Time weighted model reduction of flat plate solar collectors

This paper presents the application of time weighted model reduction using cross gramians on a state space model derived from two partial differential equations representing the instantaneous thermal balance of a differential element of length along the absorber plate and the absorber plate to fluid heat convection process respectively of a flat plate solar collector. Finite difference method is applied onto both these partial differential equations where discretization in time and space is performed resulting in a high order linear discrete time invariant Single Input Single Output (SISO) state space model. Numerical results are provided to demonstrate and compare the performance of time weighted model reduction relative to balanced truncation.