Thermos Index

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

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

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

Thermos Index