Heat is defined as a form of energy in transition which flows under the driving influence of a temperature difference. Once the transfer of heat energy is complete, it is stored in one or more forms of stored potential, kinetic, in general as internal energy. It is worth noting that the heat as energy in transition is never measured as such but is determined in term of observed changes in other forms of energy and the relevant physical properties. Strictly speaking the heat transfer anywhere else in a system is merely redistribution of internal energy within the system. There are three basic mechanisms of heat transfer – conduction, convection, and radiation. In engineering applications they may occur separately, or simultaneously.
Modes of Heat Transfer: Heat is transferred by conduction, convection, and radiation.
Conduction is recognized as the transfer of heat within a substance from high temperature regions to low temperature regions. Conduction in solids other than metals is due to longitudinal oscillations in metals due to diffusion of free electrons and in gases due to elastic impacts of molecules. As kinetic energy of motion is proportional to the absolute temperature, it is logical to imagine conduction as occurring by collisions of faster with slower moving molecules. This idea seems to be quite correct. In the case of gases, molecular interaction is responsible for energy transfer; however, in metals an electron gas rather than the molecules is the primary medium of energy transfer.
Convection involves the gross motion of the fluid (liquid and gas) itself with the result that fresh fluid is continually available for energy transfer. The physical movement of fluid generally involves smaller eddies which help in distributing heat energy. The state and nature of fluid fl ow is of great importance in convective heat transfer. The fluid is set in bodily motion either due to-
- Difference in density due to heating, i.e. buoyancy forces, this is the case of a free convection, or
- External force such as fans, blowers, pumps, etc. giving rise to forced convection.
Convection is not actually a separate process, as conduction to or from the fluid is really what constitutes the heat transfer, and the movement of the fluid carries heat transferred to another location. A household water heating system is a good example of the type of heat transfer.
Radiation is transfer of heat energy by temperature excited electromagnetic waves emitted by vibrating electrons in the molecules of material at the surface of a body. The quantity of heat radiated depends on the absolute temperature of the body.
All bodies at temperatures above absolute zero emit electromagnetic waves of diff erent wave lengths. Radiation differs from conduction and convection in this respect and is distinguished by double transformation of energy thermal is converted into radiant energy by an emitter and radiant energy into thermal energy by an absorber.
An interesting example of combined processes of heat transfer is a steam boiler. Here, heat is transferred from the flue gases to the outer surface of the water tubes through all the three modes of the transfer conduction, convection and radiation. From the outer surface of a water tube to its inner surface, heat is transferred only by conduction through a layer of soot, metal wall and a layer of deposited scale. Finally, from the inner surface of the tube to the water, heat is transferred only by convection. Individual modes of heat transfer are, therefore, met within various combinations in the course of heat flow, and it is very diffi cult to separate them. In practical calculation, it is sometimes, desirable to consider such complex processes as a whole.
Irreversibility in Heat Transfer: It may be noted that transfer of heat is on account of temperature gradient existing between two bodies, which makes the process irreversible, i.e. flow of heat cannot be reversed of its own. Thus, heat transfer in the direction of temperature gradient is a natural and spontaneous process. As it happens in all natural process, entropy increases in the system of bodies among which heat transfer takes place. Let there be two bodies A and B at temperature T1 and T2. T1 > T2 as shown in Fig. 1-1. If dQ is the quantity of heat lost by A and that gained by B, entropy lost by A is dQ/T1 & that gained by B is dQ/T2. Thus, in the system of two bodies due to heat transfer there is net increase of entropy dQ/T2-dQ/T1. The gain in entropy during heat transfer indicates fall in quality of heat energy. It is desirable to minimize irreversibility and also gain in entropy in any process in thermodynamics as it renders the process inefficient. This is accomplished by limiting temperature difference (T1-T2) in the process of heat transfer. However, with the decrease of temperature equalization is attained. Further, with the system of bodies at different temperatures, on attainment of equalization the plot of increase in entropy of the system is plotted with time, it indicates decreasing rate of increase in entropy. On equalization, entropy of the system becomes maximum and no further increase in entropy of the system is feasible.
Fields of Applications: The importance of heat transfer analysis lies in a very wide range of applications connected with power plant engineering, chemical and process engineering, manufacturing and metallurgical industries, refrigeration and air conditioning practices, cooling problems associated with electrical and electronic equipments, space technology, low temperature technology & many other applications. Condensers, evaporators, coolers, heat dissipating surfaces such as fi ns, prevention of heat losses through insulating materials, controlled release of heat energy from fossil and nuclear fuels aerodynamic heating, combustion processes, thermally operated controls, etc. are some of the specifi c examples of heat transfer applications.
