A parabolic second-order differential equation for the temperature of a substance in a region where no heat source exists: ∂t / ∂τ = (k /ρc )(∂²t / ∂x² + ∂²t / ∂y² + ∂t ²/∂z²), where x, y, and z are space coordinates, τ is the time, t (x, y, z, τ ) is the temperature, k is the thermal conductivity of the body, ρ is its density, and c is its specific heat; this equation is fundamental to the study of heat flow in bodies. Also known as Fourier heat equation; heat flow equation.