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**Energy Transfer By Heat, Work, and Mass**

Cengel & Boles, Chapter 3 ME 152

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**Energy Transfer Energy transfer to/from closed systems**

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

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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

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**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

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**Conduction Heat Transfer**

Fourier’s law of conduction: ME 152

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**Convection Heat Transfer**

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

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**Radiation Heat Transfer**

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

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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

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**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

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

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**Moving Boundary Work, cont.**

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

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**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 for derivation) ME 152

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Shaft Work Associated with a rotating shaft ME 152

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

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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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

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**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

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**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

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**Energy Transport by Mass**

Amount of energy transport: Rate of energy transport: ME 152

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