Disclaimer: The information on this page has not been checked by an independent person. Use this information at your own risk.
ROYMECH

Home

Thermodynamics/ Heat Transfer


Thermodynamic Properties of Fluids

Process Relations

Identifier Description Units (typical)
cp Specific Heat Capacity at Constant pressure kJ/(kg K)
cv Specific Heat Capacity at Constant Volume kJ/(kg K)
p Absolute Pressure N / m2
T Absolute Temperature K
v volume per unit mass m3
W Work Output per unit mass kJ/kg
M Molecular Weight -
Ro Universal Gas Constant 8.31 kJ /(kg mole.K)
R Gas Constant = Ro / M kJ /kg.K

Reversible Polytropic Process

p v n = constant

W = ( p2 v2 - p1 v1 ) / ( 1 - n ) .. (n not 0 )

For a perfect gas

W = R ( T2 - T1 ) / (1 -n )

Q = ( Cv + R /(1 - n) ) ( T2 -T1 )

T2 / T1 = ( p2 / p1 )( n-1 ) / n

For Adiabatic processes (Q = 0 ) n = g = cp / cv

g = 1.4 for Air,  H2,  O2, CO, NO, Hcl

g = 1.3 for CO2, SO2,  H2O, H2S, N2O, NH3, CL2,  CH4, C2H2, C2H4


Heat Transfer

Heat Transfer takes place by Conduction,Convect ion and Radiation

Heat Transfer by Conduction

  • q = Heat Flow Rate W
  • t1,t2 = temperature, K (heat flows down (-))
  • A = Area, m2
  • k = Coefficient of thermal conductivity, W m-1K-1
  • U = Overall Heat Transfer Coefficient,W m-1K-1
  • h = Surface Heat Transfer Coefficient, W m-2K-1

dq = kA(-dt/dx)

Q = (k.A /x). (t1-t2)

U = k/x

Therefore q = U.A(t1-t2)

Thermal resistance R = 1 / U.A

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

q = A.hs1(ts1 - t1) = k.A(t1 -t2) / x = Ahs2(t2 -ts2)

U = 1 / (1/hs1 + x/k + 1/hs2 )

R = 1/A.hs1 + 1/A.hs2 + x/A.k = Rs1 + Rs2 + R

Table Showing Various values for k at 20oC

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
   
   
   
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
   
Plastics  
Acrylic 0.2
Nylon 6 0.25;
Polythene HD 0.5
PTFE 0.25
PVC 0.19
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
   
Insulation  
Balsa 0.048
Straw-Comp 0.09
Cotton Wool 0.029
Polystyrene-Ex 0.03
Felt 0.04
Glass Wool 0.04
Kapok 0.034
Magnesia 0.07
Plywood 0.13
Rock Wool 0.045
Sawdust 0.06
Slag Wool 0.042
Wood 0.13
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

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;

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 104 to 1090.59 0.25
109 to 10120.13 0.33
Horizontal Pipes 103 to 109 0.53 0.25
Horizontal Plates
Heated Face up or Cooled Face Down		 105 to 2 x 107 0.54 0.25
2 x107 to 3 x1010 0.14 0.33
Horizontal Plates
Heated Face up or Cooled Face Down		 3 x105 to 3 x1010 0.27 0.25

Forced Convection

Laminar flow over Plate    Nu = 0.664(Re)1/2(Pr)1/3

Fully Developed pipe flow     Nu = 0.0866(D/L)Re.Pr  /  (1+0.04[D / L(Re.Pr)]2/3) + 3.66

Turbulent Flow Over Flat Plate    Nu = 0.036Pr1/3Re0.8

Turbulent Flow In Pipe     Nu = 0.023Pr0.4Re0.8

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

Sites For Thermodynamic Relationships Formualae

  1. Designing Shell & Tube Heat Exchanger..Notes on Designing Heat Exchangers
  2. Watlow.. Heat Losses From various Surfaces ->Reference -> Heat Transfer
  3. Maya Thermal Wizard...Heat Transfer Calculators and Thermal Properties of Matter
  4. Heat Transfer Notes...Informative Notes On Heat Transfer /Heat exchangers
  5. APV_Phewizard... Free Plate Heat Exchanger Software for specify plate HX
  6. Heat and mass transfer... Online book on including chapter of Heat Transfer
  7. Guide to Compact Heat Exchangers... A very informative document
  8. Emissivity Values... A table of emissivity values
  9. Introduction to Heat Exchangers... A paper providing heat exchanger design notes
  10. Heat Exchanger Design... A short course on heat exchanger design fundementals
  11. Cheresources... Various heat transfer values -Useful
  12. ProcessAssociates... Various Calculators and Tools for Shell & Tube HE;s -Excellent
  13. Heat Exchangers ... Heat Exchanger Descripton and formulea

..Page is being constructed..


Home

Send Comments to RoyBeardmore@ic24.net

Last Updated 01/07/2003