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INTRODUCTION

INTRODUCTION. What is Heat Transfer ? Continuum Hypothesis Local Thermodynamic Equilibrium Conduction Radiation Convection Energy Conservation. Crystal : a three-dimensional periodic array of atoms. WHAT IS HEAT ?. In a solid body.

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INTRODUCTION

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  1. INTRODUCTION • What is Heat Transfer ? • Continuum Hypothesis • Local Thermodynamic Equilibrium • Conduction • Radiation • Convection • Energy Conservation

  2. Crystal : a three-dimensional periodic array of atoms WHAT IS HEAT ? In a solid body Oscillation of atoms about their various positions of equilibrium (lattice vibration): The body possesses heat. Conductors: free electrons ↔ Dielectics

  3. us-1 us us+1 us+2 us-1 us+1 us+2 us us+3 s-1 s s+1 s+2 s+3 Vibration of crystals with an atom Longitudinal polarization vs. Transverse polarization The energy of the oscillatory motions: the heat-energy of the body More vigorous oscillations: the increase in temperature of the body

  4. average kinetic energy vibrational state electronic state 2 dissociation energy for state 2 Energy kB = 1.3807 × 10-23 J/K rotational state electronic state 1 atT = 300 K, airM = 28.97 kg/kmol = 468.0 m/s dissociation energy for state 1 Internuclear separation distance (diatomic molecule) In a gas The storage of thermal energy: molecular translation, vibration and rotation change in the electronic state intermolecular bond energy

  5. HEAT TRANSFER Heat transfer is the study of thermal energy transport within a medium or among neighboring media by • Molecular interaction: conduction • Fluid motion: convection • Electromagnetic wave: radiation resulting from a spatial variation in temperature. Energy carriers: molecule, atom, electron, ion, phonon (lattice vibration), photon (electro-magnetic wave)

  6. local value of density CONTINUUM HYPOTHESIS Ex) density microscopic uncertainty macroscopic uncertainty (3×107 molecules at sea level, 15°C, 1atm)

  7. Mean free path of air at STP (20°C, 1atm) lm = 66 nm, • microscopic uncertainty due to molecular random motion • macroscopic uncertainty due to the variation associated with spatial distribution of density In continuum, velocity and temperature vary smoothly. → differentiable bulk motion vs molecular random motion

  8. LOCAL THERMODYNAMIC EQUILIBRIUM hot wall at Th adibatic wall L adibatic wall gas cold wall at Tc a) lm << L : normal pressure b) lm ~ L : rarefied pressure c) lm >> L

  9. CONDUCTION Gases and Liquids • Due to interactions of • atomic or molecular • activities • Net transfer of energy by random • molecular motion • Molecular random motion→ diffusion • Transfer by collision of random • molecular motion

  10. Solids • Due to lattice waves induced by • atomic motion • In non-conductors (dielectrics): • exclusively by lattice waves • In conductors: • translational motion of free electrons • as well

  11. Fourier’s Law heat flux [J/(m2s) = W/m2] k: thermal conductivity [W/m·K] As Dx → 0,

  12. Notation Q: amount of heat transfer [J] q : heat transfer rate [W], : heat transfer rate per unit area [W/m2] : heat transfer rate per unit length [W/m]

  13. Heat Flux vector quantity

  14. Ex) T = constant line or surface: isothermal lines or surfaces (isotherms)

  15. T(x, y, z) = constant • temperature : driving potential of • heat flow • heat flux : normal to isotherms along the surface of T(x, y, z) = constant

  16. Steady-State One Dimensional Conduction T = T(x) only steady-state

  17. or As Dx → 0, When k = const.,

  18. 0.4 0.7 ultra violet infrared visible thermal radiation RADIATION Thermal Radiation 10-2m 10-1m 1m 10 m 102m 103m

  19. Ex) ice lens ice lens black carbon paper Characteristics of Thermal Radiation • Independence of existence and temperature of medium

  20. diffusion • solid: lattice vibration (phonon) free electron 2. Acting at a distance Ex) sky radiation • electromagnetic wave or photon • photon mean free path • ballistic transport • volume or integral phenomena conduction • fluid: molecular random motion diffusion or differential phenomena as long as continuum holds

  21. surface emission Blackbody spectral emissive power 3. Spectral and Directional Dependence • quanta • history of path

