Calculate the rate of heat flow through a material based on Fourier's Law of Thermal Conduction.
Results
Heat Transfer Rate (Q): 0 Watts (W)
Thermal Resistance (R): 0 K/W
Understanding Heat Transfer Rate Calculation
Heat transfer is the movement of thermal energy from a high-temperature object to a lower-temperature object. When we talk about conduction, we are specifically looking at how heat moves through solid materials. This calculator uses Fourier's Law of Heat Conduction to determine the rate at which energy moves through a specific medium.
The Formula for Conduction
The rate of heat transfer (Q) is calculated using the following equation:
Q = (k × A × ΔT) / d
Q: Heat transfer rate (measured in Watts [W] or Joules per second).
k: Thermal conductivity of the material (W/m·K). This represents how well a material conducts heat.
A: The surface area through which the heat is flowing (m²).
ΔT (Tₕ – T꜀): The temperature difference across the material.
d: The thickness of the material (m).
Practical Example: A Glass Window
Imagine a glass window during winter. You want to know how much heat is escaping from your room.
Thermal conductivity varies wildly between materials. Metals like copper have very high conductivity (~398 W/m·K), making them excellent for heat sinks. Conversely, insulators like fiberglass (~0.04 W/m·K) or air have very low conductivity, which is why they are used to keep buildings warm. Reducing the heat transfer rate is the primary goal of home insulation and energy-efficient window design.
Factors Influencing the Rate of Heat Flow
Based on the formula, we can see that the heat transfer rate increases if you increase the surface area or the temperature difference. However, it decreases if you increase the thickness of the material or use a material with lower thermal conductivity (higher insulation properties).
function calculateHeatTransfer() {
var k = parseFloat(document.getElementById("thermalK").value);
var A = parseFloat(document.getElementById("surfaceArea").value);
var Th = parseFloat(document.getElementById("tempHot").value);
var Tc = parseFloat(document.getElementById("tempCold").value);
var d = parseFloat(document.getElementById("thickness").value);
var resultBox = document.getElementById("htResultBox");
var qDisplay = document.getElementById("qResult");
var rDisplay = document.getElementById("rResult");
if (isNaN(k) || isNaN(A) || isNaN(Th) || isNaN(Tc) || isNaN(d) || d <= 0) {
alert("Please enter valid positive numbers. Thickness must be greater than zero.");
resultBox.style.display = "none";
return;
}
var deltaT = Th – Tc;
// Fourier's Law: Q = (k * A * dT) / d
var Q = (k * A * deltaT) / d;
// Thermal Resistance: R = d / (k * A)
var R = d / (k * A);
qDisplay.innerHTML = Q.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
rDisplay.innerHTML = R.toLocaleString(undefined, {minimumFractionDigits: 4, maximumFractionDigits: 4});
resultBox.style.display = "block";
resultBox.scrollIntoView({ behavior: 'smooth', block: 'nearest' });
}