I am working with heat exchange problems. I have cermic exchanger with slots for air inlet (ceramic is being heated from warmer inside air) and after period of time the direction is changing and air from the outside remove heat from the ceramic. I am modelling one tiny slot heating (square, 3mmx3mm). I have one PDE equation for solid (here: ceramic, Ts is a modeled temperature):
And other equation for the air heating (Tg is an air temperature, modeled now):
t - time; x - length, m; ro - density, kg/m^3; cp - specific heat,J/(kgK); h - convection coefficient,W/(m^2K); k - thermal conductivity of copper, W/(mK); u - fluid velocity, m/s;
Should I manage it with PDE solver and set the parameters, i.e. for Ts:
c = ro*cp;
f = -k*DuDx;
s = h*(Ts-Tg);
Then, how set the boundary conditions and make Ts nad Tg as a function of the temperature? It should be evaluated for different values during the analysis.