# Heat Exchanger LMTD Calculator (Log Mean Temperature Difference) Compute the Log Mean Temperature Difference (LMTD) of a heat exchanger for parallel or counter flow. Parallel flow: ΔT₁ = T_h,in - T_c,in and ΔT₂ = T_h,out - T_c,out; counter flow: ΔT₁ = T_h,in - T_c,out and ΔT₂ = T_h,out - T_c,in. LMTD = (ΔT₁ - ΔT₂)/ln(ΔT₁/ΔT₂), or ΔT₁ when ΔT₁ = ΔT₂. A non-positive terminal difference (temperature cross) is physically impossible and is rejected. Optionally, with the overall heat transfer coefficient U (W/(m²·K)) and the heat transfer area A (m²), the heat transfer rate Q = U·A·LMTD (W) is returned. Temperatures are used only as differences: Δ°C = ΔK and Δ°F ×5/9 = ΔK; the LMTD is reported in K. > Canonical page: https://elysiatools.com/en/tools/heat-exchanger-lmtd - **Category:** Math & Numbers - **Keywords:** LMTD, log mean temperature difference, heat exchanger, parallel flow, counter flow, terminal difference, UA, heat transfer, thermal design, shell and tube ## Overview Calculate the log mean temperature difference (LMTD) for parallel-flow or counter-flow heat exchangers using four stream temperatures. The calculator reports LMTD in K and can also calculate heat transfer rate when overall heat transfer coefficient U and area A are provided. ## Inputs - **Flow Arrangement** (select): Flow arrangement: Parallel Flow (both streams in the same direction) or Counter Flow (opposite directions). - **Hot Stream Inlet T_h,in** (number): Hot-stream inlet temperature T_h,in, in the selected Temperature Unit. - **Hot Stream Outlet T_h,out** (number): Hot-stream outlet temperature T_h,out, in the selected Temperature Unit. - **Cold Stream Inlet T_c,in** (number): Cold-stream inlet temperature T_c,in, in the selected Temperature Unit. - **Cold Stream Outlet T_c,out** (number): Cold-stream outlet temperature T_c,out, in the selected Temperature Unit. - **Temperature Unit** (select): Unit of the four stream temperatures. Only differences matter: Δ°C = ΔK and Δ°F ×5/9 = ΔK. - **Overall Heat Transfer Coefficient U (optional)** (number): Overall heat transfer coefficient U in W/(m²·K). Optional; when supplied together with A, the heat transfer rate Q = U·A·LMTD is computed. - **Heat Transfer Area A (optional)** (number): Heat transfer area A in m². Optional; when supplied together with U, the heat transfer rate Q = U·A·LMTD is computed. - **Decimal Places** (number) ## When to use - Estimate the effective temperature driving force in a heat exchanger. - Compare LMTD for parallel-flow and counter-flow arrangements. - Calculate heat transfer rate from U, A, and LMTD during thermal design. ## How it works - Enter the hot-stream inlet and outlet temperatures and the cold-stream inlet and outlet temperatures. - Select parallel flow or counter flow and choose K, °C, or °F as the input temperature unit. - The calculator determines the two terminal temperature differences and applies the LMTD formula. - Optionally enter U in W/(m²·K) and A in m² to calculate Q = U·A·LMTD in watts. ## Use cases - Thermal design of shell-and-tube and other heat exchangers. - Preliminary sizing checks using an overall heat transfer coefficient and heat transfer area. - Engineering review of inlet and outlet temperature measurements for counter-flow or parallel-flow equipment. ## Frequently asked questions ### What does the LMTD calculator calculate? It calculates the log mean temperature difference of a heat exchanger for parallel-flow or counter-flow operation. ### What temperature inputs are required? You need the hot-stream inlet and outlet temperatures and the cold-stream inlet and outlet temperatures. ### What units does the calculator use for LMTD? The result is reported in kelvin (K). Temperature differences in °C equal differences in K, while Fahrenheit differences are converted to K. ### Can it calculate heat transfer rate? Yes. Enter both U and A to calculate Q = U·A·LMTD in watts. ### What happens if a terminal temperature difference is zero or negative? 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