In the design of a plant which incorporates heat exchange with the surroundings, the size of the heat transfer equipments, the material of construction connected with them, and the auxiliary equipment required for their utilization, are basic considerations being faced by a designer. The equipment should fulfill its required objectives and at the same time should be economical to purchase and operate. This requires through understanding of the basic mechanisms of heat transfer and analysis so as to be able to evaluate quantitatively heat transfer rates and other related quantities. Unfortunately, the analysis of heat transfer involves many variables and it is impossible to separate them and treat one at a time e.g. the flow of heat through a condenser involves nine variables. This clearly requires detailed knowledge of the principles governing heat transfer.
Heat exchanges are very important parts of many thermal systems. Their first cost and the cost of their operation and maintenance are of great impertinence for efficient plant installation. As stated earlier heat transfer is an irreversible process, hence it is desirable to reduce the irreversibility that always accompanies heat transfer by reducing temperature difference between the bodies that exchange heat. With the reduction of temperature difference, the rate of heat transfer decreases and in order to maintain the given rate of heat transfer, area of heat transfer is to be increased. Thus, cost of heat exchanger increases rapidly with the reduction in temperature difference employed for heat transfer. Thus, designs should make a decision regarding economic limit to which temperature difference can be reduced.
The popular examples of heat exchanges are :
- Surface condenser of a steam plant,
- Air preheater and economizer for a boiler,
- Intercooler for air compressor,
- Heat exchanger for gas turbine plant,
- Condenser and evaporator for refrigeration unit
- Heat exchange for chemical plant, etc.
In these classes of heat exchanger, the fluids are kept separate and heat transfer take place through the intervening walls. This is often the only possible type as the fluids differ in their chemical composition and at least one is to be recirculated through the plant cycle so that they can not be allowed to mix. Thus, in such case the rate of heat transfer between fluids is limited to the capacity of the separating wall to transfer heat. This capacity of heat transfer is the basis of the design for this type of heat exchanger.
Heat transfer between a hot and a cold body by conduction may take place through material substance such as metal wall, but conduction may take place also through fluids (either gases or liquids). In process of conduction, there is no physical movement of molecules. At the hot end of the material, random movements (activities) of the molecules is increased. As a result of this increased activity of the molecules, collisions with adjacent molecules along the material take place imparting increased momentum to these adjacent molecules, resulting in increased temperature. This is transfer of heat by conduction. In gases, heat conduction occurs by molecules, and atomic interaction. In metals, the flow of energy is due mainly to the diffusion of free electrons. Here, crystal lattice vibrations are of secondary importance.
Basic Equation: The basic equation for rate of heat transfer by conduction for an elementary thickness dx of the plate is
Where, H – rate of heat transferred,
A – area of heat fl ow normal to the direction of heat flow,
K – coeffi cient of thermal conductivity,
dT/dx- temperature gradient.
For positive value of x in the direction of heat fl ow, temperature decreases, making dT/dx negative. Thus, additional negative sign is employed in eqn. (1.1) so that heat quantity is positive. Thus basic equation although introduced by Biot in 1804, is usually attributed to Foerier because of his outstanding contribution to the field. This law was formulated from the study of experimental observations.
Thermal Conductivity: The thermal conductivity of the material, K is the quantity of heat passing between opposite faces of a unit cube in unit time when unit temperature diff erence is maintained across the faces. Thermal conductivity is a physical property of a substance and characteristics the ability of the substance to conduct heat.
The thermal conductivity when expressed in S.I. Units, is
This is the system of units which will be used throughout this chapter. In many cases (particularly for insulating materials) the temperature gradient is expressed OC/cm, so that the unit of K becomes watts cm/m2 OC. In MKS system of units, K may be expressed in kcal/hr m OC.
The thermal conductivity varies with temperature. Experiments show that for most materials, this dependence is linear, i.e.
where ∝ is a constant and KO is the value of thermal conductivity at 0OC. The constant “∝” is positive for insulating materials and negative for metallic conductors. Magnesite, brass and aluminium are exceptions to this rule.
From values of the thermal conductivities of a few substances solids, liquids and gases given in Table 1, it is seen that silver is the best conductor of heat. Mercury, though placed among liquids, should be classifi ed with metals on account of its comparatively high value. Hydrogen appears to be the best conductor among gases; but helium has a slightly higher value.