Heat Exchanger Calculator
Determine the Log Mean Temperature Difference (LMTD) and required heat transfer surface area for shell-and-tube heat exchangers. Essential for engineers designing or auditing industrial heating and cooling systems.
About this calculator
A heat exchanger transfers thermal energy between two fluids separated by a wall. The driving force for heat transfer is the temperature difference, but since that difference changes along the exchanger length, engineers use the Log Mean Temperature Difference: LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁ / ΔT₂), where ΔT₁ = T_hot_in − T_cold_out and ΔT₂ = T_hot_out − T_cold_in. The heat duty is then Q = U × A × LMTD, where U is the overall heat transfer coefficient (W/m²K) and A is the surface area (m²). Rearranging gives A = Q / (U × LMTD). This approach assumes steady-state, counter-current or co-current flow, and constant fluid properties along the exchanger length.
How to use
Suppose a hot stream enters at 120 °C and leaves at 80 °C, while a cold stream enters at 30 °C and leaves at 70 °C (counter-current). ΔT₁ = 120 − 70 = 50 °C; ΔT₂ = 80 − 30 = 50 °C. Because both differences are equal, LMTD = 50 °C. If U = 400 W/m²K and the required duty Q = 200,000 W, then A = 200,000 / (400 × 50) = 10 m². Enter all four temperatures and U into the calculator to get LMTD and A instantly.
Frequently asked questions
What is LMTD and why is it used in heat exchanger design?
LMTD stands for Log Mean Temperature Difference. Because the temperature gap between the hot and cold fluids varies continuously along the exchanger, a simple average would overestimate or underestimate the driving force. The logarithmic mean correctly weights the varying difference, giving a single representative value. It is the standard method used in the LMTD design approach per heat transfer textbooks and industry standards like TEMA.
How does counter-current flow affect heat exchanger efficiency compared to co-current flow?
In counter-current flow the hot and cold fluids travel in opposite directions, maintaining a more uniform temperature difference along the entire length of the exchanger. This results in a higher LMTD compared to co-current (parallel) flow for the same inlet and outlet temperatures, meaning less surface area is needed for the same duty. Co-current flow limits the cold outlet temperature to below the hot outlet temperature, making it thermodynamically less efficient. Counter-current designs are therefore preferred whenever space and pressure drop allow.
What happens to the LMTD formula when both temperature differences are equal?
When ΔT₁ equals ΔT₂, the standard logarithmic formula produces a 0/0 indeterminate form. Mathematically, applying L'Hôpital's rule shows the limit equals ΔT₁, so LMTD simply equals that constant temperature difference. The calculator handles this edge case automatically so you still receive a valid result. In practice, equal terminal differences occur in balanced counter-current exchangers with equal capacity-rate products (ṁcₚ) on both sides.