Heat Exchanger Calculator

Sizing a heat exchanger reduces to the rate equation Q equals U times A times LMTD. The heat duty Q comes from the process itself, as mass flow times specific heat times temperature change on whichever side is fully specified. The log mean temperature difference appears rather than a simple average because the driving force decays exponentially along the exchanger; integrating the local temperature difference over the transfer area yields (dT1 minus dT2) divided by the natural log of their ratio. The logarithmic mean is always smaller than the arithmetic mean, so using an arithmetic average would undersize the unit. Which end differences to use depends on configuration: for counterflow, dT1 is hot inlet minus cold outlet and dT2 is hot outlet minus cold inlet, while for parallel flow both are taken at the same physical end. Counterflow is preferred in nearly all services because it yields a larger LMTD for identical terminal temperatures and is the only arrangement that can raise the cold outlet above the hot outlet. The overall coefficient U is a series resistance: 1 over U equals the film resistance on each side, the wall conduction term, and the fouling allowances. Typical clean-service values are 10 to 30 BTU per hour per square foot per degree F for gas-to-gas, 50 to 150 for gas-to-liquid, 150 to 300 for liquid-to-liquid with water, and 500 to 1,000 for condensing steam. Fouling factors from 0.0005 for clean river water to about 0.003 hour square foot degree F per BTU for heavy fuel oil can reduce performance by 10 to 30 percent over a run. The effectiveness-NTU formulation gives an alternative view, defining effectiveness as actual duty over the maximum thermodynamically possible duty, C_min times the inlet temperature difference, with NTU equal to UA over C_min serving as a dimensionless size. Two caveats apply to the results here: multipass shell-and-tube units require an F correction factor because they are not true counterflow, and approach temperatures below roughly 10 to 15 degrees F drive area up steeply for little additional recovery.

Surface heat exchange became an engineering discipline with the marine steam engine. Surface condensers using tube bundles inside a shell were developed in the nineteenth century to recover fresh water for boilers, since seawater feed caused rapid scaling and corrosion, and the shell-and-tube geometry established there proved general enough to survive into every branch of process industry. The theoretical apparatus arrived alongside it: the logarithmic mean temperature difference follows directly from integrating the rate equation along the exchanger, a result available once the fundamentals of convective heat transfer were established in the later nineteenth century. The twentieth century supplied standardization and alternative methods. The Tubular Exchanger Manufacturers Association was formed in 1939 and published mechanical standards defining the letter-code shell, front-head, and rear-head types still specified today, along with recommended fouling resistances that gave designers a common basis for allowances. Donald Kern's Process Heat Transfer, published in 1950, consolidated the correlations and design procedures into the text that trained several generations of process engineers, and his shell-side method remained in routine use long after more accurate stream-analysis approaches, notably the Delaware method and Bell-Delaware correlations, were developed. The effectiveness-NTU approach traces to Wilhelm Nusselt's work around 1930 on exchanger performance and was developed into its modern tabulated form by William Kays and Alexander London at Stanford, whose Compact Heat Exchangers appeared in 1955 and provided the effectiveness relations for the full range of flow arrangements. Standardized performance testing followed with codes such as ASME PTC 12.5 for single-phase exchangers.