Fourier's Law: Q = k × A × ΔT / L | Conduction Heat Flow | Thermodynamics Tool
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📝 Step-by-step solution
Select what to calculate and enter values
💡 Q = heat flow (W) | k = thermal conductivity (W/m·K) | A = area (m²) | ΔT = temp diff (K/°C) | L = thickness (m)
📖 How to Use This Heat Transfer Calculator
1
Select what you want to calculate - Heat Flow (Q), Thermal Conductivity (k), Area (A), Temperature Difference (ΔT), or Thickness (L).
2
Enter the known values - For heat flow: enter k, A, ΔT, and L. For other variables, enter the remaining four values.
3
Click "Calculate" - Get your result with a complete step-by-step solution.
🔥 Fourier's Law of Heat Conduction
Fourier's law states that the rate of heat transfer through a material is proportional to the negative temperature gradient and the area perpendicular to the heat flow. This fundamental principle of heat transfer is expressed as: Q = k × A × ΔT / L
Where Q is the heat transfer rate (Watts), k is thermal conductivity (W/m·K), A is cross-sectional area (m²), ΔT is temperature difference (K or °C), and L is thickness (m).
📊 Heat Transfer Formulas
Heat Flow (Q): Q = k × A × ΔT / L Thermal Conductivity (k): k = Q × L / (A × ΔT) Area (A): A = Q × L / (k × ΔT) Temperature Difference (ΔT): ΔT = Q × L / (k × A) Thickness (L): L = k × A × ΔT / Q
🔬 Common Thermal Conductivity Values
Diamond: 1000-2600 W/m·K (best conductor)
Silver: 429 W/m·K (best metal conductor)
Copper: 401 W/m·K (common in heat sinks)
Aluminum: 237 W/m·K (lightweight conductor)
Steel: 43-58 W/m·K (varies by alloy)
Glass: 0.8-1.0 W/m·K (insulator relative to metals)
Air: 0.026 W/m·K (trapped air is excellent insulator)
💡 Applications of Heat Transfer Calculation
Building Insulation: Calculating heat loss through walls to size heating systems
Heat Sinks: Designing cooling fins for electronics
Refrigeration: Insulation thickness for cold storage
Engine Cooling: Radiator and cooling system design
HVAC: Determining heating/cooling loads for buildings
Power Cables: Calculating temperature rise from electrical resistance
❓ Frequently Asked Questions (FAQ)
What are the three modes of heat transfer?
The three modes are: Conduction (through solids), Convection (through fluids with bulk motion), and Radiation (electromagnetic waves). This calculator focuses on conduction using Fourier's law.
What is thermal conductivity?
Thermal conductivity (k) is a material property that indicates how well it conducts heat. Higher k means better conductor (like copper), lower k means better insulator (like fiberglass).
Does the calculator handle composite walls?
This calculator is for single-layer conduction. For composite walls, you would need thermal resistance networks (R_total = R1 + R2 + ...). Individual layers can be calculated separately.
What is the difference between heat flow and heat flux?
Heat flow (Q) is the total heat transfer rate in Watts. Heat flux (q") is heat flow per unit area (W/m²). Heat flux = Q / A, also expressed as q" = k × ΔT / L.
Does temperature difference use Celsius or Kelvin?
Both work because temperature difference (ΔT) is the same in Celsius and Kelvin. A 20°C difference equals a 20 K difference. The calculator accepts either.
What is the R-value in insulation?
R-value is thermal resistance: R = L/k (m²·K/W). Higher R-value means better insulation. Building insulation often uses R-value; this calculator can solve for L or k to find equivalent values.