Modelling a solid bed cooled by an uprising gas flow gave the following system of 1st order NONLINEAR PDEs
dv/dt + f(t) * dv/dx = h*(u-v)
du/dt = -h*(u-v)
BC
v(x=0,t) = 0
dv/dx(x=1,t)=0
IC
u(x,t=0) = 1
where:
u, v are temperatures function of (x,t) range [0,1]...