Arthur Muehling received his B.S. in agricultural engineering from the University of Illinois in 1950. He then received his M.S. degree from the University of Missouri in 1951. From 1952 to 1956 he served in the U. S. Air Force as a weather officer.
He began his military training by studying meteorology and then spent three years forecasting weather at bases in Louisiana, French Morocco, and Colorado Springs.
He started in the department in January 1956 as a research associate working on environmental conditions for baby pigs. He also began teaching farm buildings courses and in 1961 became an extension buildings specialist working on livestock housing and waste management, with a major emphasis on swine. In 1968, he received a grant from the National Pork Producers Council to summarize his work on swine housing and waste management, which was printed as Swine Housing and Waste Management: A Research Review. He served on a committee that drafted the first proposed livestock waste regulations for Illinois in the early 1970s. In 1975, Muehling was local arrangements chair for the ASAE International Symposium on Livestock Waste, and in 1980, he was overall chair for the international symposium held in Amarillo.
He led Illinois swine producers on people-to-people goodwill tours to Europe and the Soviet Union in 1974, to Scandinavia and Poland with a stop in Leningrad in 1977, and to the People's Republic of China in 1982. During 1980 and 1981, he spent six months studying confinement swine housing and waste management in Australia, a venture coordinated by the Australian Pig Industry Research Committee.
In 1984, he was inducted into the Farm Builders Hall of Fame sponsored by Farm Building News and in 1985 was recognized by the Illinois Cooperative Extension Service with a Sustained Excellence in Programs and Service Award. He was named a Fellow in the American Society of Agricultural Engineers in 1993.