Jonathan Furman Leaming was an American physician and politician. Leaming was of English descent, his great-grandfather was the politician Aaron Leaming Jr. Leaming was the son of William Leaming and Sara Somers and had two sisters and Julia. Leaming attended Brown University. In 1846, he graduated from Jefferson Medical College. Leaming began practicing medicine in Cape May County the following year and did so for fourteen years before having to give up the practice due to poor health, he married Eliza Bennett on February 27, 1849. In 1854 his son Walter S. Leaming was born, who became a state senator. Another son, was born in 1857 and became a politician. Leaming subsequently practiced dentistry. Leaming held a number of county-level offices, including superintendent of schools, county school examiner, trustee of the State Normal School. In 1861 Leaming was elected to the New Jersey Assembly as a Republican, he was elected to the New Jersey Senate in 1862. Leaming served on the committee. Leaming was elected surrogate of Cape May County in 1868 and re-elected in 1873.
He resigned from this position in 1877 to return to the state senate, serving until 1880. Leaming served a number of roles in the Baptist religious organization including deacon, clerk and Sunday school superintendent. Leaming married Josephine Young, a sister of his first wife, on October 24, 1888, he retired from public life in 1898 after an attack of poor health. On April 22, 1907, a fire broke out in Leaming's house in New Jersey, his daughter, Helen F. Leaming, rescued him from the flames and was severely burned. Leaming died on April 25, 1907, from complications from the burns, aged 85
The logarithmic mean temperature difference is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger. For a given heat exchanger with constant area and heat transfer coefficient, the larger the LMTD, the more heat is transferred; the use of the LMTD arises straightforwardly from the analysis of a heat exchanger with constant flow rate and fluid thermal properties. We assume that a generic heat exchanger has two ends at which the hot and cold streams enter or exit on either side. With this definition, the LMTD can be used to find the exchanged heat in a heat exchanger: Q = U × A r × L M T D Where Q is the exchanged heat duty, U is the heat transfer coefficient and Ar is the exchange area. Note that estimating the heat transfer coefficient may be quite complicated; this holds both for cocurrent flow, where the streams enter from the same end, for counter-current flow, where they enter from different ends.
In a cross-flow, in which one system the heat sink, has the same nominal temperature at all points on the heat transfer surface, a similar relation between exchanged heat and LMTD holds, but with a correction factor. A correction factor is required for other more complex geometries, such as a shell and tube exchanger with baffles. Assume heat transfer is occurring in a heat exchanger along an axis z, from generic coordinate A to B, between two fluids, identified as 1 and 2, whose temperatures along z are T1 and T2; the local exchanged heat flux at z is proportional to the temperature difference: q = U / D = U / D, where D is the distance between the two fluids. The heat that leaves the fluids causes a temperature gradient according to Fourier's law: d T 1 d z = k a = − k a Δ T d T 2 d z = k b = k b Δ T where ka and kb are the thermal conductivities of the intervening material at points A and B respectively. Summed together, this becomes d Δ T d z = d d z = d T 2 d z − d T 1 d z = K Δ T where K=ka+kb.
The total exchanged energy is found by integrating the local heat transfer q from A to B: Q = ∫ A B q d z = U D ∫ A B Δ T d z = U D ∫ A B