Heat transfer is the process by which thermal energy moves from a hotter region to a cooler one. In engineering, heat transfer occurs through three main mechanisms: conduction, convection, and radiation. This page provides practical formulas, material data, and engineering guidance for analysing heat transfer in real systems, including heat exchangers and insulation applications.
Introduction..... Symbols..... Heat transfer by conduction..... Heat transfer by radiation..... Heat transfer by Convection..... Heat Exchangers.....
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
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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 ) |
| 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 r = radiated energy (W) 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 ) Convective heat transfer occurs between a moving fluid and
a solid surface. The symbols involved in convective heat transfer are listed below The dimensionless groups involve in convective heat transfer are listed below It is customary to express the convection coefficient (average or local),
in a non-dimensional form called the Nusselt Number. 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.. 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
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
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)
Emissivity Values
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
The rate of convective heat transfer between a
surface and a fluid is given by the Newtons Law of Cooling;
Figures identifying characteristic Dimension L Natural convection
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
D = Diameter, L = Length, mean film temperature properties assumed
Typical Values of Heat Transfer Coefficient h = W.m -2K -1
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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
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The three modes are conduction (through solids or stationary fluids), convection (through moving fluids), and radiation (via electromagnetic waves).
The heat transfer coefficient (h) represents how effectively heat is transferred between a surface and a fluid. It depends on flow conditions, geometry, and fluid properties.
Thermal conductivity (k) is a material property that indicates how well heat is conducted through a material.
The overall heat transfer coefficient accounts for all thermal resistances in a system, including conduction and convection, and is used in heat exchanger calculations.
These formulas are suitable for initial engineering estimates. For detailed design, more advanced methods or simulation tools should be used.