2. Heat equation: which model to use?

2.1 Example 1: Semi-infinite wall under 1D transient conditions

Figure 1 shows a semi-infinite mass in the x direction being excited on its x = 0 face by a heat flux of density u (W · m ^–2 ) at the initial time t = 0. The initial temperature T ₀ (x) is a priori non-uniform. A temperature sensor is implanted at a depth x _c in the massif and delivers a signal y. From the initial instant, a transient one-dimensional temperature field T (x, t) develops in the massif.