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Heat Transfer

Introduction..... Symbols..... Heat transfer by conduction..... Heat transfer by radiation..... Heat transfer by Convection..... Heat Exchangers.....

Introduction

This page provides notes on heat transfer that may be useful to mechanical engineers.  The subject is very complicated and any user who requires accurate heat transfer values is advised to refer to quality reference documents or use specialised software.

When a hot surface us surrounded by an area which is colder energy in the form of heat will be transferred from the hot surface to the cooler area.  The rate of this transfer is depended on the temperature difference and the process will continue until both the surface and the surroundings are at the same temperature.  This process in called heat transfer and takes place by one or more of the following methods

Conduction
Convection
Radiation

Conduction takes place in solids, liquids, and gases.  Solids offer the least resistance to transfer of heat by conduction.   Conduction requires physical contact between material through which the heat is transferred.  A materials temperature is related to the motion of the constituent molecules.  The conduction process involves the molecule moving at higher velocities transferring their kinetic energy to the adjacent molecures which have lower kinetic energy.

Convection results in a gas or liquid.  The fluid adjacent to a hot surface heats up as a result of conduction.   The density of this fluid is reduced and it therefore rises to be replaced by a colder fluid of higher density.  This process continues resulting in convective flow producing an enhanced transfer of heat throughout the fluid.

The transfer of heat energy by radiation can occur in a vacuum , unlike conduction and convection.   Heat radiation is the same form of wave energy transfer as light, radio, and x-ray wave energy.   The rate of emmission of heat energy is related to the temperature difference, the distance between the surfaces, and the emissivity of the surfaces.  Bright reflective surfaces have the lowest emissivity values.


Notes on thermal insulation systems are found on webpage.Thermal Insulation


Symbols

Q = Heat Flow Rate (W )
t 1 = inside(hot)temperature,( K )
t S1 = inside surface (hot)temperature,( K )
t 2 = outside(cooler)temperature,( K )
t S1 = outside surface (cooler)temperature,( K )
A = Area,( m 2 )
U = Overall Heat Transfer Coefficient, ( W m -2K -1)
R = Thermal Resistance, ( W -1.K )
Qr = Radiated transferred energy (W)
Qco = Conducted transferred energy (W)
Qcv = Convective transferred energy (W)
T1 = Temperature or radiating body (K)
T2 Temperature or Suroundings (K)
A1 = Area of Radiating surface (m2)
A2 =Area of Receiving surface (m2)
e1 = Emissivity of Radiating surface
e2 = Emissivity of Surroundings
α = Stefan Boltzman constant = 5,673 x 10-8 W m-2 K-4
ρ = fluid density (kg / m3)
μ = fluid viscosity (kg / m.s)
β = coeff. of vol expansion (1 /K)
θ = Temperature difference (k)
c = specific heat (J/kg.K )
a = velocity of Sound (m/s)
h = heat transfer coefficient (W /m2 K)
k = Thermal conductivity (W/mK)
v = Fluid velocity (m/s)
L = characteristic dimension
g = accelaration due to gravity (m/s2 )



Heat Transfer by Conduction

dQco = kA(-dt/dx)
Qco = (k.A /x). (t 1-t 2)
U = k/x
Therefore Q = U.A(t 1-t 2)
Thermal resistance R = 1 / U.A


The heat has to pass through the surface layers on both sides of the wall

q = A.h s1(t s1 - t 1) = k.A(t 1 -t 2) / x = Ah s2(t 2 -t s2)
U = 1 / (1/h s1 + x/ k + 1/ h s2 )
R = 1/ A.h s1 + 1/ A.h s2 + x/ A.k = R s1 + R s2 + R


Table Showing Various values for k at 20 oC
Metal               k=Wm-1K-1   
Aluminium 237
Antimony 18.5
Beryllium 218
Brass 110
Cadmium 92
Cobalt 69
Constantan 22
Copper 398
Gold 315
Iridium 147
Cast Iron 55
Pure Iron 80.3
Wr't Iron 59
Lead 35.2
Magnesium 156
Molybdenum 138
Monel 26
Nickel 90.5
Platinum 73
Silver 427
C.Steel 50
St.Steel 25
Tin 67
Zinc 113
   
Plastics  
Acrylic 0.2
Nylon 6 0.25;
Polythene High Den 0.5
PTFE 0.25
PVC 0.19
   
   
   
   
   
Misc.solids           k =Wm-1K-1   
Asphalt 1.26
Bitumen 0.17
Br'ze Block 0.15
Brickwork 0.6
Brick-Dense 1.6
Carbon 1.7
Conc-LD 0.2
Conc-MD 0.5
Conc-HD 1.5
Firebrick 1.09
Glass 1.05
Glass -Boro. 1.3
Ice 2.18
Limestone 1.1
Mica 0.75
Cement 1.01
Parafin Wax 0.25
Porcelain 1.05
Sand 0.06
   
Insulation k=Wm-1K-1
Balsa 0.048
Straw-Comp 0.09
Cotton Wool 0.029
Polystyrene-Exp'd 0.03
Felt 0.04
Glass Wool 0.04(20o C
Kapok 0.034
Magnesia 0.07
Plywood 0.13
Rock Wool 0.045
Sawdust 0.06
Slag Wool 0.042
Wood 0.13
Sheeps Wool 0.038
Cellulose 0.039
Liquids               k= Wm-1K-1   
Benzene 0.16
Carb Tet'ide 0.11
Acetone 0.16
Ether 0.14
Glycerol 0.28
Kerosene 0.15
Mercury 8
Methanol 0.21
Machine Oil 0.15
Water 0.58
Sodium 84
   
