.7, water ~0.6; wood ~0.15, foam ~0.03, air ~0.025 (great insulators). Applications: (1) building insulation — low-k materials (rock wool, foam), thicker walls, double glazing cut A/C heating bills, important for Hong Kong summers; (2) heat-sink design — copper/aluminum CPU coolers; (3) insulated containers, clothing (down traps air); (4) industrial furnace and pipe insulation. Notes: this is a 1-D steady-state formula; use SI units consistently; for power (rate) use P=Q/t=k·A·ΔT/d (W).
Formula
Fourier conduction: Q = k·A·ΔT·t/d (J)
Heat power: P = Q/t = k·A·ΔT/d (W)
Thicker material → higher resistance, less heat (insulation)
Smaller k → better insulation (foam, air)
$$Q = \frac{k\, A\, \Delta T\, t}{d}$$How to Use
- Enter conductivity k (W/m·K) and area A (m²).
- Enter temperature difference ΔT (K), time t (s) and thickness d (m).
- The tool shows total conducted heat Q (J) on the right.
Case Studies
Glass window heat loss in one hour
k=0.8, A=2 m², ΔT=20 K, t=3600 s, d=0.1 m.
Q = 0.8 × 2 × 20 × 3600 / 0.1.
= 1,152,000 J (~1.15 MJ).
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.