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Heat Transfer MaterialsStorage, Transport, and TransformationPart I: Physics

A Short Course byReza Toossi, Ph.D., P.E.California State University, Long Beach

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Outline

Atomic and Molecular Bonds Energy Carriers

Specific Heat Thermal Conductivity

Discussions

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History Aristotle (384 BC–323 BC) Antoine Lavoisier (1743-1794) John Dalton (1766 - 1844) Benjamin Thompson (Count Rumford) (1753-1814) Robert Mayer (1814-1878) William Thompson (Lord Kelvin) (1824-1907) Gustav Boltzmann (1844-1906) James Maxwell (1831–1879) Max Planck (1858 –1947) Neil Bohr (1855–1962) Wolfgang Pauli (1900–1958) Erwin Schrodinger (1887–1961) Enrico Fermi (1901–1954)

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Heat Transfer Medium

Gases▪ Vapors, ideal gases, and plasmas

Liquids▪ Organics▪ Inorganics

▪ Metals and Nonmetals

Solids▪ Conductors (metals)▪ Insulators (nonmetals)▪ Semiconductors

Composites ▪ Layered and non-layered

▪ Liquid-gas (aerosol spray)▪ Liquid-Liquid (emulsion)▪ Solid-solid (wood, resin-filled fiberglass)▪ Solid-gas (coal, membrane)▪ Solid-liquid-gas (nucleate boiling on a solid surface)

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Thermochemical and Thermophysical Properties

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Microscopic Heat Transfer

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Microscopic Energy Carriers

Particles Waves Quasi-Particles

▪ Phonon ▪ Acoustic▪ Optical

▪ Photon▪ Electron (and Hole)

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Strong and Weak Bonds

Strong Bonds Ionic Covalent Metallic

Weak Bonds (~kcal/mole)

Van der Waals▪ Hydrogen▪ Electrostatic

(ionic)

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Strong (Primary) Bonds

Ionic (metal to nonmetal) NaCl

Covalent (nonmetal to nonmetal) Diamond, organic matters

Metallic bonding (metal to metal) Silver

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Weak (Secondary) Bonds Hydrogen Forces (H2O, NH3)

Van der Waals Dipole-Dipole Forces (HCl-HCl)

London Dispersion Forces (Xe-Xe)

Ion-Dipole Forces

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Bond Strength

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Bonding Between Neutral Atoms

Attractive force @ large distances (van der Waals) Repulsive force @ short distances (Pauli repulsion) Models▪ Quantum mechanical (Dipole-dipole and London forces)▪ Classical (LJ)

V is the energy potential Is the equilibrium distancee is the energy of interaction (depth of the potential well)r is the distance of separation

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Cohesion and Adhesion

Cohesion: Intermolecular attraction between molecules of the same kind or phase (viscosity in fluid)

Adhesion: Intermolecular attraction between molecules of different kind or phase (water wetting of a glass, oil droplets in a hot skillet)

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Transport Phenomena

Conduction Macroscale (> 1 mm, Fourier’s Law ) Microscale (1-100 μm, Thermalization) Nanoscale (1-100 nm, Non-equilibrium)

Surface Tension Macroscale Microscale

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Continuum Approach Continuity

Species

Momentum (Navier-Stokes)

Energy

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Continuum Flow Limitations

Continuum regime (Kn < 0.01)Slip flow regime (0.01 < Kn <

0.1)Transition regime (0.1 < Kn < 3)Free molecular flow regime (Kn

> 3)

Knudsen Number:

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Statistical Approach

Boltzmann Transport Equation

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Nanoscale Considerations Nonequilibrium Phenomenon

Ultra small dimensions Ultrafast processes

Different conduction equations for electrons and the lattice Nucleation

Laser Irradiation

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Example: Laser Processing of Material

Melting of Gold Films Short-pulsed laser melting of thin films

involves two non-equilibrium processes. (1) Deposition of laser energy (2) Energy transfer between electrons and lattice (3) Melting

One –Step Model

Two –Step Model

Electron:

Lattice: Kuo, L.S., and Qui, T.Q., 1996, “Microscale Energy Transfer During Picosecond Laser Melting of Metal Films,” ASME HTD-Vol. 323, Vol. 1, pp.149-157.

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Results (Gold film with L = 1000 nm, tp =20 ps)

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Specific Heat of Various Substances

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Heat Storage

Specific Heat Capacities: Cp and Cv Gases

▪ Translational▪ Rotational▪ Vibrational▪ Electronic

Solids (metals, dielectrics, and semiconductors)▪ Lattice vibration (phonons)▪ Free electrons

Liquids▪ Near critical point (behaves like a gas)▪ Away from critical point (behaves like a solid)

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Modes of Energy Storage (H2)

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Cp 0 to ∞

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Cp for GasesSpecific Heat of Selected gases at 300 K

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Cp for solids

Einstein (Classic) Model cv = 3 k (per molecule), 3R (per mole)

Debye Model cv increases until TD

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Cp for liquids

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Cp for Water

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Thermal Conductivity

Thermal Conductivity (k) Gases Solids

▪ Metals (Drude classical theory)▪ Nonmetals (Debye model)▪ Semiconductors

Liquids Composites

▪ Effective conductivity

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Contributions from Heat Carriers

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Equilibrium vs. Transport

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Mechanism of Heat Conduction in Gases

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Mechanism of Heat Conduction in Solids Roles of the conduction electrons and the thermal

lattice vibration are significant Conduction electrons (Drude Model)

Lattice (phonons) vibration (Callaway Model)▪ Amorphous (non-periodic)▪ Crystalline (Periodic)

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k = km+ ke + kp

Molecular For an ideal monatomic gas For an ideal polyatomic gas

Electronic Contribution to thermal

conductivity

Contribution to electrical conductivity

Phonons

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Metals, Nonmetals, and Semiconductors

Metals Excellent heat conductor Excellent electrical conductor

Nonmetals Poor heat conductor Poor electrical conductor

Semiconductors Fair heat conductor Good electrical conductor

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Thermal Conductivities of Solids

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Thermal Materials:From Ideal Insulators to Perfect Conductors

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Thermal Conductivity of Liquids

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Thermal Conductivity of Composites

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Part V- Q/A

For additional questions, Please email rtoossi@csulb.edu.

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Further Readings Lee, J., Sears, F. W, and Turcotte, D. L., “Statistical

Thermodynamics,” Addison-Wesley, 1963. Tien, C. L., and Lienhard, J. H., “Statistical

Thermodynamics,” Holt, Rinehart and Winston, 1971.

Kaviany, M., “Principal of Heat Transfer,” Wiley, 2002.

Atkins, P. W., “Molecular Quantum Mechanics,” Clarendon Press, 1970.

Siegal, R., and Howell, J. R., “Thermal Radiation Heat Transfer,” Hemisphere Publishing Corporation, 3rd Ed., 1992