Heat Equation

In the special case of heat propagation in an isotropic and homogeneous medium in the 3-dimensional space, this equation is

where:
u =u(t, x, y, z) is temperature as a function of time and space;
/ is the rate of change of temperature at a point over time;
uxx, uyy, and uzz are the second spatial derivatives (thermal conductions) of temperature in the x, y, and z directions, respectively
k is a material-specific quantity depending on the thermal conductivity , the density and the heat capacity.