Completed exercises of the course

Page 1

Life Support Systems – A.A. 2017/2018 Balance equations – diffusive phenomena propagation in time Maria Laura Costantino, Giustina Casagrande Pag. 1/7 1 – Balance equations1 – Definitions and use Control volume The control volume (vc) is a portion of space delimited by a boundary-closed surface that represents the border with the outer space. This surface can be “virtual”, if it is only geometrically defined, or “real”, when it corresponds to a separation surface between two different means (for example the internal surface of the wall of a channel). If necessary, the boundary line can be considered as the connection of several partial surfaces that behave in different modes in relation with the external space. From a time evolution point of view, the control volume can be fixed or movable in relation with the chosen reference system; it can also be deformable or not. Interactions between the control volume and the outer space The control volume can interact with the external space. The interactions occurring across the boundaries concern extensive quantities (additive quantities such as mass and volume, while temperature and pressure are intensive quantities). We usually deal with mass (molecular diffusion, described by Fick’s law) energy (heat conduction, described by Fourier’s law) and momentum transport (viscosity, described by Newton’s law). It is useful remind the definitions regarding thermodynamic systems: • Open system: the boundary allows both mass and energy transfer • Closed system: the boundary allows energy transfer but it is not permeable to mass; in this case talking about control mass instead of control volume is more precise. • Isolated: the boundary is not permeable to mass and energy. Control volume, can be generally considered as an open…