Energy Transfer By Heat, Work, and Mass Cengel & Boles, Chapter 3 ME 152

Energy Transfer Energy transfer to/from closed systems Heat (Q) Work (W) Energy transfer to/from open systems (control volumes) Mass flow ME 152

Heat Heat (Q) is the transfer of energy due to a temperature difference a system w/o heat transfer is an adiabatic system SI units: kJ Heat rate, , (kJ/s or kW) Heat per unit mass, q = Q/m Sign convention: Q > 0: heat transferred to system from surroundings Q < 0: heat transferred from system to surroundings ME 152

Heat Transfer Modes Conduction Radiation Convection transfer of heat through a material due to random molecular or atomic motion; most important in solids Radiation transfer of heat due to emission of electromagnetic waves, usually between surfaces separated by a gas or vacuum Convection transfer of heat between a solid surface and fluid due to combined mechanisms of i) fluid conduction at surface; ii) fluid flow within boundary layer ME 152

Conduction Heat Transfer Fourier’s law of conduction: ME 152

Convection Heat Transfer Newton’s law of “cooling”, or convection: ME 152

Radiation Heat Transfer Stefan-Boltzmann law of radiation (between a small surface A of emissivity e and large surroundings): ME 152

Work Work (W) is the energy transfer associated with a force acting through a distance: Work rate or power Work per unit mass, w = W/m Sign convention W > 0: work done by system on surroundings W < 0: work done on system by surroundings ME 152

Types of Work Moving boundary (compression/expansion) work Shaft work Spring work Electrical work Other forms; work associated with: Acceleration Gravity Polarization Magnetization Solid deformation Liquid film stretching ME 152

Moving Boundary Work Associated with a volume change of a fluid system (aka compression-expansion work) ME 152

Moving Boundary Work, cont. Expansion: dV > 0, Wb > 0 Compression: dV < 0, Wb < 0 Work processes on P-V diagram: ME 152

Moving Boundary Work, cont. Special cases: 1) if V = constant, Wb = 0 2) if P = constant, Wb = P(V2-V1) 3) if PVn = constant (known as a polytropic process), (see pp. 135-136 for derivation) ME 152

Shaft Work Associated with a rotating shaft ME 152

Spring Work Associated with the extension or compression of a spring; if spring is linear, then force obeys Hooke’s law, ME 152

Electrical Work Associated with the motion of electrons due to an electromotive force ME 152

Work and Heat Both are energy transfers Both are path-dependent functions P and V are properties, because Q and W are path functions, because ME 152

Conservation of Mass “Mass can neither be created nor destroyed” mass and energy can be converted to each other according to Einstein’s E=mc2, but this effect is negligible except for nuclear reactions) For closed systems, this principle imposes m = constant since mass cannot cross the system boundary For control volumes, the mass entering and leaving the system may be different and must be accounted for ME 152

Mass and Volume Flow Rates Mass flow rate: fluid mass conveyed per unit time [kg/s] where Vn = velocity normal to area [m/s]  = fluid density [kg/m3] A = cross-sectional area [m2] ME 152

Mass and Volume Flow Rates, cont. For most pipe flows,  = constant and the average velocity (V) is used: Volume flow rate is given by ME 152

Conservation of Mass Principle - Control Volume Net mass transfer during a process is equal to the net change in total mass of the system during that process where i = inlet, e = exit, 1 = initial state, 2 = final state in rate form: In fluid mechanics, this is often referred to as the continuity equation ME 152

Steady-Flow Processes Steady-flow or steady-state – a condition where all fluid and flow properties, heat rates, and work rates do not change with time. mathematically: applied to mass balance: ME 152

Steady-Flow Processes, cont. Conservation of mass during a steady-flow process: If control volume is single-stream (i.e., one inlet, one exit), then ME 152

Incompressible Flow If  = constant, then the mass flow is considered incompressible for steady-flow: for single-stream, steady-flow: ME 152

Total Energy of a Flowing Fluid A flowing fluid contains internal, kinetic, and potential energies: Fluid entering or leaving a control volume has an additional form of energy known as flow energy, which represents the work required to “push” the fluid across a boundary: ME 152

Total Energy of a Flowing Fluid, cont. The total energy of a flowing fluid (on a unit-mass basis, ) becomes Using the definition of enthalpy (h), ME 152

Energy Transport by Mass Amount of energy transport: Rate of energy transport: ME 152