Heat Transfer IntroductionHeat Transfer Introductionand Conductionand Conduction

ConductionConduction If a temperature gradient exits in a continuous If a temperature gradient exits in a continuous

substance, heat can flow unaccompanied by any substance, heat can flow unaccompanied by any observable motion of matterobservable motion of matter

Metallic solids – conduction occurs from the Metallic solids – conduction occurs from the motion of unbound electronsmotion of unbound electrons

Other solids and liquids – conduction results Other solids and liquids – conduction results from the transport of momentum of individual from the transport of momentum of individual molecules along the temperature gradientmolecules along the temperature gradient

Gases – conduction occurs by random motion of Gases – conduction occurs by random motion of molecules; heat is “diffused” from hotter regions molecules; heat is “diffused” from hotter regions to colder onesto colder ones

Examples – heat flow in opaque solids, ie., brick Examples – heat flow in opaque solids, ie., brick wall of furnace or metal wall of a tubewall of furnace or metal wall of a tube

ConvectionConvection When a current or macroscopic particle of fluid When a current or macroscopic particle of fluid

crosses a specific surface, such as the boundary crosses a specific surface, such as the boundary of a control volume, it carries with it a definite of a control volume, it carries with it a definite quantity of enthalpyquantity of enthalpy

Occurs only when forces act on the particle or Occurs only when forces act on the particle or stream of fluid and maintain motion against stream of fluid and maintain motion against forces of frictionforces of friction

Thermodynamically, convection is not heat flow, Thermodynamically, convection is not heat flow, but fluxbut flux Closely associated with fluid mechanicsClosely associated with fluid mechanics

Examples – transfer of enthalpy by eddies of Examples – transfer of enthalpy by eddies of turbulent flow, current of warm air from a furnace turbulent flow, current of warm air from a furnace flowing across a roomflowing across a room

Natural and Forced ConvectionNatural and Forced Convection Natural convection – currents are the result of Natural convection – currents are the result of

buoyancy forces generated by differences in buoyancy forces generated by differences in density and differences in density are in caused density and differences in density are in caused by temperature gradients in fluid massby temperature gradients in fluid mass Flow of air across a heated radiatorFlow of air across a heated radiator

Forced convection – currents are set in motion Forced convection – currents are set in motion by action of a mechanical device such a pump or by action of a mechanical device such a pump or agitator, flow is independent of density gradientsagitator, flow is independent of density gradients Heat flow to a fluid pumped through a heated pipeHeat flow to a fluid pumped through a heated pipe

RadiationRadiation

Transfer of energy through space by Transfer of energy through space by electromagnetic waveselectromagnetic waves

If matter appears in the path, radiation will If matter appears in the path, radiation will be transmitted, reflected, or absorbedbe transmitted, reflected, or absorbed

Only absorbed energy appears as heatOnly absorbed energy appears as heat Examples – loss of heat from a radiator or Examples – loss of heat from a radiator or

uninsulated stream pipe; heat transfer in uninsulated stream pipe; heat transfer in furnacesfurnaces

Heat Transfer by ConductionHeat Transfer by Conduction Fourier’s lawFourier’s law

Temperature can vary with both location and timeTemperature can vary with both location and time Heat flow occurs from hot to coldHeat flow occurs from hot to cold

ntk

dAdq

Where A = area of isothermal surface n = distance measured normally to surface q = rate of heat flow across surface in direction normal to surface T = temperature k = proportionality constant

One-Dimensional Heat FlowOne-Dimensional Heat Flow

Hot Gas

B

Water

Tem

pera

ture

700 C

25 Cc

III

II

I

I – at instant of exposure of wall to high temperature

II – during heating at time t

III – at steady state

For Steady One-Dimensional FlowFor Steady One-Dimensional Flow

Thermal conductivity, kThermal conductivity, k Proportionality factor that represents a Proportionality factor that represents a

physical property of a substancephysical property of a substance q/A – rate of heat flow per unit areaq/A – rate of heat flow per unit area dT/dn – temperature gradientdT/dn – temperature gradient q – watts or Btu/hq – watts or Btu/h dt/dn - dt/dn - C/m or C/m or F/ftF/ft k – W/m-k – W/m-C or Btu-ft-h-C or Btu-ft-h-FF

dndTk

Aq

For small temperature ranges, k is constantFor small temperature ranges, k is constant For larger temperature ranges,For larger temperature ranges,

k = a + bTk = a + bTWhere a and b are empirical constantsWhere a and b are empirical constants

k for metalsk for metals Stainless – 17 W/m-Stainless – 17 W/m-CC Silver – 415 W/m-Silver – 415 W/m-CC

k for liquidsk for liquids Water - 0.5 – 0.7 W/m-Water - 0.5 – 0.7 W/m-CC

k for gasesk for gases Air – 0.024 W/m-Air – 0.024 W/m-CC

Solids with low k values are often used as Solids with low k values are often used as insulatorsinsulators

Steady State ConductionSteady State Conduction For a flat slab of thickness, BFor a flat slab of thickness, B

R is the thermal resistance of the solid R is the thermal resistance of the solid between two pointsbetween two points

RT

BTk

xxTTk

Aq

dxkAqdT

dxdTk

Aq

12

21

Resistances in SeriesResistances in SeriesT

TCTBTA

RA RB RC

BA BB BC

T

TC

TB

TA

RT

RRRT

kBkBkBT

Aq

TkABq

kABq

kABqTTT

CBACCBBAA

C

CC

B

BB

A

AACBA

///

Heat Flow through a Cylinder Heat Flow through a Cylinder

To Ti

dr

ri

rro

)/ln(

)/ln()(2

)(

)/ln())(2(

2

2

io

ioL

io

ioL

io

oiL

io

oi

r

r

T

T

rrrrr

rrrrLA

rrTTAkq

rrTTLkq

dTqLk

rdr

rLdrdTkq

o

i

i

o

Heat Flow in FluidsHeat Flow in Fluids Typical equipment Typical equipment

consists of a bundle consists of a bundle of parallel tube of parallel tube encased in a encased in a cylindrical shellcylindrical shell