In this article we will discuss about the conditions and significance of heat transfer.
Steady and Unsteady Conditions of Heat Transfer:
Heat exchange between two systems may take place under steady (stable) thermal conditions or under unsteady (unstable) thermal conditions. Steady state implies that temperature at each point of the system remains constant in the course of time, and it is a function only of space co-ordinates.
t = f (x, y, z); dt/dτ = 0 … (1.9)
Steady state results in a constant rate of heat exchange (heat influx equals heat efflux), and there is no change in the internal energy of the system during such a process.
Typical examples of steady state heat transfer are:
i. Cooling of an electric bulb by the surrounding atmosphere,
ii. Heat flow from the products of combustion to water in the tubes of a boiler, from the hot to cold fluid in a heat exchanger, and from a refrigerated space to cooling surface of the evaporator.
Under unsteady thermal conditions, temperature of the system changes continuously with time. Temperature is obviously a function of space and time co-ordinates.
t = f (x, y, z, τ); dt/dτ ≠ 0 …. (1.10)
Unsteady state results in heat transfer rate which changes with time. Further, a change in temperature indicates a change of internal energy of the system. Energy storage is thus a part and parcel of unsteady heat flow.
Typical examples of unsteady heat transfer are:
i. Warm-up periods of furnaces
ii. Boilers and turbines
iii. Cooling of castings in a foundry
iv. Heat treatment and stress relieving of metal castings.
A special kind of unsteady process is the transient state wherein the system is subjected to cyclic variations in the temperature of its environment. The temperature at a particular point of the system returns periodically to the same value; the rate of heat flow and energy storage also undergo periodic variations. Examples are- Heating or cooling of the water of an I.C. engine; heating or cooling of the walls of a building during the 24-hours cycle of the day.
Further, the heat transfer in a system may be in one, two or more directions. In a one dimensional heat flow, there is a single predominant direction in which temperature differential exists and obviously the heat flow takes place; heat flow in the other two directions can be safely neglected. When the temperature is a function of two co-ordinates, heat flow is two- dimensional. A three-dimensional heat flow stipulates that temperature is a function of three co-ordinates, and consequently heat flow occurs in all three directions.
Significance of Heat Transfer:
The discipline of the heat transfer encompasses a great many fascinating areas like:
i. Design of steam generators, condensers, and other heat exchange equipments in power plant engineering; solar energy conversion for space heating and for electric power production.
ii. I. C. engines, refrigeration and air-conditioning units, super heaters and condensers and many other cooling and heating appliances in mechanical engineering. The operation of refrigeration and air-conditioning units depends greatly on the effective transfer of heat in condensers and evaporators.
iii. Design of cooling systems for electric motors, generators and transformers in electrical engineering so that the heat generated during the flow of current through the windings of these machines can be effectively dissipated. This is to avoid the conditions which will cause overheating and damage the equipment.
iv. Evaporation, condensation, heating and cooling of fluids in chemical operations. Hardly any chemical operation can be identified that does not involve heating or cooling of a material at some stage or the other.
v. Construction of dams and other heavy structures, calculation of thermal expansion of suspension bridges and railway tracks, minimisation of building-heat losses by means of improved insulation techniques.
vi. Proper functioning of valves and other controls operated by temperature changes, thermal control of space vehicles.
vii. Heat treatment of metals where diffusion rate of carbon in steel is required to be made to estimate the period for which the steel component must be exposed to carburizing atmosphere.
viii. Dispersion of atmospheric pollutants; problem of thermal pollution associated with the discharge of large amounts of waste heat from a power plant to environment. Industrial exhaust gases laden with noxious pollutants are discharged high enough. This is to ensure that by the time pollutants diffuse downwards, their concentration falls below safe limits. An understanding of mass transfer is needed for accurate predication of concentration at ground of the pollutants discharged from the chimney.
An engineer utilises his knowledge of heat transfer either to transmit heat in the most effective/economic way, or to protect his equipment against excessive heat gains or losses.
The various engineering problems involving heat transfer can be categorised into two groups:
(i) Heat flow situations where maximum heat transfer is desirable with minimum possible heat exchange area. Gas turbine blades, walls of I.C. engines and combustion chambers, outer surface of a space vehicle all depend for their durability on rapid removal of heat from their surfaces. The design of heat exchangers is considered to be optimum under specified temperature conditions when maximum heat transfer occurs with minimum surface area.
(ii) Heat flow situations where heat transfer is undesirable and its flow is to be prevented. The walls of centrally heated buildings and the steam pipes in a steam power plant are properly insulated to restrict heat losses.
With few exceptions, engineering problems involve more than one of the three modes of heat transfer and this aspect results into a complicated heat exchange pattern.
The significance of heat transfer and the simultaneous occurrence of different modes of heat transfer can be well-judged by citing the following examples:
(a) Closed container filled with hot coffee and kept in a room whose air and walls are at a fixed temperature.
All three models of heat transfer contribute towards cooling of coffee, and different paths for energy transfer from coffee are:
i. Free convection from the coffee to the flask, q1
ii. Heat conduction through the flask, q2
iii. Free convection from the flask to the air, q3
iv. Radiation exchange between the outer surface of the flask and the inner surface of the cover, q4
v. Free convection from air to the cover, q5
vi. Heat conduction through the cover, q6
vii. Free convection from the cover to the room air, q7
viii. Radiation exchange between the outer surface of the cover and the surroundings, q8
(b) Automobile engine with thermo-syphon cooling system.
Here the relevant heat transfer processes are:
i. Free convection and radiation from hot combustion gases to cylinder walls
ii. Conduction through cylinder walls
iii. Free convection from cylinder walls to water and from water to radiator tubes
iv. Conduction through walls of radiator tubes
v. Convection from radiator tubes to surrounding air
(iii) Heat flow through a wall consisting of two plates separated by vacuum.
Heat is convicted from the fluid at temperature tf1 to plate A, conducted through plate A, radiated from plate A to plate B, conducted through plate B, and finally convicted from plate B to the fluid at temperature tf2.
Likewise the process of steam generation, the boiler tubes receive heat from the products of combustion by all the three modes of heat transfer.