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Thermodynamics/ Heat Transfer

Introduction
This page provides a limited notes on thermodyamics and heat transfer that may be useful to mechanical engineers.

Notation

Identifier Description Units (typical)   
c p Specific Heat Capacity at Constant pressure kJ/(kg K)
c v Specific Heat Capacity at Constant Volume kJ/(kg K)
p Absolute Pressure N / m 2
T Absolute Temperature K
v volume per unit mass m 3
W Work Output per unit mass kJ/kg
M Molecular Weight -
R o Universal Gas Constant = 8,31 kJ /(kg mole.K)
Q Heat Quantity kJ
R Gas Constant = R o / M kJ /kg.K
U Internal energy (thermal) kJ



Thermodynamic Laws


Zeroth Law of Thermodynamics...

When two objects are separately in thermodynamic equilibrium with a third they are in equilibrium with each other

Objects in thermodynamic equilibrium are at the same temperature

First Law of Thermodynamics...

This law expresses the general law of conservation of energy. and states that heat and work are mutually convertible

Heat In = Work Out over complete cycle
or Sum (d Q ) = sum (d W )

The basic energy equation results from this

dQ = dU + dW

Second Law of Thermodynamics...

This law in its simplest states that heat can only flow from hot to cold and not vice versa.  In terms of thermodynamic engine cycles the law states that the gross heat supplied to a system in a complete cycle must exceed the work done by the system.   Therefore heat must be rejected.  The thermal efficiency of an heat engine must be less than 100%.


Process Relations

Reversible Polytropic Process

p v n = constant

W = ( p 2 v 2 - p 1 v 1 ) / ( 1 - n ) .. (n not 0 )

For a perfect gas

W = R ( T 2 - T 1 ) / (1 -n )

Q = ( Cv + R /(1 - n) ) ( T 2 -T 1 )

T 2 / T 1 = ( p 2 / p 1 ) ( n-1 ) / n

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

γ = 1.4 for Air,  H 2,  O 2, CO, NO, Hcl

γ = 1.3 for CO 2, SO 2,  H 2O, H 2S, N 2O, NH 3, CL 2,  CH 4, C 2H 2, C 2H 4


Heat Transfer

Heat Transfer takes place by Conduction, Convection and Radiation

Heat Transfer by Conduction

  • q = Heat Flow Rate W
  • t 1 & t 2 = temperature, K (heat flows down (-))
  • A = Area, m 2
  • 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
  • R = Thermal Resistance, W -1.m -1.K
dq = kA(-dt/dx)
q = (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  
Balsa 0.048
Straw-Comp 0.09
Cotton Wool 0.029
Polystyrene-Expanded 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
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

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 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 = 0.0866(D/L)Re.Pr  /  (1+0.04[D / L(Re.Pr)] 2/3) + 3.66

Turbulent Flow Over Flat Plate    Nu = 0.036Pr 1/3Re 0.8

Turbulent Flow In Pipe     Nu = 0.023Pr 0.4Re 0.8

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. Guide to Compact Heat Exchangers... A very informative document
  7. Emissivity Values... A table of emissivity values
  8. Cheresources... Various heat transfer values -Useful
  9. ProcessAssociates... Various Calculators and Tools for Shell & Tube HE;s -Excellent
  10. Spirax Sarco...Excellent Reference Site . Learning centre includes heat transfer reference information

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Last Updated 18/07/2005