Lecture of Heat Transfer
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Transcript of Lecture of Heat Transfer
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Lecture Objectives:Review - Heat transferConvection Conduction Radiation
Analysis of a practical problem
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Example Problem radiant barrier in attic
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Example Problem heat transfer in window construction
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Convection
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Convection coefficient h [W/m2K]ConductionConvection Natural convectionForced convectionL characteristic lengthh natural convectionk air conductionL- characteristic lengthorNusselt number:areaSpecific heat fluxHeat flux
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Which surface in this classroom has the largest forced convectionA. Window B. CeilingC. WallsD. Floor
Which surface has the largest natural convection
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How to calculate h ?
What are the parametrs that affect h ?
What is the boundary layer ?
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Laminar and Turbulent Flowforced convection
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Forced convection governing equations1) Continuity
2) Momentumu, v velocities n air viscosityNon-dimensionless momentum equation
Using
L = characteristic length and U0 = arbitrary reference velocityReLReynolds number
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Forced convection governing equationsEnergy equation for boundary layerNon-dimensionless energy equationsT temperature, a thermal diffusivity a=k/rcp, k-conductivity, r - density, cp specific cap. Wall temperatureAir temperature outside of boundary layerInertial forceViscous forceMomentum diffusivity Thermal diffusivityReynolds number Prandtl number
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Simplified Equation for Forced convection
For laminar flow: For turbulent flow:For air: Pr 0.7, n = viscosity is constant, k = conductivity is constant General equationSimplified equation:Or:
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Natural convection
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GOVERNING EQUATIONSNatural convection Continuity
Momentum which includes gravitational force
Energyu, v velocities , n air viscosity , g gravitation, b1/T - volumetric thermal expansion T temperature, air temperature out of boundary layer, a temperature conductivity
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Characteristic Number for Natural ConvectionNon-dimensionless governing equations
Using
L = characteristic length and U0 = arbitrary reference velocity Tw- wall temperatureThe momentum equation becomeMultiplying by Re2 number Re=UL/n Gr
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Grashof number Characteristic Number for Natural Convection The Grashof number has a similar significance for natural convection as the Reynolds number has for forced convection, i.e. it represents a ratio of buoyancy to viscous forces.Buoyancy forcesViscous forces General equation
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Even more simpleNatural convection simplified equationsFor laminar flow: For turbulent flow:For air: Pr 0.7, n = constant, k= constant, b= constant, g=constant Simplified equation:Or:T - air temperature outside of boundary layer, Ts - surface temperature
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Forced and/or natural convectionIn general,Nu = f(Re, Pr, Gr)natural and forced convectionforced convectionnatural convection
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Combined forced and natural conventionChurchill and Usagi approach :This equation favors a dominant term (h1 or h2), and exponent coefficient n determines the value for hcombined when both terms have the same order of value
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Example of general forced and natural convectionEquation for convection at cooled ceiling surfacesn
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What kind of flow is the most common for indoor surfacesA. Laminar B. TurbulentC. TransitionalD. Laminar, transitional, and turbulent
What about outdoor surfaces?
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Conduction
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Conductive heat transferSteady-state
Unsteady-state
Boundary conditions
Dirichlet Tsurface = Tknown
Neumann
LTairk - conductivity of materialTS1TS2h
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Boundary conditionsBiot number
conventionconduction
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Importance of analytical solution
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What will be the daily temperature distribution profile on internal surface for styrofoam wall? A.
B.External temperature profileTtime
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What will be the daily temperature distribution profile on internal surface for tin glass? A.
B.External temperature profileTtime
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Conduction equation describes accumulation
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Important numbersInertial forceViscous forceReynolds number Momentum diffusivity Thermal diffusivityPrandtl number Buoyancy forcesViscous forces ConductionConvection Nusselt number thermal internal resistance surface film resistance Grashof number Biot number Reference book: Fundamentals of Heat and Mass Transfer, Incropera & DeWitt
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