Josef Stefan and His Contributions to Heat Transfer

Josef Stefan was a professor of physics at the University of Vienna between 1863 and 1893. During his time in Vienna he was a fruitful researcher in many scientific fields, but he is best known for his work in heat transfer. He was a gifted experimentalist and theoretician who made contributions to conduction, convection and radiation heat transfer. Stefan was the first to accurately measure the thermal conductivity of gases, using a device he invented called the diathermometer. He also determined the diffusion of two gases into each other, a process now known as Maxwell-Stefan diffusion. His work provided experimental verification of the newly formulated kinetic theory of gases published by the great Scottish physicist James Clerk Maxwell. Stefan also experimentally studied the motion of gases induced by evaporation along a liquid surface, a phenomenon known as Stefan flow. In addition, Stefan received data from various expeditions on ice formation in the arctic seas. From that solid/liquid phase change data, he formulated solutions to the moving boundary problem, now called the Stefan problem. The work for which he is most famous is the T radiation law which he deduced from the experimental work of a number of investigators. However, his theory was not widely accepted until his former student, Ludwig Boltzmann, derived the same relation from first principles. In their honor, the T radiation equation is called the Stefan-Boltzmann law. Despite his varied contributions, little is known about Stefan the man. This paper gives some details on his life and describes the seminal work he performed in broad areas of heat transfer. BRIEF HISTORY Josef Stefan (Fig. 1) was born on 24 March 1835, to poor, peasant parents, Aleš Stefan, who was a miller and baker, and Marija Startinik, a maidservant, in the village of St. Peter on the outskirts of Klagenfurt, in modern-day Austria [1]. At the time of his birth, Klagenfurt was part of the multiethnic AustroHungarian empire, and his birthplace was home to a large Slovenian population. Stefan grew up speaking Slovene at home and learned German at school, where he distinguished himself academically. He went on to study at the local Gymnasium where he taught himself mathematics and physics from textbooks [2]. Stefan was a devout Roman Catholic and seriously considered joining the Benedictine Order to become a priest, but instead enrolled at the University of Vienna in 1853. At the University he chose to study mathematics and physics and learn from faculty who could expound what he studied earlier. He graduated in 1857 and taught physics for pharmacy students. He showed an aptitude for research, and published his first paper, “General equations of oscillatory motion,” [3] in the same year that he graduated. At this time he came under the influence of Carl Ludwig, a professor of physiology, who noted Stefan’s technical ability. Under the tutelage of Prof. Ludwig, who was the head of the Physiological Institute at the University of Vienna, Stefan refined his experimental abilities as they studied fluid flow in tubes, an analogy to blood flow in vessels. In 1858, Stefan took and passed his doctoral exam, which until 1872 in Austria, was all that was required to receive a doctorate [4]. No dissertation was necessary, although Ludwig served as his de facto mentor.