The heat equation can be written as. ∂ u ∂ t = α ∇ 2 u. where u(x, y, t) is the temperature field that varies in space and time, and α is the thermal diffusivity constant.
In mathematics and physics, the heat equation is a certain partial differential equation. ... The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region
