System of 1st order nonlinear PDE's

[raultrigo]

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]
f is a variable gas velocity function of (t)
h is a constant heat transfer coeff
x is a length meassure [0,1]
t is time [0,infinite]

I would appreciate any help on this matter, thank you,

 

[raultrigo]

Please find attached a similar problem, this is a System of 1st order LINEAR PDEs,

View attachment SYSTEM OF PDE Anzelius.pdf

I have not been able to manipulate this problem in order to approxiamate a solution, thanks,