Calculate the Heat Conduction Rate Along the Rod

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Heat Conduction Rate Calculator

Unit: W/m·K
Unit: m²
Unit: °C or K
Unit: °C or K
Unit: meters (m)

Heat Conduction Rate (Q/t):

Understanding Heat Conduction in Solids

Heat conduction is the process by which thermal energy is transferred through a material via molecular collisions and the movement of free electrons. In a solid rod, when one end is heated, the atoms vibrate more vigorously, passing that energy to neighboring atoms throughout the length of the rod.

The Physics Behind the Calculation

The rate of heat transfer through a material is governed by Fourier's Law of Heat Conduction. The formula used by this calculator is:

Q/t = k × A × (Th – Tc) / L

Where:

  • Q/t: The heat conduction rate (measured in Watts or Joules per second).
  • k: Thermal conductivity of the material (W/m·K).
  • A: Cross-sectional area of the rod (m²).
  • Th: Temperature of the hot end.
  • Tc: Temperature of the cold end.
  • L: Thickness or length of the rod (m).

Common Thermal Conductivity Values (k)

Material Conductivity (W/m·K)
Copper401
Aluminum205
Steel50
Glass0.8
Wood0.12 – 0.15

Example Calculation

Suppose you have a Copper rod that is 0.5 meters long with a cross-sectional area of 0.01 m². If one end is at 100°C and the other is at 20°C:

Rate = 401 × 0.01 × (100 – 20) / 0.5
Rate = 401 × 0.01 × 80 / 0.5
Rate = 641.6 Watts

function calculateConduction() { var k = parseFloat(document.getElementById('thermalK').value); var A = parseFloat(document.getElementById('crossArea').value); var Th = parseFloat(document.getElementById('tempHot').value); var Tc = parseFloat(document.getElementById('tempCold').value); var L = parseFloat(document.getElementById('rodLength').value); var resultBox = document.getElementById('resultBox'); var conductionOutput = document.getElementById('conductionOutput'); var calcLogic = document.getElementById('calcLogic'); if (isNaN(k) || isNaN(A) || isNaN(Th) || isNaN(Tc) || isNaN(L)) { alert("Please enter valid numerical values for all fields."); return; } if (L <= 0) { alert("Length of the rod must be greater than zero."); return; } // Fourier's Law: Q/t = k * A * (Th – Tc) / L var tempDiff = Th – Tc; var rate = (k * A * tempDiff) / L; conductionOutput.innerHTML = rate.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4}) + " W"; calcLogic.innerHTML = "Based on k=" + k + ", Area=" + A + "m², ΔT=" + tempDiff + "°, Length=" + L + "m"; resultBox.style.display = 'block'; resultBox.scrollIntoView({ behavior: 'smooth', block: 'nearest' }); }

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