Heat Transfer

Introduction: Heat & temperature are the indispensable variables of our existence. A just about perfect (optimum) temperature on Earth allowed the Evolution of life here. In addition, we can say that heat is“energy in transition”. Always flowing like a fluid from high temperature to low temperature. Industrially speaking, there is no other important factor that establishes the benchmarking for economy and optimum resource utilization than the heat transfer coefficient. Heta transfer supplements First and Second Laws of Thermodynamics by providing additional experimental rules which may be used to establish energy-transfer rates. The importance of “heat transfer” science in engineering is more than the “thermodynamics” of the process because we are more interested in the rate of heat transfer (Cengel 2004, page 1) than the amount of energy required to change the system equilibrium to some other point.

• Heat Transfer is the science that seeks to predict the energy transfer (this energy transfer~ heat) that may take place between material bodies as a result of a temperature difference (Holman 2005, page 1). This science not only seeks to explain how heat is transferred but also the rate at which the exchange will take place under certain specific conditions. Thus, the determination of rate of heat transfer has a direct application in material science as well as industry in devising equipments which can withstand maximum amount of heat for the maximum possible time so that the heat sources that are used to generate heat are utilized to their utmost optimum level.

Mechanisms of Heat Transfer: heat transfer always takes place between the bodies among which one has a higher temperature than the other. The transfer takes place till both of them are at same temperature (Cengel 2004, page 17). Heat transfer takes place from body at higher temperature to the body at lower temperature for the time until both of them have equal temperature. There are basic three modes (mechanisms) of heat transfer:

• Conduction: Atomic (or molecular) process. Intraphase heat transfer.
• Convection: Conduction accompanied by adjacent fluid motion. Interphase heat transfer.
• Radiation: Heat transfer can be accomplished without any necessity of medium for transfer. Heat radiates from source to sink.

Conduction: It is the transfer of heat energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles. It can take place in solid, liquid, or gases. In gases and liquids, it is due to collision and diffusion of the molecules during their random motion. In solids, it is due to the combination of vibration of the molecules in a lattice and the energy transport by free electrons (Cengel 2004, page 17-18)

 From (Dutta 2003, page 3), It occurs in the presence of a temperature difference and is not accompanied by any macroscopic or bulk motion in the medium. Conduction is the only mode of heat transfer in a solid medium (although it occurs in stagnant liquid as well as in a gaseous medium). Basic governing Law:

         Fourier`s Law {q= -kA *(temperature gradient [dT/dx in heat flow direction)}

Energy in conduction is transferred through inter-molecular interactions, and therefore, its flux depends on the local gradient of temperature and the thermophysical properties of the medium (Gupta 2005, page 20).

Convection: It is the mode of energy transfer between a solid and the adjacent liquid or gas that is in motion, and it involves the combined effects of conduction and fluid motion. The faster the fluid motion, the greater the convection heat transfer. In the absence of any bulk fluid motion, heat transfer between a solid surface and the adjacent fluid is by pure conduction. The presence of bulk motion of the fluid enhances the heat transfer between the solid surface and the fluid, but it also complicates the determination of heat transfer rates (Cengel 2004, page 25). Convection basically is the increase in heat transfer due to fluid motion (Gupta 2005, page 6).

On the basis of the reason behind the fluid motion, the convective heat transfer process can be categorized in two parts: 1. Free convection, 2. Forced Convection.

Usual meanings are based on the fact that if the fluid motion is because of natural reasons and no artificial (blower etc) work is done, it is free convection. Otherwise, it is forced convection.

                                               Newton`s Law of cooling: Q_conv = hA (T_w – T_f)

T_w = Wall temp., T_f = Ambient Temp

Radiation: (Dutta 2003, page 3-4) A body at a temperature above absolute zero always emits energy in the form of electromagnetic waves. The rate of release of such energy is proportional to the fourth power of the absolute temperature of the body. This phenomenon is called radiation and the basic governing law is known as the: Stefan-Boltzmann law, Q_emitted= σAT⁴. 

Conduction-Convection systems (Holman 2004, page 41)

[1]

The heat that is conducted through a body must frequently be removed (or delivered) by some convection process. For example, the heat lost by conduction through a furnace wall must be dissipated to the surroundings through convection. In heat-exchangers applications a finned-tube arrangement might be used to remove heat from a hot liquid. The heat transfer from a liquid to the finned tube is by convection. The heat is conducted through material and finally dissipated to the surroundings by convection. Therefore, analysis of the combined convection-conduction systems is very important from the practical standpoint.

In the figure, E _{left face}= E _{out right face} + E _{lost by convection.}

For convection heat transfer coefficient: Q_conv = hA (T_w – T_f) 

• Insulating Materials[2]: The primary function of thermal insulation materials used in various inductrial applications is to reduce the transmission of heat walls, hatches, pipes or stanchions into the atmosphere. By reducing the amount of heat leak, the amount of heat loss can be reduced and so the efficiency of the process can be increased.  Insulation in the walls of the equipments can reduce the amount of heat that escapes from the container and so reduce the amount of heat genrerating fuel needed to keep the temperature to the required limits.

The main advantages of insulating materials are:

• To prevent heat transmission to the surrounding air and heat leaks (walls, hatches, pipes and stanchions);
• To optimize the useful heat available and that too for the maximum time;
• To help reduce energy requirements if these materials are used.

