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Heat Transfer Modeling and Applications

Heat Transfer Modeling and Applications. A Short Course Reza Toossi, Ph.D, P.E. California State University, Long Beach. Outline. Scope and Types Energy Equation Formulation Conversion Mechanisms Dimensionless Parameters in Heat Transfer Modes of Heat Transfer

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Heat Transfer Modeling and Applications

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  1. Heat Transfer Modeling and Applications A Short Course Reza Toossi, Ph.D, P.E. California State University, Long Beach

  2. Outline • Scope and Types • Energy Equation • Formulation • Conversion Mechanisms • Dimensionless Parameters in Heat Transfer • Modes of Heat Transfer • Conduction, Convection, and Radiation • Correlations • Combined Modes • Heat Transfer in Multiple Phases • Conjugate Heat Transfer • Composites • Phase Change

  3. Scales • T  0 K – 1.4x1032 K • L  1.6x10-35 m – 1.6x1026 m (15 bly) • t  5.4x10-44 s – 2.7x1017 s • m  10-69 kg - 1054 kg

  4. Mechanical Systems • Mechanically determined problems • Can be solved only by Newton’s Law of Motion and Conservation of Mass Examples: • Free fall of a body; F = ma • Dynamics of rigid bodies in absence of friction • Flow of ideal fluids between two parallel plates • Mechanically undetermined problems • Additional laws are needed Examples: • Dynamics of rigid bodies with friction • Dynamics of deformable body

  5. Thermal Systems • Thermodynamically determined problems • Can be solved by the general laws of mechanics and the first and second laws of thermodynamics. Example: • Flow of steady 1-D isentropic and subsonic fluid through a nozzle. mass d(rAV) = 0 Momentum dp+ rAdV = 0 Energy du +pd(1/r) = 0 • Thermodynamically undetermined problems • Heat Transfer (modes of heat transfer) • Gas Dynamics (equation of state)

  6. Knudsen Number • 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)

  7. Energy Equation

  8. Formulations • Differential • Integral • Integral-Differential • Thermal Nodes

  9. Differential-Volume Fire Walking Infinite flat plate Solution: Interface Temperature (no contact resistance)

  10. Integral Volume (lumped) • Heat losses under the condition of hypothermia Take cvV = 5x105 J/K, Sv = 400 W, and QA= Qr = 800 W; T = 10oC Get t =3.47 hr

  11. Surface Coating • Droplet Impingement on a Hot Surface • Temperature is uniform within the droplet (particle) • Particle temperature varies during its flight • Sensible heating until particle reaches its melting temperature. Melting occurs at T = Tsl • Time to reach melting temperature

  12. Integral-Differential

  13. Thermal Nodes - Slab - Cylinder - Sphere

  14. Energy Conversion Mechanisms

  15. Heat Source • Phase Change • Chemical Reaction • Nuclear Fission and Fusion • Surface Friction Heating • Viscous Heating • Ultrasound Heating • Microwave Heating • Joule Heating • Thermolectric Heating (and Cooling)

  16. Phase Change

  17. Chemical Reaction ar is pre-exponential factor = func (f)

  18. Nuclear Fission and Fusion

  19. Surface Friction Heating • Interfacial Energy Conversion of Mechanical Energy μF is the friction coefficient pc is the contact or joint pressure Δui is the interface relative velocity

  20. Viscous Heating • Volumetric Conversion of Mechanical Energy Due to Fluid Viscosity Example: Viscous heating in a ball bearing. The bearing is 0.2 mm in diameter, and ui = 1 m/s. Engine oil at STP has a viscosity of mf = 0.366 Pa/s

  21. Ultrasound Heating • Volumetric Conversion of Longitudinal Acoustic Waves to Thermal Energy sac acoustic absorption coefficient = 1.4 for blood = 14 for muscle = 31 for skin = 161 for bone as speed of sound = 1,519 m/s in tissues = 3,445 m/s in bones f frequency μ dynamic viscosity γ specific heat ratio g = cp/cv Pr Prandtl number

  22. Microwave (Dielectric) Heating • Volumetric Conversion of Electromagnetic to Molecular Vibration (Heat) ee (V/m) electric field intensity eec dielectric loss factor (relative permittivity) e0 permittivity of free space f (Hz) oscillation frequency

  23. Joule heating • Conversion of Electrical Energy to Heat

  24. Seebeck Thermoelectric

  25. Peltier Thermoelectric Cooling and Heating

  26. Thermoelectric Properties for Some Materials

  27. Thermoelectric Power Generation Unit • Direct Electrical Power Generation by • Heat Absorption at a Hot Junction • Rejecting the Peltier Heat at the Cold Junction • Bismuth-telluride cold p-n junction • S,p=230x10-6 V/k, S,n= -210x10-6 V/k, Je=10 A • The Peltier heat absorbed at the cold junction • Tc = 120oC  Q = -1.73 W • Tc = 20oC  Q = -1.29 W • Tc = - 80oC  Q = -0.85 W

  28. Volumetric and Surface Radiation Absorption

  29. Classification

  30. Solar Irradiation

  31. Flame Irradiation

  32. Laser Irradiation

  33. Summary of Heat Source Terms

  34. Modes of Heat Transfer • Diffusion(transfer of heat within one medium or from one medium to another medium) • Conduction (diffusion of heat in moving or stationary rigid bodies) • Convection(diffusion of heat in moving deformable bodies) • Radiation(transfer of heat by electromagnetic waves)

  35. Conduction

  36. Convection

  37. Heat Transfer Coefficient • Convective heat transfer is affected by the geometry, surface condition, and fluid properties. • To find h, the detailed flow field must be known. • Mass (1) • Momentum (3) • Energy (1) • Equation of State (1) • Solve for u, v, w, T, P, and ρ • Find qw = h A (TW -T∞) {and also tw =m du/dyw} • Π-Buckingham Theorem (f = n – m) • h = h (k, m, cp, r, L, e, DT, gbDT, hst, t) • Nu = Nu (Gr, Pr, Ste, Fo, e/L)

  38. Dimensionless Parameters in HT

  39. Dimensionless Parameters in HT

  40. Boundary Conditions • Prescribed Temperature • Prescribed Heat Flux (Fourier’s Law) • Insulation • Convective (Newton’s Cooling Law) • Radiative (Stefan-Boltzmann Law) • Prescribed Heat Flux Acting at a Distance • Interface (Continuity, Conservation Law) • Moving Boundary

  41. How to insulate a boundary? • q  0 • Efficient electric heater Guard Heater

  42. When is the assumption of isothermal or insulated wall justified? • h  0; h  ∞ • Flow through a thin heated tube • Insulated wall [ ] Ti Tm (Boiling) • k  0; k  ∞ • Lumped vs. distributed (Biot number) • Insulated wall k  large (lumped) k  small (distributed) • Bare tube, h0<< hi  (qo0)

  43. Critical thickness of Insulation

  44. Moving Boundary • Ice layer forming on surface of a pond on a clear night with calm wind Tsky = 0 K; T∞ = 3oC; Tℓ = 4oC; Tice = 0oC)

  45. Forced Convection (External Flow)

  46. Forced Convection (Internal Flow)

  47. Free Convection: Flat Plates

  48. Free Convection: Cylinders and Spheres

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