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

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

3. 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

4. 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

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

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

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

8. 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

9. 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

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

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

12. 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

13. Shaft Work
Associated with a rotating shaft
ME 152

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

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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

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

24. 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

25. 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

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