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Objectives

Objectives. Heat transfer Convection Radiation Fluid dynamics Review Bernoulli equation flow in pipes, ducts, pitot tube. T out. T in. R i / A. R o / A. R 1 / A. R 2 / A. T out. T in. T in. T out. Add resistances for series Add U-Values for parallel. l 1. l 2. k 1, A 1.

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Objectives

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  1. Objectives • Heat transfer • Convection • Radiation • Fluid dynamics • Review Bernoulli equation • flow in pipes, ducts, pitot tube

  2. Tout Tin Ri/A Ro/A R1/A R2/A Tout Tin

  3. Tin Tout • Add resistances for series • Add U-Values for parallel l1 l2 k1, A1 k2, A2 (l1/k1)/A1 R1/A1 (l2/k2)/A2 R2/A2 A2 = A1 k3, A3 (l3/k3)/A3 R3/A3 l thickness k thermal conductivity R thermal resistance A area l3

  4. Convection and Radiation • Similarity • Both are surface phenomena • Therefore, can often be combined • Difference • Convection requires a fluid, radiation does not • Radiation tends to be very important for large temperature differences • Convection tends to be important for fluid flow

  5. Forced Convection • Transfer of energy by means of large scale fluid motion In the following text: V = velocity (m/s, ft/min) Q = heat transfer rate (W, Btu/hr) ν = kinematic viscosity = µ/ρ (m2/s, ft2/min) A = area (m2, ft2) D = tube diameter (m, ft) T = temperature (°C, °F) µ = dynamic viscosity ( kg/m/s, lbm/ft/min) α = thermal diffusivity (m2/s, ft2/min) cp = specific heat (J/kg/°C, Btu/lbm/°F) k = thermal conductivity (W/m/K, Btu/hr/ft/K) h = convection or radiation heat transfer coefficient (W/m2/K, Btu/hr/ft2/F)

  6. Dimensionless Parameters • Reynolds number, Re = VD/ν • Prandtl number, Pr = µcp/k = ν/α • Nusselt number, Nu = hD/k • Rayleigh number, Ra = …

  7. k = thermal conductivity (W/m/K, Btu/hr/ft/K) ν = kinematic viscosity = µ/ρ (m2/s, ft2/min) α = thermal diffusivity (m2/s, ft2/min) µ = dynamic viscosity ( kg/m/s, lbm/ft/min) cp = specific heat (J/kg/°C, Btu/lbm/°F) k = thermal conductivity (W/m/K, Btu/hr/ft/K) α = thermal diffusivity (m2/s) What is the difference between thermal conductivity and thermal diffusivity? • Thermal conductivity, k, is the constant of proportionality between temperature difference and conduction heat transfer per unit area • Thermal diffusivity, α, is the ratio of how much heat is conducted in a material to how much heat is stored • α = k/(ρcp) • Pr = µcp/k = ν/α

  8. Analogy between mass, heat, and momentum transfer • Schmidt number, Sc • Prandtl number, Pr Pr = ν/α

  9. ReL = Reynolds number based on length Q = heat transfer rate (W, Btu/hr) ReD = Reynolds number based on tube diameter A = area (m2, ft2) L = tube length (m, ft) t = temperature (°C, °F) k = thermal conductivity (W/m/K, Btu/hr/ft/K) Pr = Prandtl number µ∞ = dynamic viscosity in free stream( kg/m/s, lbm/ft/min) µ∞ = dynamic viscosity at wall temperature ( kg/m/s, lbm/ft/min) hm = mean convection heat transfer coefficient (W/m2/K, Btu/hr/ft2/F) Forced Convection • External turbulent flow over a flat plate • Nu = hmL/k = 0.036 (Pr )0.43 (ReL0.8 – 9200 ) (µ∞ /µw )0.25 • External turbulent flow (40 < ReD <105) around a single cylinder • Nu = hmD/k = (0.4 ReD0.5 + 0.06 ReD(2/3) ) (Pr )0.4 (µ∞ /µw )0.25 • Use with care