Thermal insulation is for example the method of preventing heat from escaping a container or from entering it. In other words, thermal insulation can keep an enclosed area such as a building warm, or it can keep the inside of a container cold. Heat can be transferred as mentioned earlier on by conduction, convection and/or radiation. Insulators are used to minimize that transfer of heat energy.

The major types of insulation are associated with the major types of heat transfer: Reflectors for example are used to reduce radiative heat transfer by reflecting electromagnetic radiation. Fibrous materials or spaces are used to reduce conductive heat transfer by reducing physical contact between objects and using materials with low thermal conductivity and therefore a good thermal resistance. These materials are also used to reduce convective heat transfer by stopping or retarding the movement of fluids (liquids or gases) around an insulated object. Common insulation materials mostly rely on the principle of trapping air or another gas (which are generally known to be good insulators in absence of convection) in a large number of pockets within a material to reduce convective and conductive heat transfer. They can be fibrous (e.g. down feathers and asbestos), cellular (e.g. cork or plastic foam), or granular (e.g. sintered refractory materials).

But the quality of such an insulator depends on the degree to which air flow is eliminated (porosity) since large cells of trapped air will have internal convection currents on the one hand side but the amount of solid material surrounding the air should be kept as small as possible to reduce thermal bridging within the insulator on the other hand side. Therefore the right pore size has to be determined to achieve best insulation characteristics for the purpose. (Wikipedia, 2007a)

(c) Thermal Conductivity and Temperature:

Different materials store heat differently, and we have defined the property specific heat as a measure of a material`s ability to store thermal energy. Likewise, the thermal conductivity k is a measure of a material`s ability to conduct heat. Water is a poor heat conductor relative to iron, although water is an excellent medium to store thermal energy.

Thus Thermal Conductivity of a material can defined as the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference.

[High value of k= Conductor, Low value of k= Insulator]

Thermal conductivity of a material also depents upon the temperature, as explained by the kinetic theory of molecules, at high temperatures, the molecules move randomly at high speeds thus contributing towards the overall thermal conduction, [ k~(T)^1/2 ].

Thermal conductivity of a substance is normally high in the solid state and lowest in the gas phase. Thermal conductivities of most liquids decrease with increasing temperature, water being an exception. 

(d) Problem

The equation used for calculating the heat loss over the length of the material used,

combines conductive and convective heat transfer:

k

r

r

k

r

r

r h r h

T T

L

q

i

p

i

s

p

p p i i

inside outside

× × × × × × × × × × + + +

−

=

p p p 2p

ln

2

ln

2

1

2

1 0

The units are as follows:

L

q

m K

W

m m

m K

W

m

K

× °

+

× °

°

=

× 2

1

m

=W

Now the values are entered into the equation:

2 0.025

0.055

0.065

ln

2 40

0.05

0.055

ln

2 0.065 22

1

2 0.055 5000

1

398 291

× × × × × × × × × × + + +

−

=

p p p p

L

q

m

W

= 91.01

With an insulation thickness of 10mm the total heat loss from the pipe

to the air per meter length is 91.01 W/m.

In the following the rate of heat loss is calculated if an additional 50 mm thickness of

the insulation is added to the pipe. Hence the new insulation radius for the calculation

is ri = 0.115m.

2 0.025

0.055

0.115

ln

2 40

0.05

0.055

ln

2 0.115 22

1

2 0.055 5000

1

398 291

× × × × × × × × × × + + +

−

=

p p p p

L

q

m

W

= 22.48

With an insulation thickness of 60mm the total heat loss from the pipe to the air per

meter length is 91.01 W/m.

5.2 Payback Period

Further on the payback period is determined if the extra 50mm of insulation costs

£120 per metre of length to install, the pipe operates continuously for 48 weeks per

year, and the heat is generated at a cost of 2p per MJ.

l t

q

C C i h x = ×D ×

m s

J

m s

J

m s

J

l

q

×

=

×

−

×

D = 91.01 22.48 68.53

Costs ci = 120 £/m

ch = 120 £/MJ

Time tx = ?

l t

q

C C i h x = ×D ×

m s t

J

m MJ x ×

×

Þ120 £ = 0.02 £ ×68.53

m s t

J

MJ

J

m x ×

×

Þ6000MJ ×10 = 68.53 6

60min

min

48 7 24 60

87,552,896.45 87,552,896.45

s

day h

h

week

day

year

week

s t s x

× × × ×

Þ = =

t years x = 3.016

When the pipe operates continuously 48 weeks per year, the payback period is in 3

years and 5 days. This means that the additional costs that were necessary to install

the 60mm thick insulation will be saved after this period of time due to better

insulation characteristics.

REFERENCES

[1] Cengel Yunus A., Heat Transfer: A Practical Approach, Tata McGraw-Hill, Second Edition

     in SI units, 2004, ISBN 0-07-059417-1

[2] Dutta Binay K., Heat Transfer: Principles and Applications, Prentice Hall of India Pvt. Ltd.,

     second printing 2003, ISBN 81-203-1625-8

[3] Gupta Vijay, Elements of Heat And Mass Transfer, New Age Intr. Ltd, Publishers, Reprint

     2005, ISBN 81-224-0800-1

[4]Holman, J.P., Heat Transfer, Tata McGraw-Hill Publishing Co. Ltd., Ninth Edition, Fourth

     Reprint 2005, ISBN 0-07-058874-0

[1] Holman 2004, page 41

[2] http://www.fao.org/docrep/006/y5013e/y5013e08.htm