Gases           k= Wm -1K -1
Air 0.024
Ammonia 0.022
Argon 0.016
Carbon Dio 0.015
Carbon Mon 0.023
Helium 0.142
Hydrogen 0.168
Methane 0.030
Nitrogen 0.024
Oxygen 0.024
Water Vap. 0.016
   
   
   
   
   
   
   
   
   
   
   
   



Heat Transfer by Radiation

Q r = radiated energy (W)
T 1 = Temperature or radiating body (K)
T 2 Temperature or Suroundings (K)
A 1 = Area of Radiating surface (m2)
A 2 =Area of Receiving surface (m2)
e 1 = Emissivity of Radiating surface
e 2 = Emissivity of Surroundings
α = Stefan Boltzman constant = 5,673 x 10-8 W m-2 K-4
hr = heat Transfer coefficient for radiation (Wm-2K-1)

Heat radiation from a body to the surroundings

Q r = α e1 (T14 - T24 ) A1

Heat radiation including the effect of the surroundings

Q r = α ( e1 T14 - e2T24 ) A1

Now the heat transfer using the heat transfer coefficient =

Q r = h r A 1 ( T 1 - T 2 ) therefore h r = α e 1 (T 1 + T 2 )( T 12 + T 22 )

Emissivity Values

Refer to link Emissivity Values for better table

Surface Material Emmissity Surface Material Emmissity
Aluminium-Oxidised 0.11 Tile 0.97
Aluminium-Polished 0.05 Water 0.95
Aluminium anodised 0.77 Wood-Oak 0.9
Aluminium rough 0.07 Paint 0.96
Asbestos Board 0.94 Paper 0.93
Black Body -Matt 1.00 Plastics 0.91 Av
Brass -Dull 0.22 Rubber-Nat_Hard 0.91
Brass- Polished 0.03 Rubber _Nat_Soft 0.86
Brick -Dark 0.9 Steel_Oxidised 0.79
Concrete 0.85 Steel Polished 0.07
Copper-Oxidised 0.87 St.Steel-Weathered 0.85
Copper -Polished 0.04 St.Steel-Polished 0.15
Glass 0.92 Steel Galv. Old 0.88
Plaster 0.98 Steel Galv new 0.23



Heat Transfer by Convection

Convective heat transfer occurs between a moving fluid and a solid surface.
The rate of convective heat transfer between a surface and a fluid is given by the Newton’s Law of Cooling;

The symbols involved in convective heat transfer are listed below

The dimensionless groups involve in convective heat transfer are listed below


Figures identifying characteristic Dimension L

It is customary to express the convection coefficient (average or local), in a non-dimensional form called the Nusselt Number.

Natural convection

Nu = C(Gr.Pr) n C and n are tabled below

Note: Convection heat transfer values are very specific to the geometry of the surface and the heat transfer conditions - These example equations are very general in nature and should not be used for serious calcs. The links below provide much safer equations..

Surface (Gr.Pr) C n
Vertical Plates/Cylinders 10 4 to 10 90.59 0.25
10 9 to 10 120.13 0.33
Horizontal Pipes 10 3 to 10 9 0.53 0.25
Horizontal Plates
Heated Face up or Cooled Face Down
10 5 to 2 x 10 7 0.54 0.25
2 x10 7 to 3 x10 10 0.14 0.33
Horizontal Plates
Heated Face up or Cooled Face Down
3 x10 5 to 3 x10 10 0.27 0.25

Forced Convection

Laminar flow over Plate    Nu = 0,664(Re) 1/2(Pr) 1/3

Fully Developed pipe flow     Nu = 3,66 + 0,0866(D/L)Re.Pr  /  (1+0.04[D / L(Re.Pr)] 2/3)

Turbulent Flow Over Flat Plate    Nu = 0,036Pr 1/3Re 0.8

Turbulent Flow In Pipe     Nu = 0,023Pr 0.4Re 0.8

D = Diameter, L = Length, mean film temperature properties assumed

Typical Values of Heat Transfer Coefficient h = W.m -2K -1

  • Free Convection Over Various Shape - Air    2 - 23
  • Free Convection Over Various Shape - Water    300 - 1700
  • Turbulent Convection Over Various Shape and through tubes - Air    6 - 1400
  • Turbulent Convection Over Various Shape and through tubes - Water    1100 - 9000



Heat Exchangers

Heat exchangers normally transfer energy from a hot fluid to a colder fluid.    The energy in = The energy out.

If the fluids are the same with the same specific heat.
The mass flowrate x the temp drop of the hot fluid = the mass flow rate x the temp rise of the cold fluid.

Typical Values for Overall Heat transfer U are

  • Plate Heat Exchanger, liquid to liquid U range 1000 > 4000 W. m.-2K.-1
  • Shell and Tube, liquid inside and outside tubes U range150 > 1200 W. m.-2K.-1.
  • Spiral Heat Exchanger, liquid to liquid U range 700 > 2500 W. m.-2K.-1


Thermodynamic /Heat Transfer Links
  1. Thermodynamics..NASA - Glenn Research center at Series of informative notes on Thermodynamics
  2. Second Law of Thermodynamics..Interesting Article
  3. Designing Shell & Tube Heat Exchanger..Notes on Designing Heat Exchangers
  4. Watlow.. Heat Losses From various Surfaces ->Reference -> Heat Transfer
  5. APV_Phewizard... Free Plate Heat Exchanger Software for specify plate HX
  6. Emissivity Values... A table of emissivity values
  7. Cheresources... Various heat transfer values -Useful
  8. Spirax Sarco...Excellent Reference Site . Learning centre includes heat transfer reference information
  9. A Heat transfer handbook...Complete downloadble document. Informative but very detailed

This page is being developed


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Last Updated 26/01/2013