On observability of parallel - ow di usive heat exchanger equations with boundary output
نویسندگان
چکیده
This paper is concerned with the observability problem of a parallelow twouid heat exchanger equation with di usion term. First, the case where two uid temperatures are measured at the outlet is considered. It is shown that the observed system with the measurements becomes observable on any interval of time through a concrete series expression of the solution. Next, the two cases where each one of two uid temperatures is measured at the outlet are considered. It is also shown that the observed system with the only one measurement becomes observable on any interval of time except for the special cases of physical constants appearing in the equation. For the exceptional cases the unobservable subspace is nite dimensional and is characterized by using the eigenfunctions of heat equation with uid transfer term.
منابع مشابه
Analysis and implementation of a parallelization strategy on a Navier-Stokes solver for shear flow simulations
A parallel computational solver for the unsteady incompressible three-dimensional Navier± Stokes equations implemented for the numerical simulation of shear ¯ow cases is presented. The computational algorithms include Fourier expansions in the streamwise and spanwise directions, second-order centered ®nite dierences in the direction orthogonal to the solid walls, third-order Runge±Kutta proced...
متن کاملLongitudinal Conduction in Cross Flow Heat Exchanger with Condensation
The deterioration of the performance of a cross flow heat exchanger with condensation due to the longitudinal conduction was investigated. For a relatively small change of wall temperature along the flow directions which was shown to be common in many applications, the energy equations were solved numerically. An iterative method was used to solve the resulting equations of the finite differenc...
متن کاملA Note on Viscous Splitting of Degenerate Convection-diffusion Equations
We establish L convergence of a viscous splitting method for nonlinear possibly strongly degenerate convection-di usion problems. Since we allow the equations to be strongly degenerate, solutions can be discontinuous and they are not, in general, uniquely determined by their data. We thus consider entropy weak solutions realized by the vanishing viscosity method. This notion is broad enough to ...
متن کاملFlow and Pressure Distributions in Short Heat Exchanger Cores with Abrupt Entrance and Exit
The typical installation of a heat exchange device usually involves a flow contraction at the core entrance and a flow expansion at the core exit. Repeated flow Contraction and expansion are experienced in the flow passages of some compact heat exchangers. The latter refers to the flow passages in the plate-fin type with louvered fins or stripped fins and in the tubular type with dimpled-circul...
متن کاملHeat and mass transfer in annular liquid jets: I. Formulation
Heat and mass transfer phenomena in annular liquid jets are analyzed at high Reynolds numbers by means of a model derived from the governing equations that takes into account the eects of surface tension and boundary conditions at the gas± liquid interfaces and the large dierences between the thermal and mass diusivities, densities, dynamic viscosities, and thermal conductivities between gas...
متن کامل