  10. H = plate height (m, ft) T = temperature (°C, °F) Q = heat transfer rate (W, Btu/hr) g = acceleration due to gravity (m/s2, ft/min2) T = absolute temperature (K, °R) Pr = Prandtl number ν = kinematic viscosity = µ/ρ (m2/s, ft2/min) α = thermal diffusivity (m2/s) Natural Convection • Common regime when buoyancy is dominant • Dimensionless parameter • Rayleigh number • Ratio of diffusive to advective time scales • Book has empirical relations for • Vertical flat plates (eqns. 2.55, 2.56) • Horizontal cylinder (eqns. 2.57, 2.58) • Spheres (eqns. 2.59) • Cavities (eqns. 2.60) For an ideal gas

  11. Phase Change –Boiling • What temperature does water boil under ideal conditions?

  12. Reℓ = GDi/µℓ G = mass velocity = Vρ (kg/s/m2, lbm/min/ft2) k = thermal conductivity (W/m/K, Btu/hr/ft/K) Di = inner diameter of tube( m, ft) K = CΔxhfg/L C = 0.255 kg∙m/kJ, 778 ft∙lbm/Btu Forced Convection Boiling • Example: refrigerant in a tube • Heat transfer is function of: • Surface roughness • Tube diameter • Fluid velocity • Quality • Fluid properties • Heat-flux rate • hm for halocarbon refrigerants is 100-800 Btu/hr/°F/ft2 (500-4500 W/m2/°C) Nu =hmDi/kℓ=0.0082(Reℓ2K)0.4

  13. Condensation • Film condensation • On refrigerant tube surfaces • Water vapor on cooling coils • Correlations • Eqn. 2.62 on the outside of horizontal tubes • Eqn. 2.63 on the inside of horizontal tubes

  14. Radiation • Transfer of energy by electromagnetic radiation • Does not require matter (only requires that the bodies can “see” each other) • 100 – 10,000 nm (mostly IR)

  15. Blackbody • Idealized surface that • Absorbs all incident radiation • Emits maximum possible energy • Radiation emitted is independent of direction

  16. Radiation emission The total energy emitted by a body, regardless of the wavelengths, is given by: • Temperature always in K ! - absolute temperatures • – emissivity of surface ε= 1 for blackbody • – Stefan-Boltzmann constant A - area

  17. Q1-2 = Qrad = heat transferred by radiation (W, BTU/hr) F1-2 = shape factor hr = radiation heat transfer coefficient (W/m2/K, Btu/hr/ft2/F) A = area (ft2, m2) T,t = absolute temperature (°R , K) , temperature (°F, °C) ε = emissivity (surface property) σ = Stephan-Boltzman constant = 5.67 × 10-8 W/m2/K4= 0.1713 × 10-8 BTU/hr/ft2/°R4 Radiation Equations

  18. Short-wave & long-wave radiation • Short-wave – solar radiation • <3mm • Glass is transparent • Does not depend on surface temperature • Long-wave – surface or temperature radiation • >3mm • Glass is not transparent • Depends on surface temperature

  19. Figure 2.10 • α + ρ + τ = 1 α = ε for gray surfaces

  20. Radiation

  21. Combining Convection and Radiation • Both happen simultaneously on a surface • Slightly different temperatures • Often can use h = hc + hr

  22. Combining all modes of heat transfer

  23. Example of Conduction Convection and Radiation use: Heat Exchangers Ref: Incropera & Dewitt (2002)

  24. Shell-and-Tube Heat Exchanger Ref: Incropera & Dewitt (2002)

  25. Fluid Flow in HVAC components Fundamentals: Bernoulli’s equation Flow in pipes: • Analogy to steady-flow energy equation • Consider incompressible, isothermal flow • What is friction loss? [ft] [Pa]

  26. Pitot Tubes

  27. Summary • Use relationships in text to solve conduction, convection, radiation, phase change, and mixed-mode heat transfer problems • Calculate components of pressure for flow in pipes and ducts

  28. Any questions about review material? • Where are we going? • Psychrometrics • Psychrometric terms • Using tables for moist air • Using psychrometric charts • 7.1 – 7.5, 7.7

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