A discrete model of the heat exchange process in rotating regenerative air preheaters

We propose a mathematical model of the heat transfer process in a rotating regenerative air preheater of a thermal power plant. The model is obtained by discretizing the process as a result of averaging both temporal and spatial variables. Making a number of simplifying assumptions, we write a linear discrete system $z(n+1)=Az(n)+r(n)$ of order $2m$ with a monomial $2m\times2m$ matrix $A=(a_{ij})$ in which $a_{ij}=\alpha_i$ for $i=1$, $j=2m$ and for $i=2,\ldots, 2m$, $j=i-1$, whereas all the other elements are zero. Using the relation $A^{2m}=\left(\prod_{i = 1}^{2m}{\alpha _{i}}\right)E$ and the Cauchy formula, we study the stability, periodicity, and convergence of the Cesaro means and other properties. We also consider the identification problem consisting in finding unknown coefficients $\alpha_i$, $i=1,2,\ldots, 2m,$ from the values $z(1), z(2), \ldots, z(2m)$ of the trajectory. Under the assumption $r(n)=r=const$ for $n=1,2,\ldots, 2m$, we transform the problem to the matrix equation $AY=B$, where the square matrix $Y$ is composed of the columns $y_1=t=r-(E-A)z_0$, $y_2=Ay_1+t$, $\ldots$, $y_{2m}=Ay_{2m-1}+t$ and $B=[t-y_2, t-y_3, \ldots, t-y_{2m-1}]$. A recurrent relation is derived for $\det Y$. It is proved that, if $\Delta=\alpha_1\alpha_2\ldots\alpha_m-\alpha_{m+1}\alpha{m+2}\ldots \alpha_{2m}\neq 0$, then $\det Y\neq0$ and $A=BY^{-1}$.