Who first proposed the heat conduction equation in 1822?

• A. Joseph Fourier
• B. Isaac Newton
• C. James Clerk Maxwell
• D. Ludwig Boltzmann

Answer: (A)

Heat diffusion is modeled by a diffusion equation that links the rate of temperature change at a point to the curvature of the temperature field around that point, based on a proportionality between heat flux and the temperature gradient. Joseph Fourier first put this into a precise mathematical form in 1822 by combining the conservation of energy with a law for heat flux that flows from high to low temperature. This leads to the heat equation, which in one dimension is ∂T/∂t = α ∂^2T/∂x^2, with α being the thermal diffusivity k/(ρc). Fourier also introduced the use of Fourier series to solve conduction problems, laying down the analytical framework in his Théorie analytique de la chaleur. While earlier ideas described cooling behavior in simple terms and later scientists expanded on related physics, Fourier’s 1822 formulation was the first clear proposal of the heat conduction equation itself.