How to Calculate Heat Flow Rate

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Heat Flow Rate Calculator (Fourier's Law)

Calculation Results:

Heat Flow Rate (Q): 0 Watts (W)

Temperature Gradient (ΔT): 0 °C

*A positive value indicates heat moving from the hot side to the cold side.

function calculateHeatFlow() { var k = parseFloat(document.getElementById('thermalK').value); var A = parseFloat(document.getElementById('surfaceArea').value); var T1 = parseFloat(document.getElementById('tempHot').value); var T2 = parseFloat(document.getElementById('tempCold').value); var L = parseFloat(document.getElementById('thicknessL').value); if (isNaN(k) || isNaN(A) || isNaN(T1) || isNaN(T2) || isNaN(L) || L <= 0) { alert("Please enter valid positive numbers. Thickness must be greater than zero."); return; } var deltaT = T1 – T2; // Formula: Q = (k * A * deltaT) / L var Q = (k * A * deltaT) / L; document.getElementById('qResult').innerText = Q.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('dtResult').innerText = deltaT.toFixed(2); document.getElementById('resultBox').style.display = 'block'; }

How to Calculate Heat Flow Rate (Conduction)

Understanding heat flow rate is essential for engineering, architecture, and physics. It describes the amount of heat energy transferred per unit of time through a material. For steady-state conduction, we use Fourier's Law of Heat Conduction.

The Heat Flow Formula

Q = (k × A × ΔT) / L

Where:

  • Q: Heat flow rate, measured in Watts (W) or Joules per second (J/s).
  • k: Thermal conductivity of the material (W/m·K). This represents the material's ability to conduct heat.
  • A: The cross-sectional surface area through which heat is flowing (m²).
  • ΔT (T₁ – T₂): The temperature difference across the material (°C or K).
  • L: The thickness or length of the material through which the heat travels (m).

Practical Example

Imagine you have a single-pane glass window with the following specifications:

  • Thermal Conductivity (k): 0.8 W/m·K
  • Surface Area (A): 2.0 m²
  • Inside Temperature (T₁): 22°C
  • Outside Temperature (T₂): -5°C
  • Glass Thickness (L): 0.005 meters (5mm)

Step 1: Calculate ΔT. 22 – (-5) = 27°C.

Step 2: Apply the formula: Q = (0.8 × 2.0 × 27) / 0.005.

Step 3: Q = 43.2 / 0.005 = 8,640 Watts.

This means 8,640 Joules of energy escape through that window every second.

Common Thermal Conductivity Values (k)

Material k (W/m·K)
Copper 385.0
Concrete 0.8 – 1.3
Glass 0.8
Wood 0.12 – 0.15
Fiberglass Insulation 0.04

Frequently Asked Questions

Does the heat flow rate change with time?
In this calculator, we assume "steady-state" conduction, meaning the temperatures on both sides remain constant. In real-world scenarios (transient heat transfer), the rate changes as materials warm up or cool down.

Why is thickness in the denominator?
The thicker the material, the more resistance it provides to heat flow. Therefore, increasing the thickness (L) decreases the heat flow rate (Q).

How do I convert Celsius to Kelvin for this?
For ΔT calculations, you don't need to convert! A difference of 1 degree Celsius is the same as a difference of 1 Kelvin.

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