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 xray 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 ^{2}K ^{1})
R = Thermal Resistance, ( W ^{1}.K )
Q_{r} = Radiated transferred energy (W)
Q_{co} = Conducted transferred energy (W)
Q_{cv} = Convective transferred energy (W)
T_{1} = Temperature or radiating body (K)
T_{2} Temperature or Suroundings (K)
A_{1} = Area of Radiating surface (m^{2})
A_{2} =Area of Receiving surface (m^{2})

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}
ρ = fluid density (kg / m^{3})
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 /m^{2} K)
k = Thermal conductivity (W/mK)
v = Fluid velocity (m/s)
L = characteristic dimension
g = accelaration due to gravity (m/s^{2} )

Heat Transfer by Conduction
dQ_{co} = kA(dt/dx) 
Q_{co} = (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 ^{o}C


Metal 
k=Wm^{1}K^{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^{1}K^{1} 
Asphalt 
1.26 
Bitumen 
0.17 
Br'ze Block 
0.15 
Brickwork 
0.6 
BrickDense 
1.6 
Carbon 
1.7 
ConcLD 
0.2 
ConcMD 
0.5 
ConcHD 
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=Wm1K1 
Balsa 
0.048 
StrawComp 
0.09 
Cotton Wool 
0.029 
PolystyreneExp'd 
0.03 
Felt 
0.04 
Glass Wool 
0.04(20^{o} 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^{1}K^{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 ^{1}K ^{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 (m^{2})
A _{2} =Area of Receiving surface (m^{2})
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}
h_{r} = heat Transfer coefficient for radiation (Wm^{2}K^{1})
Heat radiation from a body to the surroundings
Q _{r} = α e_{1} (T_{1}^{4}  T_{2}^{4} ) A_{1}
Heat radiation including the effect of the surroundings
Q _{r} = α ( e_{1} T_{1}^{4}  e_{2}T_{2}^{4} ) A_{1}
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 _{1}^{2} + T _{2}^{2} )
Emissivity Values
Refer to link Emissivity Values
for better table
Surface Material 
Emmissity 
Surface Material 
Emmissity 
AluminiumOxidised 
0.11 
Tile 
0.97 
AluminiumPolished 
0.05 
Water 
0.95 
Aluminium anodised 
0.77 
WoodOak 
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 
RubberNat_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 
CopperOxidised 
0.87 
St.SteelWeathered 
0.85 
Copper Polished 
0.04 
St.SteelPolished 
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 Newtonï¿½s 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 nondimensional 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 ^{9}  0.59  0.25 
10 ^{9} to 10 ^{12}  0.13  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 ^{1/3}Re ^{0.8}
Turbulent Flow In Pipe Nu = 0,023Pr ^{0.4}Re ^{0.8}
D = Diameter, L = Length, mean film temperature properties assumed
Typical Values of Heat Transfer Coefficient h = W.m ^{2}K ^{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.^{2}K.^{1}
 Shell and Tube, liquid inside and outside tubes U range150 > 1200 W. m.^{2}K.^{1}.
 Spiral Heat Exchanger, liquid to liquid U range 700 > 2500 W. m.^{2}K.^{1}

