Heat transfer in Flow Through Conduits The flow in a commercial circular tube or pipe is usually laminar when the Reynolds number is below 2,300
The pipes were heated at a uniform rate, giving a constant temperature gradient along its axis, and the flow experienced both centrifugal and buoyancy forces (
14 déc 2013 · The heat transfer process includes the convection inside the pipe, the conduction through the pipe, and the convection outside the pipe The
Keywords: Heat flux, Mean temperature, Micropipe, Nusselt number, Thermal conductivity, Viscosity Introduction Liquid flow through micro ducts is used to
Consider steady conduction through a large plane wall of thickness ?x = L and Steady state heat transfer through pipes is in the normal direction to the
Heat transfer analysis provides a means to estimate the fluid temperature along the of the pipe due to conduction through pipe wall and any number of
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127912_3StaedyConductionHeatTransfer.pdf M.BahramiENSC388(F09)SteadyConductionHeatTransfer1
SteadyHeatConduction
Inthermodynamics,weconsideredtheamountofheattransferasasystemundergoesa processfromoneequilibriumstatetoanother.Thermodynamicsgivesnoindicationof howlongtheprocesstakes.Inheattransfer,wearemoreconcernedabouttherateof heattransfer.
Thebasicrequirementforheattransferis
thepresenceofatemperaturedifference.The temperaturedifferenceisthedrivingforceforheattransfer,justasvoltagedifferencefor electricalcurrent.ThetotalamountofheattransferQduringatimeintervalcanbe determined from:kJdtQQ t 0 Therateofheattransferperunitareaiscalledheatflux,andtheaverageheatfluxona surfaceisexpressedas 2 /mWAQq
SteadyHeatConductioninPlaneWallsConductionisthetransferofenergyfromthemoreenergeticparticlesofasubstanceto
theadjacentlessenergeticonesasresultofinteractionsbetweentheparticles.
Considersteadyconduction
throughalargeplanewallofthicknessȴx=Landsurfacearea
A.ThetemperaturedifferenceacrossthewallisȴT=T
2 -T 1 . Notethatheattransferistheonlyenergyinteraction;theenergybalanceforthewallcan beexpressed:dtdEQQ wall outin
ForsteadyͲstateoperation,
.constQQ outin Ithasbeenexperimentallyobservedthattherateofheatconductionthroughalayeris proportionaltothetemperaturedifferenceacrossthelayerandtheheattransferarea, butitisinverselyproportionaltothethicknessofthelayer.WxTkAQCond thickness)difference eraturearea)(temp (surfacefer heat trans of rate M.BahramiENSC388(F09)SteadyConductionHeatTransfer2
Fig.1:Heatconductionthroughalargeplanewall.
Theconstantproportionalitykisthethermalconductivityofthematerial.Inthelimiting casewhereȴxї0,theequationabovereducestothedifferentialform:
WdxdTkAQCond
whichiscalledFourier'slawofheatconduction.ThetermdT/dxiscalledthetemperature gradient,whichistheslopeofthetemperaturecurve(therateofchangeoftemperature
Twithlengthx).
ThermalConductivity
Thermalconductivityk[W/mK]isameasureofamaterial'sabilitytoconductheat.The thermalconductivityisdefinedastherateofheattransferthroughaunitthicknessof materialperunitareaperunittemperaturedifference. Thermalconductivitychangeswithtemperatureandisdeterminedthroughexperiments.
Thethermal
conductivityofcertainmaterialsshowadramaticchangeattemperatures nearabsolutezero,whenthesesolidsbecomesuperconductors. Anisotropicmaterialisamaterialthathasuniformpropertiesinalldirections. Insulatorsarematerialsusedprimarilytoprovideresistancetoheatflow.Theyhavelow thermalconductivity. A A
ȴxQ
• T 1 T 2 M.BahramiENSC388(F09)SteadyConductionHeatTransfer3
TheThermalResistanceConcept
TheFourierequation,forsteadyconductionthroughaconstantareaplanewall,canbe written:
LTTkAdxdTkAQ
Cond21
ThiscanbereͲarrangedas:
)/()( 12
WCkALRW
RTTQ wallwall Cond x R wall isthethermalresistanceofthewallagainstheatconductionorsimplytheconduction resistanceofthewall. Theheattransferacrossthefluid/solidinterfaceisbasedonNewton'slawofcooling: )/(1WChARWTThAQ Convs R conv isthethermalresistanceofthesurfaceagainstheatconvectionorsimplythe convectionresistanceofthesurface.
ThermalradiationbetweenasurfaceofareaAatT
s andthesurroundingsatT ь canbe expressedas: