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

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T out T in R1/AR1/A R2/AR2/A Ro/ARo/A T out Ri/ARi/A T in

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l1l1 k 1, A 1 k 2, A 2 l2l2 l3l3 k 3, A 3 A 2 = A 1 (l 1 /k 1 )/A 1 R 1 /A 1 T out T in (l 2 /k 2 )/A 2 R 2 /A 2 (l 3 /k 3 )/A 3 R 3 /A 3 1. Add resistances for series 2. Add U-Values for parallel l thickness k thermal conductivity R thermal resistance A area

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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

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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) c p = 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)

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Dimensionless Parameters Reynolds number, Re = VD/ν Prandtl number, Pr = µc p /k = ν/α Nusselt number, Nu = hD/k Rayleigh number, Ra = …

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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/(ρc p ) Pr = µc p /k = ν/α 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) c p = specific heat (J/kg/°C, Btu/lbm/°F) k = thermal conductivity (W/m/K, Btu/hr/ft/K) α = thermal diffusivity (m2/s)

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

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Forced Convection External turbulent flow over a flat plate Nu = h m L/k = (Pr ) 0.43 (Re L 0.8 – 9200 ) (µ ∞ /µ w ) 0.25 External turbulent flow (40 < Re D <10 5 ) around a single cylinder Nu = h m D/k = (0.4 Re D Re D (2/3) ) (Pr ) 0.4 (µ ∞ /µ w ) 0.25 Use with care Re L = Reynolds number based on lengthQ = heat transfer rate (W, Btu/hr) Re D = 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) h m = mean convection heat transfer coefficient (W/m2/K, Btu/hr/ft2/F)

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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 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)

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

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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 h m for halocarbon refrigerants is Btu/hr/°F/ft 2 ( W/m 2 /°C) Nu = h m D i /k ℓ =0.0082(Re ℓ 2K)0.4 Re ℓ = GD i /µ ℓ G = mass velocity = Vρ (kg/s/m2, lbm/min/ft2) k = thermal conductivity (W/m/K, Btu/hr/ft/K) D i = inner diameter of tube( m, ft) K = CΔxh fg /L C = kg∙m/kJ, 778 ft∙lbm/Btu

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

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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)

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

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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

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Radiation Equations Q 1-2 = Q rad = heat transferred by radiation (W, BTU/hr) F 1-2 = shape factor h r = 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 = × 10-8 BTU/hr/ft2/°R4

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

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

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Radiation

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Combining Convection and Radiation Both happen simultaneously on a surface Slightly different temperatures Often can use h = h c + h r

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Combining all modes of heat transfer

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

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

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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]

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Pitot Tubes

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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

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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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