The 1D transient heat equation is solved for conduction and heat transfer to the surface of a steel slab. This is useful for heat treatment, especially for estimating the soaking time.

The heat equation is a parabolic partial differential equation (PDE) that shows how heat changes over time in a solid medium. In one dimension is expressed as: ∂ w ∂ t = α ∂ 2 w ∂ x 2 where x and t ...

We examine a heat problem in 1D. Assume that a rod with given temperature distribution u_0(x) is cooled to temperature 0 on the exteriors at 0 and pi. Assume that u(x,t) for the Temperature at point x ...