Henry Brower Smith was born in Durham, North Carolina, on 1917 July 9. He received a B.S. from the North Carolina State College of Agriculture and Engineering (later North Carolina State University) in 1938, an M.S. from the Virginia Agricultural and Mechanical College and Polytechnic Institute (later Virginia Polytechnic Institute and State University) in 1939, and a Ph.D. from the University of Cincinnati in 1942. All his degrees were in chemical engineering.

Smith was an assistant professor of chemical engineering at Bucknell University from 1941 to 1942, and a research engineer at the Air Reduction Company from 1942 to 1943. After serving as a special projects officer with the U.S. Army's Chemical Warfare Service Technical Command from 1943 to 1946, he was a supervisor of research engineering at the Air Reduction Company from 1946 to 1948, and a professor of chemical engineering at Bucknell University from 1948 to 1951. He then was a technical director at General Foods Corporation from 1951 to 1957, director of research at General Foods from 1957 to 1962, and vice president of Armour Grocery Products Company from 1962 to 1965.

Smith joined the faculty of North Carolina State University as a professor of chemical engineering in 1965. During his career at North Carolina State, he was first associate dean for research and graduate studies of the School of Engineering, then vice provost and dean for university research. He retired as professor emeritus in 1983. In addition, Smith was a member of the Institute of Food Technologists, and a fellow in the American Institute of Chemical Engineers.

From 1970, Smith was a member of the board of directors of the Medical Plastics Corporation of America of Greensboro, North Carolina. Medical Plastics was the manufacturer of "Medi-Gard" brand plastic products, which contained hexachlorophene, an antibacterial agent. Just as the company was developing and marketing its line of Medi-Gard products, news reports spread great popular concern over the toxic danger of hexachlorophene, thus severely damaging consumer confidence in products containing the agent. Medical Plastics believed the U.S. Food and Drug Administration acted irresponsibly by fueling public concern over the safety of hexachlorophene. However, the company was unable to obtain any remedy from that agency, and was apparently forced out of business by the controversy. Smith resigned as a director of Medical Plastics in 1972.