Narasimhan’s article provides some interesting insights into Fourier and his times.

“In 1802, upon his return to France from Napoleon’s Egyptian campaign, Fourier was appointed perfect of the department of Isere. Despite heavy administrative responsibilities, Fourier found time to study heat diffusion. He was inspired by deep curiosity about Earth and such phenomena as the attenuation of seasonal temperature variations in Earth’s subsurface, oceanic and atmospheric variations in Earth’s subsurface, oceanic and atmospheric circulation driven by solar heat, and the background temperature of deep space. […]For more insight on Fourier’s life and times, see Keston’s article Jospeh Fourier: Policitian and Scientist. It begins

Thermal conductivity, appropriate for characterizing the internal conduction, was defined by Fourier as the quantity of heat per unit time passing through a unit cross-section divided by the temperature difference of two constant-temperature surfaces separated by unit distance […] Fourier presented his ideas in an unpublished 1807 paper submitted to the Institut de France.

Fourier was not satisfied with the 1807 work. It took him an additional three years to go beyond the discrete finite-difference description of flow between constant-temperature surfaces and to express heat flow across an infinitesimally thin surface segment in terms of the temperature gradient.

When Fourier presented his mathematical theory, the nature of heat was unknown […] Fourier considered mathematical laws governing the effects of heat to be independent of all hypotheses about the nature of heat. […] No method was available to measure flowing heat. Consequently, in order to demonstrate that his mathematical theory was physically credible, Fourier had to devise suitable experiments and methods to measure thermal conductivity.

It is not widely recognized that in his unpublished 1807 manuscript and in the prize essay he submitted to the Institut de France in 1811, Fourier provided results from transient and steady-state experiments and outlined methods to invert exponential data to estimate thermal conductivity. For some reason, he decided to restrict his 1822 masterpiece, The Analytical Theory of Heat, to mathematics and omit experimental results.”

“The life of Baron Jean Baptiste Joseph Fourier (1768 - 1830) the mathematical physicist has to be seen in the context of the French Revolution and its reverberations. One might say his career followed the peaks and troughs of the political wave. He was in turns: a teacher; a secret policeman; a political prisoner; governor of Egypt; prefect of Isère and Rhône; friend of Napoleon; and secretary of the Académie des Sciences. His major work, The Analytic Theory of Heat, (Théorie analytique de la chaleur) changed the way scientists think about functions and successfully stated the equations governing heat transfer in solids. His life spanned the eruption and aftermath of the Revolution; Napoleon's rise to power, defeat and brief return (the so-called Hundred Days); and the Restoration of the Bourbon Kings.”

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