How to Calculate Heat Transfer Rate in Heat Exchanger
by
Heat Transfer Rate & LMTD Calculator
Units: W/m²·K
Units: m²
Temperature Profiles
Counter-Flow (Most Efficient)
Parallel-Flow
Calculation Results
Log Mean Temperature Difference (LMTD):
–°C
Heat Transfer Rate (Q):
–Watts
How to Calculate Heat Transfer Rate in a Heat Exchanger
Calculating the heat transfer rate (Q) is fundamental for sizing heat exchangers in industrial processes, HVAC systems, and power plants. The most common method used is the Log Mean Temperature Difference (LMTD) method.
The Heat Transfer Equation
The primary formula for heat transfer in a steady-state heat exchanger is:
Q = U × A × ΔTlm
Where:
Q: Heat transfer rate (measured in Watts or BTU/hr).
U: Overall heat transfer coefficient (W/m²·K). This represents how well heat is conducted through the material and the fluid films.
A: Surface area available for heat transfer (m²).
ΔTlm: Log Mean Temperature Difference (LMTD).
Calculating LMTD (Log Mean Temperature Difference)
LMTD accounts for the fact that temperatures of both fluids change as they flow through the exchanger. The formula is:
ΔTlm = (ΔT1 – ΔT2) / ln(ΔT1 / ΔT2)
The definition of ΔT1 and ΔT2 depends on the flow arrangement:
Counter-Flow Arrangement
Hot and cold fluids move in opposite directions. This is the most efficient configuration.
ΔT1 = Th,in – Tc,out
ΔT2 = Th,out – Tc,in
Parallel-Flow Arrangement
Hot and cold fluids move in the same direction.
ΔT1 = Th,in – Tc,in
ΔT2 = Th,out – Tc,out
Example Calculation
Suppose you have a counter-flow heat exchanger with the following data:
Overall coefficient (U): 600 W/m²·K
Area (A): 5 m²
Hot In: 90°C, Hot Out: 60°C
Cold In: 20°C, Cold Out: 50°C
Calculate ΔT1 = 90 – 50 = 40°C
Calculate ΔT2 = 60 – 20 = 40°C
If ΔT1 = ΔT2, the LMTD is simply 40°C (arithmetic mean).
Q = 600 × 5 × 40 = 120,000 Watts (or 120 kW).
function calculateHeatTransfer() {
var u = parseFloat(document.getElementById('u_coeff').value);
var a = parseFloat(document.getElementById('surface_area').value);
var thi = parseFloat(document.getElementById('t_h_in').value);
var tho = parseFloat(document.getElementById('t_h_out').value);
var tci = parseFloat(document.getElementById('t_c_in').value);
var tco = parseFloat(document.getElementById('t_c_out').value);
var flow = document.getElementById('flow_type').value;
var errorDiv = document.getElementById('error_msg');
var resultDiv = document.getElementById('results_section');
errorDiv.style.display = 'none';
resultDiv.style.display = 'none';
if (isNaN(u) || isNaN(a) || isNaN(thi) || isNaN(tho) || isNaN(tci) || isNaN(tco)) {
errorDiv.innerHTML = "Please enter all values to perform the calculation.";
errorDiv.style.display = 'block';
return;
}
var dt1, dt2;
if (flow === 'counter') {
dt1 = thi – tco;
dt2 = tho – tci;
} else {
dt1 = thi – tci;
dt2 = tho – tco;
}
// Validation: Heat must flow from hot to cold
if (dt1 <= 0 || dt2 <= 0) {
errorDiv.innerHTML = "Temperature cross detected or invalid temperature inputs. The hot fluid must be hotter than the cold fluid at both ends.";
errorDiv.style.display = 'block';
return;
}
var lmtd;
if (Math.abs(dt1 – dt2) < 0.001) {
lmtd = dt1; // Avoid division by zero, use arithmetic mean if delta T's are equal
} else {
lmtd = (dt1 – dt2) / Math.log(dt1 / dt2);
}
var q = u * a * lmtd;
document.getElementById('lmtd_val').innerHTML = lmtd.toFixed(2);
document.getElementById('q_val_watts').innerHTML = q.toLocaleString(undefined, {maximumFractionDigits: 0});
document.getElementById('q_val_kw').innerHTML = "(" + (q/1000).toFixed(2) + " kW)";
resultDiv.style.display = 'block';
}
This calculator provides a fast way to determine the heat transfer performance of industrial equipment. Whether you are sizing a shell and tube exchanger or a plate heat exchanger, understanding the relationship between surface area and temperature driving force is critical for engineering accuracy.