05 Mass and energy balances for open systems

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L.D.D Advanced Building Physics - Mass and Energy balances for open systems We need to introduce the concept of control volume to discuss mass and energy balances.  The Control Volume is a defined portion of the space which is fixed with respect to a generic inertial system. In general, the balance of a quantity X in a control volume can be written as: Note that in transport phenomena, flux is defined as the rate of flow of a property per unit area, which has the dimensions of [quantity/(time x area)] We denote by: The quantity which passes through a surface is represented by the surface integral of the flux (sum of all the fluxes through every element of the surface). How to explain those formulas? Consider the movement of a fluid through a surface of area A. Consider a portion of the surface dA small enough to consider approximately the same velocity in each point of dA. Each small element of the surface can be described by an area dA, a velocity vector w and a unit vector normal to the surface n. L.D.D We can calculate the volume of solid passing through the surface in one second (as the velocity is w (m/s) they will all move of a distance of w meters in one second.  The Volumetric flux (or volumetric flow rate) is defined as:  The Mass flux (or mass flow rate), in the general case in which the density changes form point to point, is defined as: L.D.D 1 - MASS BALANCE  Mass balance for an open system in the most general case: non steady-state conditions, arbitrary number of inputs and outputs of mass, presence of mass sinks and sources. - Simple case Consider as control volume the following open system with a single input and a single output, no internal source or sink. Mass balance for the control volume: If we consider a situation in which the temperature, the…