  22. Two Points of View • Electromagnetic wave • Maxwell’s electromagnetic theory • Useful for interaction between radiation and matter 2. Photons • Planck’s quantum theory • Useful for the prediction of spectral properties of absorbing, emitting medium

  23. Radiating Medium • Transparent medium • ex: air • Participating medium • emitting, absorbing and scattering • ex: CO2, H2O • Opaque material

  24. Stefan by experiment (1879): Boltzmann by theory (1884): Stefan-Boltzmann’s law a perfect absorber • Blackbody: • Blackbody emissive power

  25. C0: speed of light in vacuum: 2.9979×108 m/s h: Planck constant: 6.6260755×10-34 J•s k: Boltzmann constant: 1.380658×10-23 J/K Planck’s law (The Theory of Heat Radiation, Max Planck, 1901) spectral distribution of hemispherical emissive power of a blackbody in vacuum

  26. El,b (W/m2.mm) For a real surface, Wavelength, l (mm) e : emissivity Blackbody spectral emissive power

  27. Surface Radiation G Kirchihoff’s law Ray-tracing method vs Net-radiation method G: irradiation [W/m2] J J: radiosity [W/m2] r : reflectivity e diffuse-gray surface at T a : absorptivity

  28. aG esT4 e diffuse-gray surface at T

  29. [W] when Tsur q Ts, e, a, A Ex) a body in an enclosure T2, e2, A2 q1 T1, e1, A1 e = a Surrounding can be regarded as a blackbody.

  30. Why is the irradiation on the small object the same as ? A1 A2

  31. A2 A1 F: view factor Reciprocity:

  32. CONVECTION energy transfer due to bulk or macro- scopic motion of fluid bulk motion: large number of molecules moving collectively • convection: random molecular motion • + bulk motion • advection: bulk motion only

  33. solid wall • hydrodynamic (or velocity) • boundary layer • thermal (or temperature) • boundary layer at y = 0, velocity is zero: heat transfer only by molecular random motion

  34. solid wall When radiation is negligible, h : convection heat transfer coefficient [W/m2.K] Newton’s Law of Cooling

  35. Convection Heat Transfer Coefficient not a property: depends on geometry and fluid dynamics • forced convection • free (natural) convection • external flow • Internal flow • laminar flow • turbulent flow

  36. control volume ENERGY CONSERVATION First law of thermodynamics • control volume (open system) • material volume (closed system) In a time interval Dt: steady-state:

  37. sur. Ex) Surface Energy Balance

  38. Find: • Surface emissive power E and irradiation G • Pipe heat loss per unit length, Example 1.2 air • Assumptions: • Steady-state conditions • Radiation exchange between the pipe and the room is between a small surface in a much larger enclosure. • Surface emissivity = absorptivity

  39. air 1. Surface emissive power and irradiation

  40. air 2. Heat loss from the pipe

  41. Q: Why not ? Example 1.2 air Conduction does not take place ?

  42. T r air

  43. Anode: (exothermic) Cathode: The convection heat coefficient, h Example 1.4 Hydrogen-air Proton Exchange Membrane (PEM) fuel cell Three-layer membrane electrode assembly (MEA) • Role of electrolytic membrane • transfer hydrogen ions • serve as a barrier to electron • transfer Membrane needs a moist state to conduct ions. Liquid water in cathode: block oxygen from reaching cathode reaction site → need to control Tc

  44. Find: The required cooling air velocity, V, needed to maintain steady state operation at Tc = 56.4ºC. • Assumptions: • Steady-state conditions • Negligible temperature variations within the fuel cell • Large surroundings • Insulated edge of fuel cell • Negligible energy flux by the gas or liquid flows

  45. Energy balance on the fuel cell

  46. Assumptions: 1) Inner surface of wall is at through the process. 2) Constant properties 3) Steady-states, 1-D conduction through each wall 4) Conduction area of one wall = Example 1.5 section A-A A A cubical cavity ice of mass M at the fusion temperature Find: Expression for time needed to melt the ice,tm

  47. : latent heat of fusion section A-A

  48. Find: 1) Cure temperature T for 2) Effect of air flow on the cure temperature for Value of h for which the cure temperature is 50°C. • Assumptions: • Steady-state conditions • Negligible heat loss from back surface of plate • Plate is very thin and a small object in large surroundings, • coating absorptivity w.r.t. irradiation from the surroundings Example 1.7 air Coating to be cured

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